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.
Citation: Xiaoqian Gong, Benedetto Piccoli. A measure model for the spread of viral infections with mutations[J]. Networks and Heterogeneous Media, 2022, 17(3): 427-442. doi: 10.3934/nhm.2022015
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.
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Xiaoqian Gong, Benedetto Piccoli. A measure model for the spread of viral infections with mutations[J]. Networks and Heterogeneous Media, 2022, 17(3): 427-442. doi: 10.3934/nhm.2022015
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