2068:
197:"Stochastic" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. Stochastic models depend on the chance variations in risk of exposure, disease and other illness dynamics. Statistical agent-level disease dissemination in small or large populations can be determined by stochastic methods.
1179:
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2062:
81:, in 1662. The bills he studied were listings of numbers and causes of deaths published weekly. Graunt's analysis of causes of death is considered the beginning of the "theory of competing risks" which according to Daley and Gani is "a theory that is now well established among modern epidemiologists".
1943:
252:
on top of its contact network. The combination of disease dynamics under the influence of interventions, if any, on a contact network may be modeled with another network, known as a transmission network. In a transmission network, all the links are responsible for transmitting the disease. If such a
182:
is widespread. For example, most people in London only make contact with other
Londoners. Further, within London then there are smaller subgroups, such as the Turkish community or teenagers (just to give two examples), who mix with each other more than people outside their group. However, homogeneous
247:
and is called the contact network. Every node in a contact network is a representation of an individual and each link (edge) between a pair of nodes represents the contact between them. Links in the contact networks may be used to transmit the disease between the individuals and each disease has its
149:. Epidemiological ABMs, in spite of their complexity and requiring high computational power, have been criticized for simplifying and unrealistic assumptions. Still, they can be useful in informing decisions regarding mitigation and suppression measures in cases when ABMs are accurately calibrated.
205:
When dealing with large populations, as in the case of tuberculosis, deterministic or compartmental mathematical models are often used. In a deterministic model, individuals in the population are assigned to different subgroups or compartments, each representing a specific stage of the epidemic.
3124:
If a vaccination program causes the proportion of immune individuals in a population to exceed the critical threshold for a significant length of time, transmission of the infectious disease in that population will stop. If elimination occurs everywhere at the same time, then this can lead to
209:
The transition rates from one class to another are mathematically expressed as derivatives, hence the model is formulated using differential equations. While building such models, it must be assumed that the population size in a compartment is differentiable with respect to time and that the
1536:
There are many modifications of the SIR model, including those that include births and deaths, where upon recovery there is no immunity (SIS model), where immunity lasts only for a short period of time (SIRS), where there is a latent period of the disease where the person is not infectious
222:
where 1 person tags 2, those 2 tag 4 others who've never been tagged and so on. As this game progresses it becomes increasing frenetic as the tagged run past the previously tagged to hunt down those who have never been tagged. Thus this model of an epidemic leads to a curve that
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level for the disease, then the disease can no longer persist in the population and its transmission dies out. Thus, a disease can be eliminated from a population if enough individuals are immune due to either vaccination or recovery from prior exposure to disease. For example,
2232:
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due to the presence of the vaccinated group. For a disease that leads to greater clinical severity in older populations, the unvaccinated proportion of the population may experience the disease relatively later in life than would occur in the absence of vaccine.
3136:
Interruption of endemic transmission of an infectious disease, which occurs if each infected individual infects less than one other, is achieved by maintaining vaccination coverage to keep the proportion of immune individuals above the critical immunization
1526:
is the compartment used for the individuals of the population who have been infected and then removed from the disease, either due to immunization or due to death. Those in this category are not able to be infected again or to transmit the infection to
157:
Models are only as good as the assumptions on which they are based. If a model makes predictions that are out of line with observed results and the mathematics is correct, the initial assumptions must change to make the model useful.
1954:
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3106:
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613:) is a measure of how transferable a disease is. It is the average number of people that a single infectious person will infect over the course of their infection. This quantity determines whether the infection will increase
333:
2546:
177:
Homogeneous mixing of the population, i.e., individuals of the population under scrutiny assort and make contact at random and do not mix mostly in a smaller subgroup. This assumption is rarely justified because
65:
The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic.
516:
2955:
2105:
736:, the higher the basic reproduction number, the lower the proportion of the population susceptible must be, and vice versa. This expression has limitations concerning the susceptibility proportion, e.g. the
174:) there is the same number of people in the population. This is often well-justified for developed countries where there is a low infant mortality and much of the population lives to the life expectancy.
218:
A common explanation for the growth of epidemics holds that 1 person infects 2, those 2 infect 4 and so on and so on with the number of infected doubling every generation. It is analogous to a game of
2100:
408:. It is, however, not always straightforward to find the transmission network out of the contact network and the disease dynamics. For example, if a contact network can be approximated with an
1034:. A classic compartmental model in epidemiology is the SIR model, which may be used as a simple model for modelling epidemics. Multiple other types of compartmental models are also employed.
4564:
Costris-Vas C, Schwartz EJ, Smith? RJ (November 2020). "Predicting COVID-19 using past pandemics as a guide: how reliable were mathematical models then, and how reliable will they be now?".
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729:) must be one (since those who are not susceptible do not feature in our calculations as they cannot contract the disease). Notice that this relation means that for a disease to be in the
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Models have the advantage of examining multiple outcomes simultaneously, rather than making a single forecast. Models have shown broad degrees of reliability in past pandemics, such as
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individuals in a population. The
Kermack–McKendrick epidemic model was successful in predicting the behavior of outbreaks very similar to that observed in many recorded epidemics.
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epidemic process is deterministic. In other words, the changes in population of a compartment can be calculated using only the history that was used to develop the model.
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Assume the rectangular stationary age distribution and let also the ages of infection have the same distribution for each birth year. Let the average age of infection be
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2057:{\displaystyle {\frac {\operatorname {\operatorname {E} } (T_{L})}{\operatorname {\operatorname {E} } (T_{S})}}=1+{\frac {\lambda }{\mu }}={\frac {\beta N}{v}}.}
266:
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1495:
denotes the individuals of the population who have been infected with the disease and are capable of spreading the disease to those in the susceptible category.
2255:). It is the minimum proportion of the population that must be immunized at birth (or close to birth) in order for the infection to die out in the population.
1938:{\displaystyle R_{0}={\frac {N}{S}}={\frac {\mu N\operatorname {E} (T_{L})}{\mu N\operatorname {E} }}={\frac {\operatorname {E} (T_{L})}{\operatorname {E} }},}
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is the age at which in this model every individual is assumed to die. But the mathematical definition of the endemic steady state can be rearranged to give:
249:
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521:
863:
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3332:
Blower S, Bernoulli D (2004). "An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it".
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1345:
In 1927, W. O. Kermack and A. G. McKendrick created a model in which they considered a fixed population with only three compartments: susceptible,
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when it can be sustained in a population without the need for external inputs. This means that, on average, each infected person is infecting
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are immune (or infectious). Then it can be shown by an easy argument that the proportion of the population that is susceptible is given by:
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468:
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is used to represent the individuals not yet infected with the disease at time t, or those susceptible to the disease of the population.
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programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
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145:. For example, epidemiological ABMs have been used to inform public health (nonpharmaceutical) interventions against the spread of
2227:{\displaystyle {\begin{aligned}&R_{0}\cdot (1-q)=1,\\&1-q={\frac {1}{R_{0}}},\\&q=1-{\frac {1}{R_{0}}}.\end{aligned}}}
7587:
6562:
5994:
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725:) of the disease, assuming everyone is susceptible, multiplied by the proportion of the population that is actually susceptible (
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1677:, with the last wild case in 1977, and certification of the eradication of indigenous transmission of 2 of the 3 types of wild
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Thus, the vaccination program may raise the average age of infection, and unvaccinated individuals will experience a reduced
4995:
1337:. If there is no medicine or vaccination available, it is only possible to reduce the infection rate (often referred to as "
119:
2655:
If the vaccine used is insufficiently effective or the required coverage cannot be reached, the program may fail to exceed
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Remember that this is the threshold level. Die out of transmission will only occur if the proportion of immune individuals
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for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass
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409:
3884:"Improved susceptible–infectious–susceptible epidemic equations based on uncertainties and autocorrelation functions"
49:
and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find
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3663:"Agent-based modelling for SARS-CoV-2 epidemic prediction and intervention assessment: A methodological appraisal"
1681:(type 2 in 2015, after the last reported case in 1999, and type 3 in 2019, after the last reported case in 2012).
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network is a locally tree-like network, meaning that any local neighborhood in such a network takes the form of a
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2662:. Such a program will protect vaccinated individuals from disease, but may change the dynamics of transmission.
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92:. Trained as a physician, Bernoulli created a mathematical model to defend the practice of inoculating against
4710:"Mathematical models of disease transmission: a precious tool for the study of sexually transmitted diseases"
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This change occurs simply because there are now fewer susceptibles in the population who can be infected.
730:
651:
127:
100:
from 26 years 7 months to 29 years 9 months. Daniel
Bernoulli's work preceded the modern understanding of
85:
4195:"Epidemic spreading and digital contact tracing: Effects of heterogeneous mixing and quarantine failures"
340:
96:. The calculations from this model showed that universal inoculation against smallpox would increase the
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1185:
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5598:
4411:"A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2"
764:
123:
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631:< 1, then each person infects fewer than one person on average so the disease will die out; and if
624:> 1, then each person on average infects more than one other person so the disease will spread; if
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401:
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1615:
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672:
405:
258:
254:
34:
3988:"Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China"
3809:"Efficient method for comprehensive computation of agent-level epidemic dissemination in networks"
2094:
must equal one (since in this simplified model, everyone is either susceptible or immune). Then:
638:= 1, then each person will infect on average exactly one other person, so the disease will become
7887:
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30:
2067:
4517:"FBA reveals guanylate kinase as a potential target for antiviral therapies against SARS-CoV-2"
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5010:
4801:: Open source framework for Epidemiological Modeling available through the Eclipse Foundation.
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3143:
Elimination everywhere at the same time such that the infectious agent dies out (for example,
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1645:
1288:
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419:
179:
89:
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7069:
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6819:
6809:
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5000:
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3200:
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minus those that would normally be infected but that cannot be now since they are immune.
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1406:
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equals 0.5 implicates S has to be 2, however this proportion exceeds the population size.
614:
240:
97:
70:
4648:
3553:
Squazzoni F, Polhill JG, Edmonds B, Ahrweiler P, Antosz P, Scholz G, et al. (2020).
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5134:
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4908:
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3245:
1554:
1550:
3555:"Computational Models That Matter During a Global Pandemic Outbreak: A Call to Action"
416:, and the disease spreading parameters are as defined in the example above, such that
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6042:
5755:
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5119:
4896:
4532:
4246:
3647:
3598:
3539:
3464:
2424:{\displaystyle \lim _{t\to \infty }S(t)=e^{-\int _{0}^{\infty }\lambda (t)\,dt}=1-p.}
1669:
1623:
1600:
1031:
228:
46:
17:
4179:
3318:
3101:{\displaystyle A_{q}={\frac {L}{(L/A)(1-q)}}={\frac {AL}{L(1-q)}}={\frac {A}{1-q}}.}
2071:
Graph of herd immunity threshold vs basic reproduction number with selected diseases
436:
is the transmission rate per person and the disease has a mean infectious period of
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733:
581:{\displaystyle {\langle k^{2}\rangle }-{\langle k\rangle }^{2}={\langle k\rangle }}
244:
243:
of contact between people. Such a network can be represented mathematically with a
4808:
929:{\displaystyle {\frac {1}{R_{0}}}={\frac {A}{L}}\Rightarrow R_{0}={\frac {L}{A}}.}
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4795:: Enables simulation of emerging infectious diseases spreading across the world.
