From Methods of the Mathematical Kinetic Theory for Active Particles to Modeling Virus Mutations

The paper presents a model of virus mutations and evolution of epidemics in a system of interacting individuals, where the intensity of the pathology, described by a real discrete positive variable, is heterogeneously distributed, and the virus is in competition with the immune system or therapeutical actions. The model is developed within the framework of the Kinetic Theory of Active Particles (KTAP), extending the case of interacting particles with discrete microscopic state. The paper presents also a qualitative analysis developed to study the well-posedness of the mathematical problem associated to the general framework. Finally, simulations show the ability of the model to observe some interesting emerging phenomena, such as the mutation to a subsequent virus stage, the heterogeneous evolution of the pathology with the co-presence of individuals carriers of the virus at different levels of progression, and the presence of oscillating time phases of virus evolution and immune system control.