Analysis of control measures inducing the evolution of infectious viral diseases

With the continuation of the infectious disease, pathogens mutate and interact with the resident pathogen. In this paper, we develop an SIR model that considers the evolution of viral virulence under the regulation of different defense strengths. By using infectious disease dynamics and evolutionary adaptive dynamics, we obtain the evolutionary criteria allowing for evolutionary branching and continuously stable strategy across varying intensities of prevention and control measures. Our study finds that robust prevention and control measures can contribute to a rapid evolutionary trend toward higher virulence. We perform a critical function analysis to reveal the evolutionary consequences of trade-offs of arbitrary shape and analyze a diverse range of evolutionary dynamics. Furthermore, we investigate the coexistence of two different strains and construct an evolutionary model to obtain their invasion fitness functions and the evolutionarily singular coalition of the dimorphism. We contemplate the presence of secondary branching on a significantly extended evolutionary time scale. Last, we conduct the numerical simulations to prove our theoretical findings. This reveals the law that the evolutionary state of pathogens is affected by the intensity of prevention and control strategies. The results and methods can be used as references for studying the effects of other factors on virus evolution.