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54:
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4789:: Interactive (GUI-based) software to build, simulate, and analyze ODE models.
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4811:: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena
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Pastor-Satorras R, Castellano C, Van
Mieghem P, Vespignani A (2015-08-31).
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328:{\displaystyle R_{0}={\frac {\langle k^{2}\rangle }{\langle k\rangle }}-1,}
227:
until it crashes to zero as all the population have been infected. i.e. no
4743:
4661:
An introductory book on infectious disease modelling and its applications.
4346:
3712:"Mathematical modelling and prediction in infectious disease epidemiology"
3498:"Special report: The simulations driving the world's response to COVID-19"
3441:"Spatial pattern formation facilitates eradication of infectious diseases"
666:, any less and the disease will die out). In mathematical terms, that is:
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3144:
2541:{\displaystyle p=1-e^{-\int _{0}^{\infty }\beta I(t)\,dt}=1-e^{-R_{0}p}.}
1609:
1558:
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93:
38:
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1285:. The animation shows the effect of reducing the rate of infection from
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27:
Using mathematical models to understand infectious disease transmission
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4261:"Basic Reproduction Number - an overview | ScienceDirect Topics"
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it will move throughout the population but not increase or decrease.
3964:
3345:
4468:"A guide to vaccinology: From basic principles to new developments"
4211:
3825:
3807:
Nakamura GM, Monteiro AC, Cardoso GC, Martinez AS (February 2017).
511:{\displaystyle R_{0}={\dfrac {\beta }{\gamma }}{\langle k\rangle }}
79:
Natural and
Political Observations made upon the Bills of Mortality
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one other person (any more and the number of people infected will
183:
mixing is a standard assumption to make the mathematics tractable.
4043:
2950:{\displaystyle A_{q}={\frac {L}{R_{q}}}={\frac {L}{R_{0}(1-q)}}.}
1432:. The compartments used for this model consist of three classes:
1008:
This allows for the basic reproduction number of a disease given
6724:
5614:
5083:
4980:
4305:"Contributions to the mathematical theory of epidemics--I. 1927"
3173:
3161:
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and animals, including humans, are concerned with this problem.
7670:
6535:
4818:
4798:
3753:"COVID-19: Data-Driven Mean-Field-Type Game Perspective. Games"
1668:
If the proportion of the population that is immune exceeds the
1549:
Mathematical models need to integrate the increasing volume of
3289:
Hethcote HW (2000). "The mathematics of infectious diseases".
257:, then the basic reproduction can be written in terms of the
4753:
Mathematical
Structures of Epidemic Systems. Second Printing
3953:
Journal of the Royal
Statistical Society. Series A (General)
4792:
4193:
K Rizi A, Faqeeh A, Badie-Modiri A, Kivelä M (2022-04-20).
4276:"Data over Space and Time; Lecture 21: Compartment Models"
3426:
Mathematical Models in
Population Biology and Epidemiology
2317:
Because the fraction of the final size of the population
118:
The 1920s saw the emergence of compartmental models. The
69:
The first scientist who systematically tried to quantify
4667:"Mathematical models of infectious disease transmission"
3376:"Germ Theory - an overview | ScienceDirect Topics"
2086:
is the proportion of the population that is immune and
1541:), and where infants can be born with immunity (MSIR).
365:
is the mean-degree (average degree) of the network and
4362:"Mathematical epidemiology: Past, present, and future"
3882:
Nakamura GM, Cardoso GC, Martinez AS (February 2020).
2816:. Assuming that life expectancy has not changed, now:
1317:
1291:
1265:
1188:
1155:
1129:
1052:
3559:
Journal of
Artificial Societies and Social Simulation
2984:
2876:
2825:
2714:
2651:
When mass vaccination cannot exceed the herd immunity
2587:
2557:
2443:
2330:
2264:
2103:
1957:
1742:
1697:
1503:
1472:
1441:
1409:
1380:
1351:
1341:") by appropriate measures such as social distancing.
962:
939:
This provides a simple way to estimate the parameter
866:
813:
767:
675:
524:
486:
471:
444:
442:
422:
371:
343:
269:
4061:"Second look at the spread of epidemics on networks"
239:
Epidemics can be modeled as diseases spreading over
231:
and no peak and gradual decline as seen in reality.
7880:
7834:
7808:
7752:
7704:
7596:
7535:
7467:
7358:
7330:
7297:
6971:
6802:
6795:
6714:
6642:
6594:
6473:
6365:
6157:
6006:
5993:
5898:
5789:
5711:
5683:
5669:
5655:
5639:
5607:
5569:
5498:
5460:
5453:
5435:
5367:
5334:
5327:
5291:
5284:
5196:
5187:
5074:
4971:
4865:
4858:
4622:
Modeling
Infectious Diseases: In Humans and Animals
3100:
2949:
2861:
2755:
2680:) is immunised at birth against an infection with
2639:
2570:
2540:
2423:
2306:
2226:
2056:
1937:
1722:
1642:statistical and mathematical tools and innovations
1518:
1487:
1456:
1424:
1395:
1366:
1329:
1303:
1277:
1251:
1167:
1141:
1115:
997:
928:
842:
789:
703:
580:
510:
457:
428:
392:
357:
327:
7582:Cedillo v. Secretary of Health and Human Services
166:, i.e., everybody in the population lives to age
2332:
2241:this level due to a mass vaccination programme.
1894:
1817:
88:of spread of disease was carried out in 1760 by
4650:An Introduction to Infectious Disease Modelling
3120:When mass vaccination exceeds the herd immunity
1182:Animation of the SIR model with initial values
1561:interactions. Many theoretical studies of the
141:(ABMs) have been used in exchange for simpler
126:(1928) both describe the relationship between
107:In the early 20th century, William Hamer and
7682:
6547:
4830:
4600:: CS1 maint: DOI inactive as of April 2024 (
2640:{\displaystyle R_{0}={\frac {-\ln(1-p)}{p}}.}
1046:Diagram of the SIR model with initial values
750:, for instance when individuals younger than
8:
4632:Computational Modeling of Infectious Disease
2665:Suppose that a proportion of the population
574:
568:
554:
548:
539:
526:
504:
498:
386:
373:
351:
345:
310:
304:
299:
286:
2307:{\displaystyle q_{c}=1-{\frac {1}{R_{0}}}.}
1016:in either type of population distribution.
7689:
7675:
7667:
6799:
6554:
6540:
6532:
6003:
5457:
5331:
5288:
5193:
4862:
4837:
4823:
4815:
3667:Journal of Evaluation in Clinical Practice
2798:in those who have been left unvaccinated.
2321:that is never infected can be defined as:
37:progress to show the likely outcome of an
4733:
4690:
4577:
4540:
4491:
4442:
4385:
4328:
4228:
4210:
4169:
4151:
4110:
4076:
4045:Network Science by Albert-László Barabási
4019:
3923:
3858:
3824:
3770:
3760:
3727:
3686:
3629:
3580:
3570:
3521:
3472:
3077:
3042:
3010:
2998:
2989:
2983:
2920:
2910:
2899:
2890:
2881:
2875:
2862:{\displaystyle R_{q}={\frac {L}{A_{q}}},}
2848:
2839:
2830:
2824:
2732:
2719:
2713:
2601:
2592:
2586:
2562:
2556:
2524:
2516:
2494:
2473:
2468:
2460:
2442:
2397:
2379:
2374:
2366:
2335:
2329:
2293:
2284:
2269:
2263:
2209:
2200:
2172:
2163:
2113:
2104:
2102:
2036:
2023:
2002:
1987:
1976:
1961:
1958:
1956:
1917:
1904:
1874:
1858:
1840:
1827:
1791:
1769:
1756:
1747:
1741:
1702:
1696:
1502:
1471:
1440:
1408:
1379:
1350:
1316:
1290:
1264:
1187:
1154:
1128:
1051:
982:
967:
961:
913:
904:
887:
876:
867:
865:
829:
820:
812:
774:
766:
683:
674:
567:
558:
547:
533:
525:
523:
497:
485:
476:
470:
443:
441:
421:
380:
372:
370:
344:
342:
293:
283:
274:
268:
4635:. Cambridge, MA: Elsevier/Academic Press
4624:. Princeton: Princeton University Press.
4566:Mathematical Biosciences and Engineering
4136:"Epidemic processes in complex networks"
1684:The herd immunity level will be denoted
465:, then the basic reproduction number is
5911:Ear-Nose-Throat/Upper respiratory tract
5084:Access to water, sanitation and hygiene
4515:Renz A, Widerspick L, Dräger A (2020).
3278:. New York: Cambridge University Press.
3263:
1030:Compartmental models are formulated as
998:{\displaystyle R_{0}=1+{\frac {L}{A}}.}
393:{\displaystyle {\langle k^{2}\rangle }}
261:of the transmission network such that:
170:and then dies, and for each age (up to
7857:Construction and management simulation
6494:Infectious disease (medical specialty)
6386:Antimicrobial resistance surveillance
4758:
4593:
3789:
3778:
4409:Britton T, Ball F, Trapman P (2020).
4059:Kenah E, Robins JM (September 2007).
3612:Sridhar D, Majumder MS (April 2020).
3269:
3267:
1620:persistence of pathogens within hosts
843:{\displaystyle S={\frac {1}{R_{0}}}.}
754:are susceptible and those older than
458:{\displaystyle {\dfrac {1}{\gamma }}}
7:
7939:Mathematical and theoretical biology
7893:List of computer simulation software
5741:Compartmental models in epidemiology
3439:Eisinger D, Thulke HH (April 2008).
3424:Brauer F, Castillo-Chávez C (2001).
3419:
3417:
3196:Compartmental models in epidemiology
1026:Compartmental models in epidemiology
1020:Compartmental models in epidemiology
650:An infectious disease is said to be
3716:Clinical Microbiology and Infection
2791:will also change to some new value
1688:. Recall that, for a stable state:
1252:{\textstyle S(0)=997,I(0)=3,R(0)=0}
1116:{\textstyle S(0)=997,I(0)=3,R(0)=0}
358:{\displaystyle {\langle k\rangle }}
7609:Eradication of infectious diseases
7366:Androvax (androstenedione albumin)
4708:Boily MC, Mâsse B (Jul–Aug 1997).
