{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:30:15Z","timestamp":1762432215495},"reference-count":23,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2022]]},"abstract":"<p style='text-indent:20px;'>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 <inline-formula><tex-math id=\"M1\">\\begin{document}$ S $\\end{document}<\/tex-math><\/inline-formula> and removed <inline-formula><tex-math id=\"M2\">\\begin{document}$ R $\\end{document}<\/tex-math><\/inline-formula> populations by ODEs and the infected <inline-formula><tex-math id=\"M3\">\\begin{document}$ I $\\end{document}<\/tex-math><\/inline-formula> population by a MDE comprised of a probability vector field (PVF) and a source term. In addition, the ODEs for <inline-formula><tex-math id=\"M4\">\\begin{document}$ S $\\end{document}<\/tex-math><\/inline-formula> and <inline-formula><tex-math id=\"M5\">\\begin{document}$ R $\\end{document}<\/tex-math><\/inline-formula> contains terms that are related to the measure <inline-formula><tex-math id=\"M6\">\\begin{document}$ I $\\end{document}<\/tex-math><\/inline-formula>. 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.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2022015","type":"journal-article","created":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T09:56:07Z","timestamp":1648806967000},"page":"427","source":"Crossref","is-referenced-by-count":4,"title":["A measure model for the spread of viral infections with mutations"],"prefix":"10.3934","volume":"17","author":[{"given":"Xiaoqian","family":"Gong","sequence":"first","affiliation":[{"name":"School of Mathematical and Statistical Science, Arizona State University, Tempe, AZ, 85281, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benedetto","family":"Piccoli","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University, Camden, NJ, 08102, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2022015-1","unstructured":"S. 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