一类SIS模型病原体毒力进化动力学分析

Evolutionary Dynamics Analysis of Pathogen Virulence in a Class of SIS Model

摘要: 本文利用适应性动力学等理论对病原体的毒力演化进行分析，讨论可能出现的进化效果，能够为疾病的治疗方案设计、防控策略的制订提供一定的理论依据。通过引入经典的传染病SIS模型，应用进化入侵分析方法来讨论病原体能否产生进化分支，结合进化动力学理论研究了进化稳定性与感染者的恢复率、出生率之间的关系. 研究结果表明，如果权衡函数在进化奇异策略处是凹的，则该策略是收敛稳定并且是进化稳定的，即该策略为连续稳定策略，病原体不会产生进化分支。

Abstract: In this paper, adaptive dynamics and other theories are used to analyze the virulence evolution of pathogens and discuss the possible evolutionary effects, which can provide a certain theoretical basis for the design of disease treatment and the formulation of prevention and control strategies. By introducing the classic infectious disease SIS model and applying evolutionary intrusion analysis methods, this paper discusses whether pathogens can generate evolutionary branches, and combines evolutionary dynamics theory to study the relationship between evolutionary stability and the recovery rate and birth rate of infected individuals. The results show that under this model, if the trade-off function is concave at the evolutionary singular strategy, then the strategy is convergence stable and evolutionarily stable, that is, the strategy is continuously stable and the pathogen does not have evolutionary branching.