4665:Grassly NC, Fraser C (June 2008).
4303:Kermack WO, McKendrick AG (1991).
4274:Cosma Shalizi (15 November 2018).
3661:Maziarz M, Zach M (October 2020).
3276:Epidemic Modeling: An Introduction
2474:
2380:
2342:
1988:
1962:
1885:
1861:
1808:
1778:
617:, die out, or remain constant: if
25:
7199:Respiratory syncytial virus (RSV)
4714:Canadian Journal of Public Health
3949:"Epidemics and Rumours: A Survey"
1654:, spread and control of infection
790:{\displaystyle S={\frac {A}{L}}.}
120:Kermack–McKendrick epidemic model
7588:Alternative vaccination schedule
6563:Artificial induction of immunity
6490:Economics of Infectious Diseases
4309:Bulletin of Mathematical Biology
3465:10.1111/j.1365-2664.2007.01439.x
2801:Recall the relation that linked
2756:{\displaystyle R_{q}=R_{0}(1-q)}
7821:Integrated assessment modelling
2787:, the average age of infection
2783:As a consequence of this lower
2246:critical immunization threshold
1723:{\displaystyle R_{0}\cdot S=1.}
1664:Mathematics of mass vaccination
115:to explain epidemic behaviour.
7420:Ovandrotone albumin (Fecundin)
6499:Infectious disease informatics
6330:Transmission-based precautions
4533:10.1093/bioinformatics/btaa813
4466:Pollard AJ, Bijker EM (2021).
3986:Maier BF, Brockmann D (2020).
3445:The Journal of Applied Ecology
3068:
3056:
3033:
3021:
3018:
3004:
2938:
2926:
2750:
2738:
2625:
2613:
2491:
2485:
2394:
2388:
2356:
2350:
2339:
2134:
2122:
2008:
1995:
1982:
1969:
1926:
1923:
1897:
1891:
1880:
1867:
1849:
1846:
1820:
1814:
1797:
1784:
1513:
1507:
1482:
1476:
1451:
1445:
1419:
1413:
1390:
1384:
1361:
1355:
1240:
1234:
1219:
1213:
1198:
1192:
1104:
1098:
1083:
1077:
1062:
1056:
897:
414:Poissonian degree distribution
1:
6956:Group B streptococcal disease
6775:Vaccines for Children Program
5916:Chest/Lower respiratory tract
5691:Ocular (Eye) mucosal membrane
5052:Behavioral/lifestyle factors
4755:. Heidelberg, 2008: Springer.
3710:Huppert A, Katriel G (2013).
1565:, structure and evolution of
946:using easily available data.
704:{\displaystyle \ R_{0}S\ =1.}
7790:Hydrological transport model
7744:Protein structure prediction
7739:Modelling biological systems
5478:Aerosol-generating procedure
5256:Silent/Subclinical infection
4956:Multidrug-resistant bacteria
4671:Nature Reviews. Microbiology
4366:Infectious Disease Modelling
2244:We have just calculated the
1634:role of host genetic factors
951:exponential age distribution
588:for a Poisson distribution.
404:of the transmission network
7734:Metabolic network modelling
6142:Vaccine-preventable disease
6090:Monoclonal antibody therapy
4527:(Supplement_2): i813–i821.
4230:10.1103/PhysRevE.105.044313
3334:Reviews in Medical Virology
1628:role and identification of
1545:Infectious disease dynamics
235:Epidemic Models on Networks
162:Rectangular and stationary
7965:
7847:Business process modelling
6283:Respiratory source control
4484:10.1038/s41577-020-00479-7
4283:Carnegie Mellon University
4095:10.1103/PhysRevE.76.036113
3888:Royal Society Open Science
3523:10.1038/d41586-020-01003-6
1648:structure and interactions
1532:Other compartmental models
1123:, and rates for infection
1023:
595:
7719:Chemical process modeling
7627:
6427:Global Health Initiatives
6417:Evolutionary epidemiology
6112:Post-exposure prophylaxis
6048:Antimicrobial stewardship
5771:Multiplicity of infection
5736:Basic reproduction number
5512:Percutaneous inoculation
4996:Host–pathogen interaction
4472:Nature Reviews Immunology
4378:10.1016/j.idm.2017.02.001
4171:10.1103/RevModPhys.87.925
4140:Reviews of Modern Physics
3407:The Prevention of Malaria
3311:10.1137/S0036144500371907
3274:Daley DJ, Gani J (2005).
3191:Basic reproduction number
2785:basic reproduction number
1576:Research topics include:
1278:{\textstyle \gamma =0.04}
1168:{\textstyle \gamma =0.04}
949:For a population with an
716:basic reproduction number
604:basic reproduction number
598:Basic reproduction number
124:Reed–Frost epidemic model
7765:Chemical transport model
7729:Infectious disease model
6951:Clostridioides difficile
6245:Protective sequestration
6107:Pre-exposure prophylaxis
5398:Generational difference
4951:Horizontal gene transfer
4941:Antimicrobial resistance
4765:: CS1 maint: location (
3614:"Modelling the pandemic"
3391:Epidemiology Old and New
1948:which is approximately:
1330:{\textstyle \beta =0.12}
188:Types of epidemic models
84:The earliest account of
7209:Tick-borne encephalitis
6432:Microbial phylogenetics
6350:Wastewater surveillance
5871:Geographic distribution
5746:Critical community size
5544:Surgical site infection
5392:Iatrogenic/Medical care
5311:Microbial translocation
5307:Endogenous reactivation
5302:Normal flora overgrowth
5251:Opportunistic infection
5023:Opportunistic infection
4582:(inactive 2024-04-24).
4435:10.1126/science.abc6810
4012:10.1126/science.abb4557
3729:10.1111/1469-0691.12308
3206:Critical community size
2687: > 1. The
2078:will be (1 −
1304:{\textstyle \beta =0.5}
1259:, and rate of recovery
1142:{\textstyle \beta =0.4}
7619:List of vaccine topics
6619:Mathematical modelling
6504:Microbial bioterrorism
6127:efficacy/effectiveness
5535:Surgical intervention
5427:Breakthrough infection
5049:Genetic predisposition
5033:Susceptible individual
4880:Germ theory of disease
4647:Vynnycky E, White RG.
3788:Cite journal requires
3231:Next-generation matrix
3226:Landscape epidemiology
3102:
2951:
2863:
2757:
2641:
2572:
2542:
2425:
2308:
2228:
2072:
2058:
1939:
1724:
1520:
1489:
1458:
1426:
1397:
1368:
1342:
1331:
1305:
1279:
1253:
1175:
1169:
1143:
1117:
999:
930:
853:Therefore, due to the
844:
791:
705:
660:grow sub-exponentially
582:
512:
459:
430:
429:{\displaystyle \beta }
394:
359:
329:
214:Sub-exponential growth
86:mathematical modelling
7898:Mathematical modeling
7842:Biopsychosocial model
7614:Vaccinate Your Family
7065:Japanese encephalitis
6340:Universal precautions
5298:Endogenous overgrowth
5150:Poultry and livestock
4620:Keeling M, Rohani P.
3496:Adam D (April 2020).
3428:. New York: Springer.
3393:. London: Kegan Paul.
3103:
2952:
2864:
2758:
2642:
2573:
2571:{\displaystyle R_{0}}
2543:
2426:
2309:
2229:
2070:
2059:
1940:
1725:
1521:
1490:
1459:
1427:
1398:
1369:
1332:
1306:
1280:
1254:
1181:
1170:
1144:
1118:
1045:
1000:
931:
845:
792:
706:
662:and there will be an
583:
513:
460:
431:
395:
360:
330:
259:average excess degree
18:Epidemiological model
7852:Catastrophe modeling
7698:Scientific modelling
7497:John Franklin Enders
6442:Genomic reassortment
6422:Genetic epidemiology
6261:Health communication
6189:Flattening the curve
6179:Disease surveillance
5962:Systemic/Generalized
5726:Animal disease model
5206:Asymptomatic carrier
3211:Disease surveillance
2982:
2874:
2823:
2712:
2585:
2555:
2441:
2328:
2262:
2101:
1955:
1740:
1695:
1675:smallpox eradication
1638:spatial epidemiology
1630:infection reservoirs
1519:{\displaystyle R(t)}
1501:
1488:{\displaystyle I(t)}
1470:
1457:{\displaystyle S(t)}
1439:
1425:{\displaystyle R(t)}
1407:
1396:{\displaystyle I(t)}
1378:
1367:{\displaystyle S(t)}
1349:
1339:flattening the curve
1315:
1289:
1263:
1186:
1153:
1127:
1050:
960:
864:
811:
765:
673:
646:Endemic steady state
522:
469:
440:
420:
369:
341:
267:
143:compartmental models
7795:Modular Ocean Model
6683:Virus-like particle
6607:Vaccine ingredients
6509:Pandemic prevention
6465:Viral phylodynamics
6446:Re-emerging disease
6335:Travel restrictions
5539:Postoperative wound
5508:Blood-borne disease
5490:Respiratory droplet
5402:Vertical/Congenital
5387:Nosocomial/Hospital
5344:Spillover infection
4683:10.1038/nrmicro1845
4579:10.3934/mbe.2020383
4427:2020Sci...369..846B
4321:1927RSPSA.115..700K
4221:2022PhRvE.105d4313R
4162:2015RvMP...87..925P
4087:2007PhRvE..76c6113K
4004:2020Sci...368..742M
3908:10.1098/rsos.191504
3900:2020RSOS....791504N
3835:2017NatSR...740885N
3572:10.18564/jasss.4298
3514:2020Natur.580..316A
3457:2008JApEc..45..415E
3303:2000SIAMR..42..599H
2478:
2384:
1616:population genetics
1606:intra-host dynamics
1567:infectious diseases
1563:population dynamics
1553:being generated on
855:transitive property
592:Reproduction number
406:degree distribution
225:grows exponentially
35:infectious diseases
31:Mathematical models
7949:Medical statistics
7888:Data visualization
7872:Input–output model
7785:Hydrological model
7775:Geologic modelling
7654:Never to phase III
7453:Hexavalent vaccine
7267:Epstein–Barr virus
7162:Oxford–AstraZeneca
6855:NmVac4-A/C/Y/W-135
6455:Selection pressure
5751:Force of infection
5379:Contagious disease
5314:Endogenous seeding
5211:Chain of infection
5135:Injection drug use
5046:Vaccination status
4929:Case fatality rate
4847:infectious disease
4793:GLEaMviz Simulator
4726:10.1007/BF03404793
4330:10.1007/BF02464423
4071:(3 Pt 2): 036113.
