@article{Gong2022, 
author = {Xiaoqian Gong and Benedetto Piccoli},
title = {A measure model for the spread of viral infections with mutations},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {3},
pages = {427-442},
keywords = {measure differential equation, generalized Wasserstein distance, SIR model, viral infections, mutations},
url = {https://www.sciopen.com/article/10.3934/nhm.2022015},
doi = {10.3934/nhm.2022015},
abstract = {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.}
}