Coevolutionary dynamics of host-pathogen interaction with density-dependent mortality

This study explores the coevolutionary dynamics of host-pathogen interaction based on a susceptible-infected population model with density-dependent mortality. We assume that both the host's resistance and the pathogen's virulence will adaptively evolve, but there are inevitable costs in terms of host birth rate and disease-related mortality rate. Particularly, it is assumed that both the host resistance and pathogen virulence can affect the transmission rate. By using the approach of adaptive dynamics and numerical simulation, we find that the finally coevolutionary outcome depends on the strength of host-pathogen asymmetric interaction, the curvature of trade-off functions, and the intensity of density-dependent natural mortality. To be specific, firstly, we find that if the strengths of host-pathogen asymmetric interaction and disease-related mortality are relatively weak, or the density-dependent natural mortality is relatively strong, then the host resistance and pathogen virulence will evolve to a continuously stable strategy. However, if the strength of host-pathogen asymmetric interaction and disease-related mortality becomes stronger, then the host resistance and pathogen virulence will evolve periodically. Secondly, we find that if the intensities of both the birth rate trade-off function and the density-dependent natural mortality are relatively weak, but the strength of host-pathogen asymmetric interaction becomes relatively strong, then the evolution of host resistance will have a relatively strongly accelerating benefit, the evolutionary branching of host resistance will first arise. However, if the strength of host-pathogen asymmetric interaction is relatively weak, but the intensity of the trade-off function of disease-related mortality becomes relatively strong, then the evolution of pathogen virulence will have a relatively strongly decelerating cost, and the evolutionary branching of pathogen virulence will first arise. Thirdly, after the evolutionary branching of host resistance and pathogen virulence, we further study the coevolutionary dynamics of two-hosts-one-pathogen interaction and one-host-two-pathogens interaction. We find that if the evolutionary branching of host resistance arises firstly, then the finally evolutionary outcome contains a dimorphic host and a monomorphic pathogen population. If the evolutionary branching of pathogen virulence arises firstly, then the finally evolutionary outcome may contain a monomorphic host and a dimorphic pathogen population.