3813:Scientific Reports
3221:Force of infection
3113:force of infection
3098:
2947:
2859:
2753:
2691:programme changes
2637:
2568:
2538:
2464:
2421:
2370:
2346:
2304:
2224:
2222:
2073:
2054:
1935:
1720:
1516:
1485:
1454:
1422:
1393:
1364:
1343:
1327:
1301:
1275:
1249:
1176:
1165:
1139:
1113:
995:
926:
840:
800:We reiterate that
787:
701:
578:
508:
495:
455:
453:
426:
390:
355:
325:
139:agent-based models
113:law of mass action
45:) and help inform
7921:
7920:
7800:Wildfire modeling
7780:Groundwater model
7760:Atmospheric model
7664:
7663:
7576:Vaccines and SIDS
7463:
7462:
7237:Hepatitis A and B
7213:Varicella zoster
6675:Subunit/component
6529:
6528:
6519:Tropical medicine
6460:Synthetic biology
6361:
6360:
6320:Social distancing
6273:Outbreak response
5894:
5893:
5721:Agent-based model
5707:
5706:
5703:
5702:
5699:
5698:
5246:Natural reservoir
5236:Infectious period
5226:Incubation period
5183:
5182:
5139:Natural disaster
5108:Tropical diseases
5091:Biodiversity loss
5028:Risk of infection
5018:Microbiome health
5011:Immunosuppression
4629:von Csefalvay C.
4421:(6505): 846–849.
4360:Brauer F (2017).
4199:Physical Review E
4065:Physical Review E
3998:(6492): 742–746.
3843:10.1038/srep40885
3762:10.3390/g11040051
3755:. Games Journal.
3679:10.1111/jep.13459
3631:10.1136/bmj.m1567
3508:(7803): 316–318.
3093:
3072:
3037:
2942:
2905:
2854:
2632:
2331:
2299:
2215:
2178:
2049:
2031:
2012:
1930:
1853:
1764:
1403:; and recovered,
1149:and for recovery
990:
921:
895:
882:
835:
782:
694:
678:
615:sub-exponentially
494:
452:
410:Erdős–Rényi graph
314:
16:(Redirected from
7956:
7913:Visual analytics
7908:Systems thinking
7826:Population model
7691:
7684:
7677:
7668:
7555:MMR autism fraud
7502:Maurice Hilleman
7487:Hilary Koprowski
6800:
6556:
6549:
6542:
6533:
6514:Tropical disease
6450:Reverse zoonosis
6437:One Health Model
6266:Health education
6255:Community health
6174:Cordon sanitaire
6147:Ring vaccination
6117:Repurposed drugs
6004:
5923:Gastrointestinal
5766:Machine learning
5570:Gastrointestinal
5521:Intravenous line
5458:
5372:/Cross-infection
5359:Reverse zoonosis
5332:
5289:
5194:
5175:War and conflict
5043:Nutrition status
5006:Immunodeficiency
4863:
4839:
4832:
4825:
4816:
4770:
4764:
4756:
4747:
4737:
4704:
4694:
4660:
4658:
4657:
4643:
4641:
4640:
4625:
4606:
4605:
4599:
4591:
4581:
4572:(6): 7502–7518.
4561:
4555:
4554:
4544:
4512:
4506:
4505:
4495:
4463:
4457:
4456:
4446:
4406:
4400:
4399:
4389:
4357:
4351:
4350:
4332:
4300:
4294:
4293:
4291:
4289:
4280:
4271:
4265:
4264:
4257:
4251:
4250:
4232:
4214:
4190:
4184:
4183:
4173:
4155:
4131:
4125:
4124:
4114:
4080:
4056:
4050:
4049:
4040:
4034:
4033:
4023:
3983:
3977:
3976:
3947:Dietz K (1967).
3944:
3938:
3937:
3927:
3879:
3873:
3872:
3862:
3828:
3804:
3798:
3797:
3791:
3786:
3784:
3776:
3774:
3764:
3748:
3742:
3741:
3731:
3722:(11): 999–1005.
3707:
3701:
3700:
3690:
3673:(5): 1352–1360.
3658:
3652:
3651:
3633:
3609:
3603:
3602:
3584:
3574:
3550:
3544:
3543:
3525:
3493:
3487:
3486:
3476:
3436:
3430:
3429:
3421:
3412:
3411:
3401:
3395:
3394:
3389:Hamer W (1928).
3386:
3380:
3379:
3372:
3366:
3365:
3329:
3323:
3322:
3286:
3280:
3279:
3271:
3107:
3105:
3104:
3099:
3094:
3092:
3078:
3073:
3071:
3051:
3043:
3038:
3036:
3014:
2999:
2994:
2993:
2956:
2954:
2953:
2948:
2943:
2941:
2925:
2924:
2911:
2906:
2904:
2903:
2891:
2886:
2885:
2868:
2866:
2865:
2860:
2855:
2853:
2852:
2840:
2835:
2834:
2762:
2760:
2759:
2754:
2737:
2736:
2724:
2723:
2646:
2644:
2643:
2638:
2633:
2628:
2602:
2597:
2596:
2577:
2575:
2574:
2569:
2567:
2566:
2547:
2545:
2544:
2539:
2534:
2533:
2529:
2528:
2502:
2501:
2477:
2472:
2430:
2428:
2427:
2422:
2405:
2404:
2383:
2378:
2345:
2313:
2311:
2310:
2305:
2300:
2298:
2297:
2285:
2274:
2273:
2233:
2231:
2230:
2225:
2223:
2216:
2214:
2213:
2201:
2186:
2179:
2177:
2176:
2164:
2149:
2118:
2117:
2107:
2063:
2061:
2060:
2055:
2050:
2045:
2037:
2032:
2024:
2013:
2011:
2007:
2006:
1991:
1985:
1981:
1980:
1965:
1959:
1944:
1942:
1941:
1936:
1931:
1929:
1922:
1921:
1909:
1908:
1883:
1879:
1878:
1859:
1854:
1852:
1845:
1844:
1832:
1831:
1800:
1796:
1795:
1770:
1765:
1757:
1752:
1751:
1729:
1727:
1726:
1721:
1707:
1706:
1646:Strain (biology)
1525:
1523:
1522:
1517:
1494:
1492:
1491:
1486:
1463:
1461:
1460:
1455:
1431:
1429:
1428:
1423:
1402:
1400:
1399:
1394:
1373:
1371:
1370:
1365:
1336:
1334:
1333:
1328:
1310:
1308:
1307:
1302:
1284:
1282:
1281:
1276:
1258:
1256:
1255:
1250:
1174:
1172:
1171:
1166:
1148:
1146:
1145:
1140:
1122:
1120:
1119:
1114:
1004:
1002:
1001:
996:
991:
983:
972:
971:
935:
933:
932:
927:
922:
914:
909:
908:
896:
888:
883:
881:
880:
868:
849:
847:
846:
841:
836:
834:
833:
821:
796:
794:
793:
788:
783:
775:
710:
708:
707:
702:
692:
688:
687:
676:
587:
585:
584:
579:
577:
563:
562:
557:
542:
538:
537:
517:
515:
514:
509:
507:
496:
487:
481:
480:
464:
462:
461:
456:
454:
445:
435:
433:
432:
427:
399:
397:
396:
391:
389:
385:
384:
364:
362:
361:
356:
354:
334:
332:
331:
326:
315:
313:
302:
298:
297:
284:
279:
278:
180:social structure
164:age distribution
90:Daniel Bernoulli
33:can project how
21:
7964:
7963:
7959:
7958:
7957:
7955:
7954:
7953:
7924:
7923:
7922:
7917:
7876:
7830:
7816:Energy modeling
7804:
7748:
7724:Ecosystem model
7700:
7695:
7665:
7660:
7659:
7644:Clinical trials
7623:
7592:
7531:
7507:Stanley Plotkin
7469:
7459:
7371:Cancer vaccines
7354:
7348:Schistosomiasis
7326:
7320:Trypanosomiasis
7293:
7257:Cytomegalovirus
7167:Pfizer–BioNTech
6967:
6791:
6740:Vaccine wastage
6710:
6638:
6590:
6560:
6530:
6525:
6469:
6382:Antigenic shift
6377:Antigenic drift
6368:
6357:
6221:Barrier nursing
6169:Contact tracing
6160:
6153:
5998:
5996:
5989:
5900:
5890:
5791:
5785:
5776:Serial interval
5695:
5679:
5670:Cervico-vaginal
5665:
5656:Trans-placental
5651:
5635:
5603:
5565:
5501:Vascular system
5500:
5494:
5449:
5437:
5431:
5371:
5363:
5323:
5280:
5198:
5179:
5070:
5001:Immune response
4967:
4946:Drug resistance
4890:Infectious dose
4854:
4843:
4778:
4773:
4757:
4750:
4707:
4664:
4655:
4653:
4646:
4638:
4636:
4628:
4619:
4615:
4613:Further reading
4610:
4609:
4592:
4563:
4562:
4558:
4514:
4513:
4509:
4465:
4464:
4460:
4408:
4407:
4403:
4359:
4358:
4354:
4302:
4301:
4297:
4287:
4285:
4278:
4273:
4272:
4268:
4259:
4258:
4254:
4192:
4191:
4187:
4133:
4132:
4128:
4058:
4057:
4053:
4042:
4041:
4037:
3985:
3984:
3980:
3965:10.2307/2982521
3946:
3945:
3941:
3881:
3880:
3876:
3806:
3805:
3801:
3787:
3777:
3750:
3749:
3745:
3709:
3708:
3704:
3660:
3659:
3655:
3611:
3610:
3606:
3552:
3551:
3547:
3495:
3494:
3490:
3438:
3437:
3433:
3423:
3422:
3415:
3404:Ross R (1910).
