Compartmental Models in Epidemiology

Brauer, Fred

doi:10.1007/978-3-540-78911-6_2

Cited by 407 publications

(391 citation statements)

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“…It is possible to model infectious disease dynamics without these assumptions. For example, a discussion of models that include demography with variable population size can be found in Brauer (2008), Hethcote (2000), and Ledder (2017). The simple SIR model with demography is given by:…”

Section: Finding Equilibriamentioning

confidence: 99%

“…Keep in mind, this is by no means meant to be a all-encompassing discussion of infectious disease modeling but a resource to supplement other more comprehensive texts (e.g. Anderson, May, & Anderson, 1992;Brauer, 2008;Brauer & Castillo-Chavez, 2001;Brauer & Kribs, 2015;Brauer, vanden Driessche, & Wu, 2008;Keeling & Rohani, 2008;Martcheva, 2015;Vynnycky & White, 2010).…”

Section: Introductionmentioning

confidence: 99%

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An introduction to compartmental modeling for the budding infectious disease modeler

Blackwood

Childs

2018

Letters in Biomathematics

109

146

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Section: Finding Equilibriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An introduction to compartmental modeling for the budding infectious disease modeler

Blackwood

Childs

2018

Letters in Biomathematics

109

146

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“…These simple models implicitly assume that the time an individual spends in each disease stage (e.g. latent or infectious) is drawn from exponential distributions [2,5], which are unlike real distributions of disease stage durations.…”

Section: Introductionmentioning

confidence: 99%

Effects of the infectious period distribution on predicted transitions in childhood disease dynamics

Krylova

Earn

2013

J. R. Soc. Interface.

101

140

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The population dynamics of infectious diseases occasionally undergo rapid qualitative changes, such as transitions from annual to biennial cycles or to irregular dynamics. Previous work, based on the standard seasonally forced 'susceptible-exposed-infectious -removed' (SEIR) model has found that transitions in the dynamics of many childhood diseases result from bifurcations induced by slow changes in birth and vaccination rates. However, the standard SEIR formulation assumes that the stage durations (latent and infectious periods) are exponentially distributed, whereas real distributions are narrower and centred around the mean. Much recent work has indicated that realistically distributed stage durations strongly affect the dynamical structure of seasonally forced epidemic models. We investigate whether inferences drawn from previous analyses of transitions in patterns of measles dynamics are robust to the shapes of the stage duration distributions. As an illustrative example, we analyse measles dynamics in New York City from 1928 to 1972. We find that with a fixed mean infectious period in the susceptible -infectious -removed (SIR) model, the dynamical structure and predicted transitions vary substantially as a function of the shape of the infectious period distribution. By contrast, with fixed mean latent and infectious periods in the SEIR model, the shapes of the stage duration distributions have a less dramatic effect on model dynamical structure and predicted transitions. All these results can be understood more easily by considering the distribution of the disease generation time as opposed to the distributions of individual disease stages. Numerical bifurcation analysis reveals that for a given mean generation time the dynamics of the SIR and SEIR models for measles are nearly equivalent and are insensitive to the shapes of the disease stage distributions.

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“…The susceptible are the uninfected individuals, but are able to become infected if exposed. The infective individuals are those with the disease and can transmit the infection to other susceptible individuals [16][17][18]. The recovered comprises of individuals who have been recovered from the infection and are immune to reinfection.…”

Section: The Sir Modelmentioning

confidence: 99%