The COVID-19 pandemic lit a fire under researchers who have subsequently raced to build models which capture various physical aspects of both the biology of the virus and its mobility throughout the human population. These models could include characteristics such as different genders, ages, frequency of interactions, mutation of virus, etc. Here, we propose two mathematical formulations to include virus mutation dynamics. The first uses a compartmental epidemiological model coupled with a discrete-time finite-state Markov chain. If one includes a nonlinear dependence of the transition matrix on current infected, the model is able to reproduce pandemic waves due to different variants. The second approach expands such an idea to a continuous state-space leveraging a combination of ordinary differential equations with an evolution equation for measure. This approach allows to include reinfections with partial immunity with respect to variants genetically similar to that of first infection.

COVID-19 大流行在研究人员的领导下点燃了一把火，他们随后竞相建立模型，捕捉病毒生物学及其在整个人群中的流动性的各个物理方面。这些模型可能包括不同性别、年龄、相互作用频率、病毒突变等特征。在这里，我们提出了两个数学公式来包括病毒突变动力学。第一个使用与离散时间有限状态马尔可夫链相结合的区室流行病学模型。如果一个包含转换矩阵对当前感染者的非线性依赖性，则该模型能够再现由于不同变体而导致的大流行波。第二种方法将这种想法扩展到连续状态空间，利用常微分方程与进化方程的组合进行测量。这种方法允许包括对与第一次感染基因相似的变异体具有部分免疫的再感染。