3403:
3402:
3398:
3388:
3387:
3383:
3374:
3373:
3369:
3346:10.1002/rmv.443
3331:
3330:
3326:
3288:
3287:
3283:
3273:
3272:
3265:
3260:
3255:
3216:Ecosystem model
3201:Contact tracing
3186:
3158:
3122:
3082:
3052:
3044:
3003:
2985:
2980:
2979:
2966:
2916:
2915:
2895:
2877:
2872:
2871:
2844:
2826:
2821:
2820:
2807:
2796:
2779:
2771:
2728:
2715:
2710:
2709:
2703:
2697:
2686:
2678:
2660:
2653:
2603:
2588:
2583:
2582:
2558:
2553:
2552:
2520:
2512:
2456:
2439:
2438:
2362:
2326:
2325:
2289:
2265:
2260:
2259:
2253:
2221:
2220:
2205:
2184:
2183:
2168:
2147:
2146:
2109:
2099:
2098:
2038:
1998:
1986:
1972:
1960:
1953:
1952:
1913:
1900:
1884:
1870:
1860:
1836:
1823:
1801:
1787:
1771:
1743:
1738:
1737:
1698:
1693:
1692:
1666:
1586:epidemiological
1581:antigenic shift
1547:
1534:
1499:
1498:
1468:
1467:
1437:
1436:
1405:
1404:
1376:
1375:
1347:
1346:
1313:
1312:
1287:
1286:
1261:
1260:
1184:
1183:
1151:
1150:
1125:
1124:
1048:
1047:
1040:
1028:
1022:
963:
958:
957:
945:
900:
872:
862:
861:
825:
809:
808:
763:
762:
742:
724:
679:
671:
670:
648:
637:
630:
623:
612:
600:
594:
546:
529:
520:
519:
472:
467:
466:
438:
437:
418:
417:
376:
367:
366:
339:
338:
303:
289:
285:
270:
265:
264:
237:
216:
203:
195:
190:
155:
130:, infected and
122:(1927) and the
98:life expectancy
71:causes of death
63:
28:
23:
22:
15:
12:
11:
5:
7962:
7960:
7952:
7951:
7946:
7941:
7936:
7926:
7925:
7919:
7918:
7916:
7915:
7910:
7905:
7903:Systems theory
7900:
7895:
7890:
7884:
7882:
7881:Related topics
7878:
7877:
7875:
7874:
7869:
7867:Economic model
7864:
7859:
7854:
7849:
7844:
7838:
7836:
7832:
7831:
7829:
7828:
7823:
7818:
7812:
7810:
7809:Sustainability
7806:
7805:
7803:
7802:
7797:
7792:
7787:
7782:
7777:
7772:
7767:
7762:
7756:
7754:
7750:
7749:
7747:
7746:
7741:
7736:
7731:
7726:
7721:
7716:
7714:Cellular model
7710:
7708:
7702:
7701:
7696:
7694:
7693:
7686:
7679:
7671:
7662:
7661:
7658:
7657:
7656:
7655:
7652:
7641:
7635:
7629:
7628:
7625:
7624:
7622:
7621:
7616:
7611:
7606:
7600:
7598:
7594:
7593:
7591:
7590:
7585:
7578:
7573:
7568:
7563:
7558:
7545:
7539:
7537:
7533:
7532:
7530:
7529:
7524:
7522:Katalin Karikó
7519:
7514:
7509:
7504:
7499:
7494:
7489:
7484:
7479:
7473:
7471:
7465:
7464:
7461:
7460:
7458:
7457:
7456:
7455:
7450:
7445:
7440:
7432:
7427:
7422:
7417:
7412:
7411:
7410:
7405:
7404:
7403:
7398:
7388:
7383:
7378:
7368:
7362:
7360:
7356:
7355:
7353:
7352:
7351:
7350:
7345:
7336:
7334:
7328:
7327:
7325:
7324:
7323:
7322:
7314:
7313:
7312:
7301:
7299:
7295:
7294:
7292:
7291:
7290:
7289:
7284:
7279:
7277:Herpes simplex
7274:
7269:
7264:
7259:
7251:
7250:
7249:
7244:
7239:
7231:
7226:
7225:
7224:
7219:
7211:
7206:
7201:
7196:
7195:
7194:
7189:
7184:
7179:
7177:Sinopharm BIBP
7174:
7169:
7164:
7159:
7154:
7149:
7144:
7139:
7134:
7129:
7127:Bharat Biotech
7124:
7114:
7109:
7104:
7099:
7098:
7097:
7092:
7082:
7077:
7072:
7067:
7062:
7061:
7060:
7055:
7045:
7040:
7035:
7030:
7025:
7024:
7023:
7018:
7013:
6998:
6997:
6996:
6986:
6981:
6975:
6973:
6969:
6968:
6966:
6965:
6964:
6963:
6958:
6953:
6945:
6944:
6943:
6938:
6930:
6925:
6924:
6923:
6918:
6908:
6907:
6906:
6896:
6891:
6886:
6885:
6884:
6879:
6869:
6864:
6859:
6858:
6857:
6852:
6842:
6837:
6832:
6827:
6822:
6817:
6812:
6806:
6804:
6797:
6793:
6792:
6790:
6789:
6788:
6787:
6782:
6777:
6772:
6767:
6759:
6758:
6757:
6755:Vaccine injury
6752:
6747:
6742:
6737:
6732:
6727:
6718:
6716:
6715:Administration
6712:
6711:
6709:
6708:
6703:
6698:
6689:
6672:
6671:
6670:
6665:
6657:
6652:
6646:
6644:
6640:
6639:
6637:
6636:
6631:
6626:
6621:
6616:
6615:
6614:
6604:
6598:
6596:
6592:
6591:
6561:
6559:
6558:
6551:
6544:
6536:
6527:
6526:
6524:
6523:
6522:
6521:
6511:
6506:
6501:
6496:
6491:
6488:
6483:
6477:
6475:
6471:
6470:
6468:
6467:
6462:
6457:
6452:
6447:
6444:
6439:
6434:
6429:
6424:
6419:
6414:
6412:Emergent virus
6409:
6404:
6399:
6394:
6393:
6392:
6384:
6379:
6373:
6371:
6363:
6362:
6359:
6358:
6356:
6355:
6352:
6347:
6345:Vector control
6342:
6337:
6332:
6327:
6322:
6317:
6312:
6307:
6302:
6301:
6300:
6295:
6290:
6288:N95 respirator
6280:
6275:
6270:
6269:
6268:
6263:
6258:
6247:
6242:
6241:
6240:
6230:
6225:
6224:
6223:
6213:
6212:
6211:
6206:
6201:
6191:
6186:
6181:
6176:
6171:
6165:
6163:
6161:pharmaceutical
6155:
6154:
6152:
6151:
6150:
6149:
6144:
6139:
6134:
6129:
6119:
6114:
6109:
6104:
6099:
6094:
6093:
6092:
6082:
6077:
6072:
6067:
6062:
6057:
6052:
6051:
6050:
6040:
6039:
6038:
6028:
6023:
6022:
6021:
6010:
6008:
6007:Pharmaceutical
6001:
5991:
5990:
5988:
5987:
5984:
5979:
5974:
5969:
5964:
5959:
5958:Cardiovascular
5956:
5951:
5946:
5943:
5938:
5937:Nervous system
5935:
5932:
5931:
5930:
5920:
5919:
5918:
5913:
5904:
5902:
5896:
5895:
5892:
5891:
5889:
5888:
5883:
5878:
5873:
5868:
5863:
5858:
5853:
5848:
5843:
5838:
5833:
5828:
5823:
5822:
5821:
5816:
5806:
5801:
5795:
5793:
5787:
5786:
5784:
5783:
5778:
5773:
5768:
5763:
5761:Infection rate
5758:
5753:
5748:
5743:
5738:
5733:
5728:
5723:
5717:
5715:
5709:
5708:
5705:
5704:
5701:
5700:
5697:
5696:
5694:
5693:
5687:
5685:
5681:
5680:
5678:
5677:
5673:
5671:
5667:
5666:
5664:
5663:
5659:
5657:
5653:
5652:
5650:
5649:
5643:
5641:
5637:
5636:
5634:
5633:
5627:
5622:
5617:
5611:
5609:
5605:
5604:
5602:
5601:
5596:
5591:
5586:
5585:
5584:
5573:
5571:
5567:
5566:
5564:
5563:
5562:
5561:
5556:
5548:
5547:
5546:
5541:
5533:
5532:
5531:
5526:
5523:
5518:
5516:Injection site
5510:
5504:
5502:
5496:
5495:
5493:
5492:
5487:
5485:Dental aerosol
5482:
5481:
5480:
5470:
5464:
5462:
5455:
5451:
5450:
5448:
5447:
5441:
5439:
5433:
5432:
5430:
5429:
5424:
5423:
5422:
5417:
5416:
5415:
5410:
5407:
5396:
5395:
5394:
5389:
5381:
5375:
5373:
5369:Human-to-human
5365:
5364:
5362:
5361:
5356:
5351:
5346:
5340:
5338:
5329:
5325:
5324:
5322:
5321:
5315:
5312:
5309:
5304:
5299:
5295:
5293:
5286:
5282:
5281:
5279:
5278:
5273:
5268:
5266:Super-spreader
5263:
5261:Superinfection
5258:
5253:
5248:
5243:
5238:
5233:
5228:
5223:
5218:
5213:
5208:
5202:
5200:
5191:
5185:
5184:
5181:
5180:
5178:
5177:
5172:
5170:Vector control
5167:
5162:
5157:
5152:
5147:
5146:
5145:
5137:
5132:
5127:
5122:
5117:
5112:
5111:
5110:
5105:
5099:Climate zones
5097:
5095:Climate change
5092:
5089:
5086:
5080:
5078:
5072:
5071:
5069:
5068:
5067:
5066:
5063:
5060:
5059:
5058:
5050:
5047:
5044:
5041:
5038:
5030:
5025:
5020:
5015:
5014:
5013:
5008:
4998:
4993:
4988:
4983:
4977:
4975:
4969:
4968:
4966:
4965:
4960:
4959:
4958:
4953:
4948:
4938:
4937:
4936:
4931:
4926:
4921:
4911:
4909:Quorum sensing
4906:
4905:
4904:
4894:
4893:
4892:
4882:
4877:
4871:
4869:
4860:
4856:
4855:
4844:
4842:
4841:
4834:
4827:
4819:
4813:
4812:
4802:
4796:
4790:
4783:
4782:
4777:
4776:External links
4774:
4772:
4771:
4748:
4705:
4662:
4644:
4626:
4616:
4614:
4611:
4608:
4607:
4556:
4521:Bioinformatics
4507:
4458:
4401:
4372:(2): 113–127.
4352:
4315:(1–2): 33–55.
4295:
4266:
4252:
4185:
4146:(3): 925–979.
4126:
4051:
4035:
3978:
3959:(4): 505–528.
3939:
3874:
3799:
3790:|journal=
3743:
3702:
3653:
3604:
3545:
3488:
3451:(2): 415–423.
3431:
3413:
3396:
3381:
3367:
3324:
3297:(4): 599–653.
