2019/09/22 by Shanshan Chen, Chen, Shanshan, Junping Shi +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Applied mathematics #Basic reproduction number #Biology #COVID-19 epidemiological studies #Computer science #Constant (computer programming) #Demography #Diffusion #Dynamical Systems (math.DS) #Ecology #Eigenvalues and eigenvectors #Epidemic model #Evolution and Genetic Dynamics #FOS: Mathematics #Infinity #Limit (mathematics) #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Physics #Population #Reproduction #Spectral radius #Zero (linguistics) #math.DS
paper · pdf · doi:10.48550/arxiv.1909.10107
published in arXiv (Cornell University) (Cornell University) · 34 pages
arxiv created 2019/09/22 · openalex publication_date 2019/09/22 · arxiv updated 2019/09/24 · openalex created_date 2019/09/26 · openalex updated_date 2026/08/06
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.