Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment

Evolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-dependent cure rate (recovery rate) that dramatically affects the outcome of evolution. With the methods of critical function analysis and adaptive dynamics, we identify the evolutionary conditions for continuously stable strategies, evolutionary repellers, and evolutionary branching points. First, the results show that a high-intensity strength drug treatment can result in evolutionary branching and the evolution of pathogen strains will tend towards a higher virulence with the increase of the strength of the treatment. Second, we use the critical function analysis to investigate the evolution of virulence-related traits and show that evolutionary outcomes strongly depend on the shape of the trade-off between virulence and transmission. Third, after evolutionary branching, the two infective species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist, and no further branching is possible, which is independent of the cure rate function.