3281:
3262:
3261:
3259:
3256:
3254:
3253:
3248:
3246:Sexual network
3243:
3238:
3233:
3228:
3223:
3218:
3213:
3208:
3203:
3198:
3193:
3187:
3185:
3182:
3157:
3154:
3153:
3152:
3141:
3138:
3134:
3121:
3118:
3109:
3108:
3097:
3091:
3088:
3085:
3081:
3076:
3070:
3067:
3064:
3061:
3058:
3055:
3050:
3047:
3041:
3035:
3032:
3029:
3026:
3023:
3020:
3017:
3013:
3009:
3006:
3002:
2997:
2992:
2988:
2964:
2958:
2957:
2946:
2940:
2937:
2934:
2931:
2928:
2923:
2919:
2914:
2909:
2902:
2898:
2894:
2889:
2884:
2880:
2869:
2858:
2851:
2847:
2843:
2838:
2833:
2829:
2805:
2794:
2777:
2769:
2764:
2763:
2752:
2749:
2746:
2743:
2740:
2735:
2731:
2727:
2722:
2718:
2701:
2695:
2684:
2676:
2658:
2652:
2649:
2648:
2647:
2636:
2631:
2627:
2624:
2621:
2618:
2615:
2612:
2609:
2606:
2600:
2595:
2591:
2565:
2561:
2549:
2548:
2537:
2532:
2527:
2523:
2519:
2515:
2511:
2508:
2505:
2500:
2497:
2493:
2490:
2487:
2484:
2481:
2476:
2471:
2467:
2463:
2459:
2455:
2452:
2449:
2446:
2432:
2431:
2420:
2417:
2414:
2411:
2408:
2403:
2400:
2396:
2393:
2390:
2387:
2382:
2377:
2373:
2369:
2365:
2361:
2358:
2355:
2352:
2349:
2344:
2341:
2338:
2334:
2315:
2314:
2303:
2296:
2292:
2288:
2283:
2280:
2277:
2272:
2268:
2251:
2235:
2234:
2219:
2212:
2208:
2204:
2199:
2196:
2193:
2190:
2187:
2185:
2182:
2175:
2171:
2167:
2162:
2159:
2156:
2153:
2150:
2148:
2145:
2142:
2139:
2136:
2133:
2130:
2127:
2124:
2121:
2116:
2112:
2108:
2106:
2065:
2064:
2053:
2048:
2044:
2041:
2035:
2030:
2027:
2022:
2019:
2016:
2010:
2005:
2001:
1997:
1994:
1990:
1984:
1979:
1975:
1971:
1968:
1964:
1946:
1945:
1934:
1928:
1925:
1920:
1916:
1912:
1907:
1903:
1899:
1896:
1893:
1890:
1887:
1882:
1877:
1873:
1869:
1866:
1863:
1857:
1851:
1848:
1843:
1839:
1835:
1830:
1826:
1822:
1819:
1816:
1813:
1810:
1807:
1804:
1799:
1794:
1790:
1786:
1783:
1780:
1777:
1774:
1768:
1763:
1760:
1755:
1750:
1746:
1731:
1730:
1719:
1716:
1713:
1710:
1705:
1701:
1665:
1662:
1661:
1660:
1655:
1649:
1643:
1640:
1635:
1632:
1626:
1621:
1618:
1612:
1607:
1604:
1598:
1594:and spread of
1589:
1583:
1546:
1543:
1533:
1530:
1529:
1528:
1515:
1512:
1509:
1506:
1496:
1484:
1481:
1478:
1475:
1465:
1453:
1450:
1447:
1444:
1421:
1418:
1415:
1412:
1392:
1389:
1386:
1383:
1363:
1360:
1357:
1354:
1326:
1323:
1320:
1300:
1297:
1294:
1274:
1271:
1268:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1164:
1161:
1158:
1138:
1135:
1132:
1112:
1109:
1106:
1103:
1100:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1055:
1039:
1036:
1024:Main article:
1021:
1018:
1006:
1005:
994:
989:
986:
981:
978:
975:
970:
966:
943:
937:
936:
925:
920:
917:
912:
907:
903:
899:
894:
891:
886:
879:
875:
871:
851:
850:
839:
832:
828:
824:
819:
816:
798:
797:
786:
781:
778:
773:
770:
740:
722:
712:
711:
700:
697:
691:
686:
682:
647:
644:
635:
628:
621:
610:
596:Main article:
593:
590:
576:
573:
570:
566:
561:
556:
553:
550:
545:
541:
536:
532:
528:
506:
503:
500:
493:
490:
484:
479:
475:
451:
448:
425:
400:is the second
388:
383:
379:
375:
353:
350:
347:
324:
321:
318:
312:
309:
306:
301:
296:
292:
288:
282:
277:
273:
236:
233:
215:
212:
202:
199:
194:
191:
189:
186:
185:
184:
175:
154:
151:
62:
59:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7961:
7950:
7947:
7945:
7942:
7940:
7937:
7935:
7932:
7931:
7929:
7914:
7911:
7909:
7906:
7904:
7901:
7899:
7896:
7894:
7891:
7889:
7886:
7885:
7883:
7879:
7873:
7870:
7868:
7865:
7863:
7862:Crime mapping
7860:
7858:
7855:
7853:
7850:
7848:
7845:
7843:
7840:
7839:
7837:
7833:
7827:
7824:
7822:
7819:
7817:
7814:
7813:
7811:
7807:
7801:
7798:
7796:
7793:
7791:
7788:
7786:
7783:
7781:
7778:
7776:
7773:
7771:
7770:Climate model
7768:
7766:
7763:
7761:
7758:
7757:
7755:
7753:Environmental
7751:
7745:
7742:
7740:
7737:
7735:
7732:
7730:
7727:
7725:
7722:
7720:
7717:
7715:
7712:
7711:
7709:
7707:
7703:
7699:
7692:
7687:
7685:
7680:
7678:
7673:
7672:
7669:
7653:
7651:
7648:
7647:
7645:
7642:
7639:
7636:
7634:
7631:
7630:
7626:
7620:
7617:
7615:
7612:
7610:
7607:
7605:
7602:
7601:
7599:
7595:
7589:
7586:
7584:
7583:
7579:
7577:
7574:
7572:
7569:
7567:
7564:
7562:
7559:
7556:
7554:
7549:
7546:
7544:
7541:
7540:
7538:
7534:
7528:
7527:Drew Weissman
7525:
7523:
7520:
7518:
7515:
7513:
7512:H. Fred Clark
7510:
7508:
7505:
7503:
7500:
7498:
7495:
7493:
7490:
7488:
7485:
7483:
7482:Louis Pasteur
7480:
7478:
7477:Edward Jenner
7475:
7474:
7472:
7466:
7454:
7451:
7449:
7448:DTwP-HepB-Hib
7446:
7444:
7443:DTaP-IPV-HepB
7441:
7439:
7436:
7435:
7434:combination:
7433:
7431:
7428:
7426:
7423:
7421:
7418:
7416:
7413:
7409:
7406:
7402:
7399:
7397:
7394:
7393:
7392:
7389:
7387:
7384:
7382:
7379:
7377:
7374:
7373:
7372:
7369:
7367:
7364:
7363:
7361:
7357:
7349:
7346:
7344:
7341:
7340:
7338:
7337:
7335:
7333:
7332:Helminthiasis
7329:
7321:
7318:
7317:
7315:
7311:
7308:
7307:
7306:
7303:
7302:
7300:
7296:
7288:
7285:
7283:
7280:
7278:
7275:
7273:
7270:
7268:
7265:
7263:
7260:
7258:
7255:
7254:
7252:
7248:
7245:
7243:
7240:
7238:
7235:
7234:
7233:combination:
7232:
7230:
7227:
7223:
7220:
7218:
7215:
7214:
7212:
7210:
7207:
7205:
7202:
7200:
7197:
7193:
7190:
7188:
7185:
7183:
7180:
7178:
7175:
7173:
7170:
7168:
7165:
7163:
7160:
7158:
7155:
7153:
7150:
7148:
7145:
7143:
7140:
7138:
7135:
7133:
7130:
7128:
7125:
7123:
7120:
7119:
7118:
7115:
7113:
7110:
7108:
7105:
7103:
7100:
7096:
7093:
7091:
7088:
7087:
7086:
7083:
7081:
7078:
7076:
7073:
7071:
7068:
7066:
7063:
7059:
7056:
7054:
7051:
7050:
7049:
7046:
7044:
7041:
7039:
7036:
7034:
7031:
7029:
7026:
7022:
7019:
7017:
7014:
7011:
7007:
7004:
7003:
7002:
6999:
6995:
6992:
6991:
6990:
6987:
6985:
6982:
6980:
6977:
6976:
6974:
6970:
6962:
6959:
6957:
6954:
6952:
6949:
6948:
6946:
6942:
6939:
6937:
6936:DPT/DTwP/DTaP
6934:
6933:
6932:combination:
6931:
6929:
6926:
6922:
6919:
6917:
6914:
6913:
6912:
6909:
6905:
6902:
6901:
6900:
6897:
6895:
6892:
6890:
6887:
6883:
6880:
6878:
6875:
6874:
6873:
6870:
6868:
6865:
6863:
6860:
6856:
6853:
6851:
6848:
6847:
6846:
6845:Meningococcus
6843:
6841:
6838:
6836:
6835:Leptospirosis
6833:
6831:
6828:
6826:
6823:
6821:
6818:
6816:
6813:
6811:
6808:
6807:
6805:
6801:
6798:
6794:
6786:
6783:
6781:
6778:
6776:
6773:
6771:
6770:Vaccine court
6768:
6766:
6763:
6762:
6760:
6756:
6753:
6751:
6748:
6746:
6743:
6741:
6738:
6736:
6733:
6731:
6728:
6726:
6725:GAVI Alliance
6723:
6722:
6720:
6719:
6717:
6713:
6707:
6704:
6702:
6699:
6697:
6693:
6690:
6688:
6684:
6680:
6676:
6673:
6669:
6666:
6664:
6661:
6660:
6658:
6656:
6653:
6651:
6648:
6647:
6645:
6641:
