Virulence evolution of within a multi-host system.

Current research on the virulence evolution of is mainly conducted via experiments, and studies using mathematical models are still limited. Here, we constructed a complex cycle model of in a multi-host system considering multiple transmission routes and cat-mouse interaction. Based on this model, we studied how the virulence of evolves with the factors related to transmission routes and the regulation of infection on host behavior under an adaptive dynamics framework. The study shows that all factors that enhance the role of mice favored decreased virulence of , except the decay rate of oocysts that led to different evolutionary trajectories under different vertical transmission. The same was true of the environmental infection rate of cats, whose effect was different under different vertical transmission. The effect of the regulation factor on the virulence evolution of was the same as that of the inherent predation rate depending on its net effect on direct and vertical transmissions. The global sensitivity analysis on the evolutionary outcome suggests that changing the vertical infection rate and decay rate was most effective in regulating the virulence of . Furthermore, the presence of coinfection would favor virulent and make evolutionary bifurcation easy to occur. The results reveal that the virulence evolution of had a compromise between adapting to different transmission routes and maintaining the cat-mouse interaction thereby leading to different evolutionary scenarios. This highlights the significance of evolutionary ecological feedback to evolution. In addition, the qualitative verification of virulence evolution in different areas by the present framework will provide a new perspective for the study of evolution.