2007/10/27 by Lamia Belhadji, Belhadji, Lamia
Mathematics · Medicine · Physics and Astronomy · #60K35 #82C22 #COVID-19 epidemiological studies #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Probability (math.PR) #math.PR #msc:60K35 #msc:82C22
paper · pdf · doi:10.48550/arxiv.0710.5185
arxiv created 2007/10/27 · openalex publication_date 2007/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two approaches to study the spread of infectious diseases within a spatially structured population distributed in social clusters. According whether we consider only the population of infected individuals or both populations of infected individuals and healthy ones, two models are given to study an epidemic phenomenon. Our first approach is at a microscopic level, its goal is to determine if an epidemic may occur for those models. The second one is the derivation of hydrodynamics limits. By using the relative entropy method we prove that the empirical measures of infected and healthy individuals converge to a deterministic measure absolutely continuous with respect to the Lebesgue measure, whose density is the solution of a system of reaction-diffusion equations.