6635:
6632:
6630:
6627:
6625:
6622:
6620:
6617:
6613:
6610:
6609:
6608:
6605:
6603:
6600:
6599:
6597:
6593:
6588:
6584:
6580:
6576:
6572:
6568:
6564:
6557:
6552:
6550:
6545:
6543:
6538:
6537:
6534:
6520:
6517:
6516:
6515:
6512:
6510:
6507:
6505:
6502:
6500:
6497:
6495:
6492:
6489:
6487:
6484:
6482:
6479:
6478:
6476:
6472:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6448:
6445:
6443:
6440:
6438:
6435:
6433:
6430:
6428:
6425:
6423:
6420:
6418:
6415:
6413:
6410:
6408:
6405:
6403:
6400:
6398:
6395:
6391:
6388:
6387:
6385:
6383:
6380:
6378:
6375:
6374:
6372:
6370:
6364:
6353:
6351:
6348:
6346:
6343:
6341:
6338:
6336:
6333:
6331:
6328:
6326:
6325:Sterilization
6323:
6321:
6318:
6316:
6313:
6311:
6308:
6306:
6303:
6299:
6296:
6294:
6293:Surgical mask
6291:
6289:
6286:
6285:
6284:
6281:
6279:
6276:
6274:
6271:
6267:
6264:
6262:
6259:
6256:
6253:
6252:
6251:
6250:Public health
6248:
6246:
6243:
6239:
6236:
6235:
6234:
6231:
6229:
6226:
6222:
6219:
6218:
6217:
6214:
6210:
6207:
6205:
6202:
6200:
6197:
6196:
6195:
6192:
6190:
6187:
6185:
6182:
6180:
6177:
6175:
6172:
6170:
6167:
6166:
6164:
6162:
6156:
6148:
6145:
6143:
6140:
6138:
6135:
6133:
6130:
6128:
6125:
6124:
6123:
6120:
6118:
6115:
6113:
6110:
6108:
6105:
6103:
6102:Phage therapy
6100:
6098:
6095:
6091:
6088:
6087:
6086:
6085:Immunotherapy
6083:
6081:
6078:
6076:
6073:
6071:
6068:
6066:
6063:
6061:
6058:
6056:
6053:
6049:
6046:
6045:
6044:
6043:Antimicrobial
6041:
6037:
6034:
6033:
6032:
6029:
6027:
6024:
6020:
6017:
6016:
6015:
6012:
6011:
6009:
6005:
6002:
6000:
5992:
5985:
5983:
5980:
5978:
5975:
5973:
5970:
5968:
5965:
5963:
5960:
5957:
5955:
5952:
5950:
5947:
5944:
5942:
5939:
5936:
5934:Genitourinary
5933:
5929:
5926:
5925:
5924:
5921:
5917:
5914:
5912:
5909:
5908:
5906:
5905:
5903:
5897:
5887:
5884:
5882:
5879:
5877:
5874:
5872:
5869:
5867:
5864:
5862:
5859:
5857:
5854:
5852:
5849:
5847:
5844:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5820:
5817:
5815:
5812:
5811:
5810:
5807:
5805:
5802:
5800:
5797:
5796:
5794:
5792:in population
5788:
5782:
5779:
5777:
5774:
5772:
5769:
5767:
5764:
5762:
5759:
5757:
5756:Herd immunity
5754:
5752:
5749:
5747:
5744:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5724:
5722:
5719:
5718:
5716:
5714:
5710:
5692:
5689:
5688:
5686:
5682:
5675:
5674:
5672:
5668:
5661:
5660:
5658:
5654:
5648:
5645:
5644:
5642:
5640:Genitourinary
5638:
5632:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5612:
5610:
5606:
5600:
5597:
5595:
5592:
5590:
5587:
5583:
5582:Contamination
5580:
5579:
5578:
5575:
5574:
5572:
5568:
5560:
5557:
5555:
5552:
5551:
5550:Vector-borne
5549:
5545:
5542:
5540:
5537:
5536:
5534:
5530:
5527:
5524:
5522:
5519:
5517:
5514:
5513:
5511:
5509:
5506:
5505:
5503:
5497:
5491:
5488:
5486:
5483:
5479:
5476:
5475:
5474:
5471:
5469:
5466:
5465:
5463:
5459:
5456:
5452:
5446:
5443:
5442:
5440:
5434:
5428:
5425:
5421:
5418:
5414:
5411:
5408:
5405:
5404:
5403:
5400:
5399:
5397:
5393:
5390:
5388:
5385:
5384:
5382:
5380:
5377:
5376:
5374:
5370:
5366:
5360:
5357:
5355:
5352:
5350:
5347:
5345:
5342:
5341:
5339:
5337:
5336:Cross-species
5333:
5330:
5326:
5319:
5316:
5313:
5310:
5308:
5305:
5303:
5300:
5297:
5296:
5294:
5290:
5287:
5283:
5277:
5276:Window period
5274:
5272:
5269:
5267:
5264:
5262:
5259:
5257:
5254:
5252:
5249:
5247:
5244:
5242:
5241:Latent period
5239:
5237:
5234:
5232:
5229:
5227:
5224:
5222:
5219:
5217:
5214:
5212:
5209:
5207:
5204:
5203:
5201:
5195:
5192:
5190:
5186:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5156:
5153:
5151:
5148:
5144:
5141:
5140:
5138:
5136:
5133:
5131:
5128:
5126:
5123:
5121:
5120:Deforestation
5118:
5116:
5113:
5109:
5106:
5104:
5101:
5100:
5098:
5096:
5093:
5090:
5087:
5085:
5082:
5081:
5079:
5077:
5073:
5065:Stress levels
5064:
5061:
5057:
5054:
5053:
5051:
5048:
5045:
5042:
5039:
5036:
5035:
5034:
5031:
5029:
5026:
5024:
5021:
5019:
5016:
5012:
5009:
5007:
5004:
5003:
5002:
4999:
4997:
4994:
4992:
4989:
4987:
4984:
4982:
4979:
4978:
4976:
4974:
4970:
4964:
4961:
4957:
4954:
4952:
4949:
4947:
4944:
4943:
4942:
4939:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4916:
4915:
4912:
4910:
4907:
4903:
4900:
4899:
4898:
4897:Pathogenicity
4895:
4891:
4888:
4887:
4886:
4883:
4881:
4878:
4876:
4873:
4872:
4870:
4868:
4864:
4861:
4857:
4852:
4848:
4840:
4835:
4833:
4828:
4826:
4821:
4820:
4817:
4810:
4806:
4803:
4800:
4797:
4794:
4791:
4788:
4787:Model-Builder
4785:
4784:
4780:
4779:
4775:
4768:
4762:
4754:
4749:
4745:
4741:
4736:
4731:
4727:
4723:
4720:(4): 255–65.
4719:
4715:
4711:
4706:
4702:
4698:
4693:
4688:
4684:
4680:
4677:(6): 477–87.
4676:
4672:
4668:
4663:
4652:
4651:
4645:
4634:
4633:
4627:
4623:
4618:
4617:
4612:
4603:
4597:
4589:
4585:
4580:
4575:
4571:
4567:
4560:
4557:
4552:
4548:
4543:
4538:
4534:
4530:
4526:
4522:
4518:
4511:
4508:
4503:
4499:
4494:
4489:
4485:
4481:
4478:(2): 83–100.
4477:
4473:
4469:
4462:
4459:
4454:
4450:
4445:
4440:
4436:
4432:
4428:
4424:
4420:
4416:
4412:
4405:
4402:
4397:
4393:
4388:
4383:
4379:
4375:
4371:
4367:
4363:
4356:
4353:
4348:
4344:
4340:
4336:
4331:
4326:
4322:
4318:
4314:
4310:
4306:
4299:
4296:
4288:September 19,
4284:
4277:
4270:
4267:
4262:
4256:
4253:
4248:
4244:
4240:
4236:
4231:
4226:
4222:
4218:
4213:
4208:
4205:(4): 044313.
4204:
4200:
4196:
4189:
4186:
4181:
4177:
4172:
4167:
4163:
4159:
4154:
4149:
4145:
4141:
4137:
4130:
4127:
4122:
4118:
4113:
4108:
4104:
4100:
4096:
4092:
4088:
4084:
4079:
4078:q-bio/0610057
4074:
4070:
4066:
4062:
4055:
4052:
4047:
4046:
4039:
4036:
4031:
4027:
4022:
4017:
4013:
4009:
4005:
4001:
3997:
3993:
3989:
3982:
3979:
3974:
3970:
3966:
3962:
3958:
3954:
3950:
3943:
3940:
3935:
3931:
3926:
3921:
3917:
3913:
3909:
3905:
3901:
3897:
3894:(2): 191504.
3893:
3889:
3885:
3878:
3875:
3870:
3866:
3861:
3856:
3852:
3848:
3844:
3840:
3836:
3832:
3827:
3822:
3818:
3814:
3810:
3803:
3800:
3795:
3782:
3773:
3768:
3763:
3758:
3754:
3747:
3744:
3739:
3735:
3730:
3725:
3721:
3717:
3713:
3706:
3703:
3698:
3694:
3689:
3684:
3680:
3676:
3672:
3668:
3664:
3657:
3654:
3649:
3645:
3641:
3637:
3632:
3627:
3623:
3619:
3615:
3608:
3605:
3600:
3596:
3592:
3588:
3583:
3578:
3573:
3568:
3564:
3560:
3556:
3549:
3546:
3541:
3537:
3533:
3529:
3524:
3519:
3515:
3511:
3507:
3503:
3499:
3492:
3489:
3484:
3480:
3475:
3470:
3466:
3462:
3458:
3454:
3450:
3446:
3442:
3435:
3432:
3427:
3420:
3418:
3414:
3409:
3408:
3400:
3397:
3392:
3385:
3382:
3377:
3371:
3368:
3363:
3359:
3355:
3351:
3347:
3343:
3340:(5): 275–88.
