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Gong, Xiaoqian ; Piccoli, Benedetto ( , Networks and Heterogeneous Media)
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
and removed\begin{document}$ S $\end{document} populations by ODEs and the infected\begin{document}$ R $\end{document} population by a MDE comprised of a probability vector field (PVF) and a source term. In addition, the ODEs for\begin{document}$ I $\end{document} and\begin{document}$ S $\end{document} contains terms that are related to the measure\begin{document}$ R $\end{document} . We establish analytically the well-posedness of the coupled ODE-MDE system by using generalized Wasserstein distance. We give two examples to show that the proposed ODE-MDE model coincides with the classical SIR model in case of constant or time-dependent parameters as special cases.\begin{document}$ I $\end{document} -
Kardous, Nicolas ; Hayat, Amaury ; McQuade, Sean T. ; Gong, Xiaoqian ; Truong, Sydney ; Mezair, Tinhinane ; Arnold, Paige ; Delorenzo, Ryan ; Bayen, Alexandre ; Piccoli, Benedetto ( , The European Physical Journal Special Topics)
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Lee, Jonathan W. ; Gunter, George ; Ramadan, Rabie ; Almatrudi, Sulaiman ; Arnold, Paige ; Aquino, John ; Barbour, William ; Bhadani, Rahul ; Carpio, Joy ; Chou, Fang-Chieh ; et al ( , The Workshop on Data-Driven and Intelligent Cyber-Physical Systems)