2022/03/28 by Gong, Xiaoqian, Piccoli, Benedetto
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2203.14515
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 an MDE comprised of a probability vector field (PVF) and a source term. In addition, the ODEs for S and R contain 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 the case of constant or time-dependent