3339:
3335:
3328:
3325:
3320:
3316:
3312:
3308:
3304:
3300:
3296:
3292:
3285:
3282:
3277:
3270:
3268:
3264:
3257:
3252:
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3222:
3219:
3217:
3214:
3212:
3209:
3207:
3204:
3202:
3199:
3197:
3194:
3192:
3189:
3188:
3183:
3181:
3179:
3175:
3171:
3167:
3163:
3155:
3150:
3146:
3142:
3139:
3135:
3132:
3131:
3130:
3128:
3119:
3117:
3114:
3095:
3089:
3086:
3083:
3079:
3074:
3065:
3062:
3059:
3053:
3048:
3045:
3039:
3030:
3027:
3024:
3015:
3011:
3007:
3000:
2995:
2990:
2986:
2978:
2977:
2976:
2974:
2970:
2963:
2944:
2935:
2932:
2929:
2921:
2917:
2912:
2907:
2900:
2896:
2892:
2887:
2882:
2878:
2870:
2856:
2849:
2845:
2841:
2836:
2831:
2827:
2819:
2818:
2817:
2815:
2811:
2804:
2799:
2797:
2790:
2786:
2781:
2776:
2772:
2747:
2744:
2741:
2733:
2729:
2725:
2720:
2716:
2708:
2707:
2706:
2704:
2694:
2690:
2683:
2679:
2672:
2668:
2663:
2661:
2650:
2634:
2629:
2622:
2619:
2616:
2610:
2607:
2604:
2598:
2593:
2589:
2581:
2580:
2579:
2578:, we obtain:
2563:
2559:
2535:
2530:
2525:
2521:
2517:
2513:
2509:
2506:
2503:
2498:
2495:
2488:
2482:
2479:
2469:
2465:
2461:
2457:
2453:
2450:
2447:
2444:
2437:
2436:
2435:
2418:
2415:
2412:
2409:
2406:
2401:
2398:
2391:
2385:
2375:
2371:
2367:
2363:
2359:
2353:
2347:
2336:
2324:
2323:
2322:
2320:
2301:
2294:
2290:
2286:
2281:
2278:
2275:
2270:
2266:
2258:
2257:
2256:
2254:
2247:
2242:
2240:
2217:
2210:
2206:
2202:
2197:
2194:
2191:
2188:
2180:
2173:
2169:
2165:
2160:
2157:
2154:
2151:
2143:
2140:
2137:
2131:
2128:
2125:
2119:
2114:
2110:
2097:
2096:
2095:
2093:
2090: +
2089:
2085:
2081:
2077:
2069:
2051:
2046:
2042:
2039:
2033:
2028:
2025:
2020:
2017:
2014:
2003:
1999:
1992:
1977:
1973:
1966:
1951:
1950:
1949:
1932:
1918:
1914:
1910:
1905:
1901:
1888:
1875:
1871:
1864:
1855:
1841:
1837:
1833:
1828:
1824:
1811:
1805:
1802:
1792:
1788:
1781:
1775:
1772:
1766:
1761:
1758:
1753:
1748:
1744:
1736:
1735:
1734:
1717:
1714:
1711:
1708:
1703:
1699:
1691:
1690:
1689:
1687:
1682:
1680:
1676:
1671:
1670:herd immunity
1663:
1659:
1656:
1653:
1650:
1647:
1644:
1641:
1639:
1636:
1633:
1631:
1627:
1625:
1624:phylodynamics
1622:
1619:
1617:
1613:
1611:
1608:
1605:
1603:-epidemiology
1602:
1599:
1597:
1593:
1590:
1587:
1584:
1582:
1579:
1578:
1577:
1574:
1572:
1568:
1564:
1560:
1556:
1552:
1544:
1542:
1540:
1539:SEIS and SEIR
1531:
1510:
1504:
1497:
1479:
1473:
1466:
1448:
1442:
1435:
1434:
1433:
1416:
1410:
1387:
1381:
1358:
1352:
1340:
1324:
1321:
1318:
1298:
1295:
1292:
1272:
1269:
1266:
1246:
1243:
1237:
1231:
1228:
1225:
1222:
1216:
1210:
1207:
1204:
1201:
1195:
1189:
1180:
1162:
1159:
1156:
1136:
1133:
1130:
1110:
1107:
1101:
1095:
1092:
1089:
1086:
1080:
1074:
1071:
1068:
1065:
1059:
1053:
1044:
1038:The SIR model
1037:
1035:
1033:
1032:Markov chains
1027:
1019:
1017:
1015:
1011:
992:
987:
984:
979:
976:
973:
968:
964:
956:
955:
954:
952:
947:
942:
923:
918:
915:
910:
905:
901:
892:
889:
884:
877:
873:
869:
860:
859:
858:
856:
837:
830:
826:
822:
817:
814:
807:
806:
805:
803:
784:
779:
776:
771:
768:
761:
760:
759:
757:
753:
749:
744:
739:
735:
732:
728:
721:
717:
698:
695:
689:
684:
680:
669:
668:
667:
665:
661:
657:
653:
645:
643:
641:
634:
627:
620:
616:
609:
605:
599:
591:
589:
571:
564:
559:
551:
543:
534:
530:
501:
491:
488:
482:
477:
473:
449:
446:
423:
415:
411:
407:
403:
381:
377:
348:
335:
322:
319:
316:
307:
294:
290:
280:
275:
271:
262:
260:
256:
251:
246:
242:
234:
232:
230:
229:herd immunity
226:
221:
213:
211:
207:
201:Deterministic
200:
198:
192:
187:
181:
176:
173:
169:
165:
161:
160:
159:
152:
150:
148:
144:
140:
135:
133:
129:
125:
121:
116:
114:
110:
105:
103:
99:
95:
91:
87:
82:
80:
76:
72:
67:
60:
58:
56:
52:
48:
47:public health
44:
40:
36:
32:
19:
7934:Epidemiology
7604:Epidemiology
7580:
7552:
7438:DTaP-IPV/Hib
7229:Yellow fever
7142:EpiVacCorona
6899:Tuberculosis
6872:Pneumococcal
6840:Lyme disease
6668:Heterologous
6618:
6567:Immunization
6233:Notification
6204:Hand washing
6199:Food hygiene
6184:Disinfection
6080:Immunization
6031:Anthelmintic
6019:prophylactic
5907:Respiratory
5831:Hyperendemic
5781:WAIFW matrix
5436:Environment-
5189:Transmission
5165:Urbanization
4963:Host tropism
4859:Determinants
4845:Concepts in
4809:surveillance
4752:
4717:
4713:
4674:
4670:
4654:. Retrieved
4649:
4637:. Retrieved
4631:
4621:
4596:cite journal
4569:
4565:
4559:
4524:
4520:
4510:
4475:
4471:
4461:
4418:
4414:
4404:
4369:
4365:
4355:
4312:
4308:
4298:
4286:. Retrieved
4282:
4269:
4255:
4202:
4198:
4188:
4143:
4139:
4129:
4068:
4064:
4054:
4044:
4038:
3995:
3991:
3981:
3956:
3952:
3942:
3891:
3887:
3877:
3819:(1): 40885.
3816:
3812:
3802:
3781:cite journal
3772:10419/257469
3746:
3719:
3715:
3705:
3670:
3666:
3656:
3621:
3617:
3607:
3562:
3558:
3548:
3505:
3501:
3491:
3448:
3444:
3434:
3425:
3406:
3399:
3390:
3384:
3370:
3337:
3333:
3327:
3294:
3290:
3284:
3275:
3251:WAIFW matrix
3159:
3123:
3110:
2972:
2968:
2961:
2959:
2813:
2809:
2802:
2800:
2792:
2788:
2782:
2774:
2767:
2765:
2699:
2692:
2681:
2674:
2670:
2666:
2664:
2656:
2654:
2551:Solving for
2550:
2433:
2318:
2316:
2249:
2245:
2243:
2238:
2236:
2091:
2087:
2083:
2079:
2075:
2074:
1947:
1732:
1685:
1683:
1667:
1652:transmission
1575:
1548:
1535:
1374:; infected,
1344:
1029:
1013:
1009:
1007:
948:
940:
938:
852:
801:
799:
755:
751:
747:
745:
737:
734:steady state
726:
719:
713:
655:
649:
639:
632:
625:
618:
607:
606:(denoted by
603:
601:
336:
263:
238:
217:
208:
204:
196:
171:
167:
156:
136:
117:
111:applied the
106:
83:
78:
77:in his book
68:
64:
29:
7944:Vaccination
7640:from market
7536:Controversy
7470:researchers
7386:Hepatitis B
7272:Hepatitis C
7217:Chicken pox
7043:Hepatitis E
7038:Hepatitis B
7033:Hepatitis A
6984:Chikungunya
6961:Shigellosis
6815:Brucellosis
6701:Therapeutic
6655:Inactivated
6595:Development
6583:Inoculation
6575:Vaccination
6486:Eradication
6397:Biosecurity
6122:Vaccination
6097:Inoculation
6075:Drug safety
6070:Combination
5997:and Control
5945:Soft tissue
5899:Anatomical
5866:Seasonality
5846:Mesoendemic
5826:Holoendemic
5819:Farr's laws
5731:Attack rate
5529:Animal bite
5525:Insect bite
5461:Respiratory
5088:Air quality
5076:Environment
4986:Comorbidity
4902:Attack rate
4885:Infectivity
4751:Capasso V.
3751:Tembine H.
3582:10037/19057
3291:SIAM Review
3241:Risk factor
3156:Reliability
3140:Eradication
3133:Elimination
3127:eradication
2689:vaccination
153:Assumptions
128:susceptible
109:Ronald Ross
102:germ theory
75:John Graunt
55:vaccination
41:(including
7928:Categories
7706:Biological
7571:Thiomersal
7517:Paul Offit
7492:Jonas Salk
7468:Inventors/
7339:research:
7316:research:
7253:research:
7182:Skycovione
7172:Sanofi–GSK
7117:SARS-CoV-2
7028:Hantavirus
6994:rVSV-ZEBOV
6979:Adenovirus
6947:research:
6825:Diphtheria
6663:Attenuated
6369:infections
6310:Sanitation
6278:Quarantine
6137:resistance
6055:Antiseptic
6036:Ascaricide
6026:Antifungal
6014:Antibiotic
5995:Prevention
5928:Intestinal
5861:Prevalence
5841:Inequality
5790:Occurrence
5589:Breastmilk
5473:Bioaerosol
5445:Sapronosis
5420:Horizontal
5292:Endogenous
5271:Viral load
5231:Index case
4656:2016-02-15
4639:2023-02-27
4212:2103.12634
3826:1606.07825
3258:References
3166:SARS-CoV-2
3149:rinderpest
3137:threshold.
2773:is simply
1679:poliovirus
1596:resistance
193:Stochastic
147:SARS-CoV-2
137:Recently,
51:parameters
7650:Phase III
7638:Withdrawn
7566:Pox party
7376:ALVAC-CEA
7298:Protozoan
7187:Sputnik V
7137:CoronaVac
7107:Rotavirus
7010:Pandemrix
6862:Pertussis
6803:Bacterial
6687:Synthetic
6650:Conjugate
6602:Adjuvants
6579:Infection
6481:Discovery
6407:Disease X
6367:Emerging
6315:Screening
6216:Isolation
6060:Antiviral
5886:Twindemic
5836:Incidence
5713:Modelling
5676:Perinatal
5608:Cutaneous
5499:Linked to
5409:Perinatal
5328:Exogenous
5320:formation
5062:Pregnancy
4919:Endotoxin
4914:Virulence
4761:cite book
4247:232320251
4153:1408.2701
4103:1539-3755
3916:2054-5703
3851:2045-2322
3648:216074714
3624:: m1567.
3599:216426533
3591:1460-7425
3565:(2): 10.
3540:214771531
3410:. Dutton.
3170:Swine flu
3087:−
3063:−
3028:−
2933:−
2745:−
2620:−
2611:
2605:−
2518:−
2510:−
2480:β
2475:∞
2466:∫
2462:−
2454:−
2413:−
2386:λ
2381:∞
2372:∫
2368:−
2343:∞
2340:→
2282:−
2248:(denoted
2198:−
2155:−
2129:−
2120:⋅
2082:), since
2040:β
2029:μ
2026:λ
1993:
1967:
1889:
1865:
1812:
1803:μ
1782:
1773:μ
1733:In turn,
1709:⋅
1658:virulence
1614:pathogen
1592:evolution
1319:β
1293:β
1267:γ
1157:γ
1131:β
898:⇒
575:⟩
569:⟨
555:⟩
549:⟨
544:−
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