A MEASURE MODEL FOR THE SPREAD OF VIRAL INFECTIONS WITH MUTATIONS

Genetic variations in the COVID-19 virus are one of the main causes of the COVID-19 pandemic outbreak in 2020 and 2021. In this article, we aim to introduce a new type of model, a system coupled with ordinary differential equations (ODEs) and measure differential equation (MDE), stemming from the classical SIR model for the variants distribution. Specifically, we model the evolution of susceptible S and removed R populations by ODEs and the infected I population by a MDE comprised of a probability vector field (PVF) and a source term. In addition, the ODEs for S and R contains terms that are related to the measure I. We establish analytically the well-posedness of the coupled ODE-MDE system by using generalized Wasserstein distance. We give two examples to show that the proposed ODE-MDE model coincides with the classical SIR model in case of constant or time-dependent parameters as special cases.

Automated summary

This article introduces a new type of model, which combines ordinary differential equations (ODEs) and measure differential equations (MDE) to simulate the impact of genetic variations in the COVID-19 virus on the pandemic outbreak. Through mathematical analysis, the well-posedness of the coupled ODE-MDE system is established, and two examples demonstrate the consistency of the proposed model with the classical SIR model.