Asymptotic profiles of basic reproduction number for epidemic spreading in heterogeneous environment

2019/09/22 by Shanshan Chen, Chen, Shanshan, Junping Shi +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1909.10107

openalex publication_date 2019/09/22 · openalex created_date 2019/09/26 · openalex updated_date 2026/07/28

Abstract

The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the basic reproduction number is the maximum value of the local reproduction number on the spatial domain. On the other hand when the diffusion rates tend to infinity, the basic reproduction number tends to the spectral radius of the "average"~next generation matrix. These asymptotic limits of basic reproduction number hold for a class of general spatially heterogeneous compartmental epidemic models, and they are applied to a wide variety of examples.

Citations

• The differential infectivity and staged progression models for the transmission of HIV
• On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations
• Global stability of the steady states of an SIS epidemic reaction–diffusion model
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• On a vector-host epidemic model with spatial structure
• A Reaction–Diffusion Model of Vector-Borne Disease with Periodic Delays

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