Evolution of transmissibility and virulence of pathogens in spatially distributed populations

Abstract

The SARS-CoV2 pandemic has led to the development of a large amount of theoretical work aimed at modeling and describing the evolution of the disease under various conditions. The role of quarantine, vaccinations and the geographic distribution of populations were studied. Some works have taken into account neutral mutations looking for clues to the emergence of new variants. In this project we intend to study a model developed in 2003 by Rauch et al. where the propagation of a virus through a spatially distributed population was studied. One of the main results of this work is that, when the virus undergoes mutations in its transmission rate, variants with moderate transmission are fixed, since the most transmissible ones kill the host very quickly. In this work we intend to allow virulence (death rate induced by the virus) to also mutate. We intend to study the endemic equilibrium state of this virus both in terms of transmissibility and virulence. The study of the evolution of transmissibility and virulence can contribute to unravel the belief that viruses always evolve in such a way as to become weak and endemic.