2020/06/15 by Jean‐François Delmas, Delmas, Jean-François, Dylan Dronnier +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Medicine · #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Epidemiology and Ecology Models #Spectral Theory (math.SP) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2006.08241
openalex publication_date 2020/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number R0 which determines whether there exists a stable endemic steady state (super-critical case: R0>1) or if the only equilibrium is disease-free (critical and sub-critical case: R0≤1). As an application of this general study, we prove that the so-called ``leaky'' and ``all-or-nothing'' vaccination mechanism have the same effect on R0. This framework is also very natural and intuitive to model lockdown policies and study their impact.