Abstract
In this article, we introduce an infinite-dimensional deterministic metapopulation 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.
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