Coupling compartmental models with Markov chains and measure evolution equations to capture virus mutability

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.

Automated summary

The COVID-19 pandemic prompted researchers to study pandemic modeling with considerations for various characteristics and virus mutation dynamics. Two mathematical models were proposed to study the effects of virus mutations, with the first model reproducing pandemic waves caused by different variants and the second model including reinfections with genetically similar variants.