Basic Models in Epidemiology

Brauer, Fred; Castillo‐Chavez, Carlos

doi:10.1007/978-1-4615-6881-0_19

Ecological Time Series 1995

DOI: 10.1007/978-1-4615-6881-0_19

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Basic Models in Epidemiology

Fred Brauer¹,

Carlos Castillo‐Chavez²

Abstract: Abstract. This chapter gives an introduction to epidemiological models for homogeneously mixing populations. A flexible framework for modeling deterministic and stochastic--continuous time Markov processes--pair-formation processes is revisited.This framework is used to formulate demographic models for heterogeneous mixing populations which can be used in the construction of models for communicable and sexually-transmitted diseases. Extensions to stochastic epidemiological processes are outlined.

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2022

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Cited by 1 publication

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Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

Elamraoui

Essoufi

Zafrar

2022

Int. J. Appl. Comput. Math

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This paper presents the SIR space-time model, which is a coupled reaction–diffusion system with nonlinear Robin boundary conditions. These boundary conditions are supposed to lock the border (no outflow neither immigration nor migration) when the number of infected individuals explode, and this may be considered as an automatic containment or lock-down. In practice, we can precise some threshold for the number of infected individuals and when it is reached the model locks the region automatically. This work provides a thorough study of the presented model, including the existence and uniqueness of the solution, its boundedness and its asymptotic behaviour. We end with some numerical experiments performed on the basis of the finite difference approach and Newton’s method to highlight and validate the theoretical results.

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Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

Elamraoui

Essoufi

Zafrar

2022

Int. J. Appl. Comput. Math

View full text Add to dashboard Cite

show abstract

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Basic Models in Epidemiology

Cited by 1 publication

References 95 publications

Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

Spatio-Temporal SIR Model with Robin Boundary Condition and Automatic Lockdown Policy

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