Abstract
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.
Highlights
Virus leads to the spread of the disease, which attracts the attention and research of many researchers [1,2,3,4,5,6,7,8,9,10]
We employ the susceptible-infected epidemic model under drug treatment to explore the adaptive evolution of pathogen virulence
Our results show that the strength of treatment noticeably affects the outcome of evolution: continuously stable strategies, evolutionary repellers, and evolutionary branching points
Summary
Virus leads to the spread of the disease, which attracts the attention and research of many researchers [1,2,3,4,5,6,7,8,9,10]. The evolution of pathogens recently has focused especially on influence virulence and on reasons for the coexistence of parasite strains [2, 7, 8]. We develop an epidemiological model to study the effect of drug treatment on the evolution of pathogen virulence. The model is based upon adaptive dynamics [11,12,13,14,15,16,17,18,19], in which we explore the coexistence of parasite strains and continuously stable strategy and evolutionary branching.
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