A multiscale active particle model of epidemic spreading with heterogeneous interactions

During this talk I will present a mathematical model of contagion and spread of a viral disease. The model is based on the kinetic theory for active particles and was developed using a multiscale framework accounting for the interaction of different spatial scales: from the small scale of viral particles and immune cells, to the larger scale of individuals and further up to the collective behavior of populations.The overall population is divided into compartments (susceptible, infectious, recovered and dead). Interactions between individual entities (hosts, viral particles, immune cells) are described at the micro-scale. A model of contagion through interactions is then proposed, depending on the interaction rate and a parameter describing the so-called social distance. Within infected hosts, viral particles and the immune system develop competitive interactions with transitions that may end up in a recovery or death. The dynamics of the system is then described by distribution functions at the meso-scale. The knowledge of these distribution functions allows to compute macroscopic variables (i.e. positive cases or deaths). Some case-studies are proposed in order to perform parameter sensitivity analyses and to understand responses of the system to different control measures aimed to reduce the impact of the disease.