Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains, preventing a build up of immunity in the host population. In this paper, a parsimonious epidemic model is defined that attempts to capture the dynamics of evolving strains within a host population. The ‘evolving strains’ epidemic model has many properties that lie in-between the Susceptible–Infected–Susceptible and the Susceptible–Infected–Removed epidemic models, due to the fact that individuals can only be infected by each strain once, but remain susceptible to reinfection by newly emerged strains. Coupling results are used to identify key properties, such as the time to extinction. A range of reproduction numbers are explored to characterise the model, including a novel quasi-stationary reproduction number that can be used to describe the re-emergence of the pathogen into a population with ‘average’ levels of strain immunity, analogous to the beginning of the winter peak in influenza. Finally the quasi-stationary distribution of the evolving strains model is explored via simulation.

在大流行之间，流感病毒会通过称为抗原漂移的过程表现出逐渐进化的阶段。该过程产生了一系列病原体菌株，其被新的菌株连续替代，从而防止了宿主群体中免疫力的建立。在本文中，定义了一个简化的流行病模型，该模型试图捕获宿主种群中不断演变的菌株的动态。“进化毒株”流行病模型具有许多特性，介于“易感病原”和“易感病菌去除”流行病模型之间，这是因为每个人只能感染每种毒株一次，但仍然易感。新出现的菌株再感染。耦合结果用于识别关键特性，例如灭绝时间。探索了一系列繁殖数量来表征模型，包括一个新的准平稳繁殖数量，该数量可以用来描述病原体重新进入具有“平均”水平的菌株免疫力的种群，类似于流感的冬季高峰。最后，通过仿真探索了演化应变模型的准平稳分布。