A coupled evolutionary model of the viral virulence in an SIS community

The heterogeneity of viral virulence induced by virus evolution plays an essential role in shaping disease transmission dynamics. In this study, we propose a coupled model linking the evolutionary dynamics of viral virulence to transmission dynamics in order to investigate the influence of evolutionary dynamics on transmission dynamics. This modeling approach does realize a bidirectional couple, that is, the nested coupling from evolutionary dynamics to transmission dynamics via virulence-dependent transmission and disease-related mortality, and vice versa for the trait evolution model. We investigate the threshold dynamics and examine the global stability of the coupled system by formulating appropriate Lyapunov functions and employing the geometric approach. Further we rigorously prove that the mutant virus can invade and cause virulence substitution on extremely slow adaptive evolutionary speed, and the globally asymptotically stable virulence is the continuously stable strategy, which represents the final endpoint of the evolutionary process and maximizes the basic reproduction number of a rare mutant. We demonstrate that the speed of evolutionary adaptation will not qualitatively affect the asymptotical property of the coupled system but the peak levels of disease and virulence. Furthermore, considering viral evolution may cause disease persistence more likely, indicating that ignoring viral evolution may lead to an underestimation of disease infection.