{"title":"Input to state stability of the Kermack-Mckendrick age structured epidemic model*","authors":"Jorge San Martín, Takéo Takahashi, M. Tucsnak","doi":"10.1109/CDC45484.2021.9683436","DOIUrl":null,"url":null,"abstract":"We are interested in a system nonlinearly coupling a transport equation and an ODE. This system, inspired by the classical Kermack-Mckendrick epidemic model with age of infection, describes the evolution of an epidemic in the presence of vaccination and of a flux of susceptible population. Our main result provides effective input to state stability (ISS) estimates, assuming the application of an appropriate vaccination policy. The nonlinear character of the system and the presence of state constraints require a detailed preliminary analysis of the system well-posedness.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 60th IEEE Conference on Decision and Control (CDC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC45484.2021.9683436","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We are interested in a system nonlinearly coupling a transport equation and an ODE. This system, inspired by the classical Kermack-Mckendrick epidemic model with age of infection, describes the evolution of an epidemic in the presence of vaccination and of a flux of susceptible population. Our main result provides effective input to state stability (ISS) estimates, assuming the application of an appropriate vaccination policy. The nonlinear character of the system and the presence of state constraints require a detailed preliminary analysis of the system well-posedness.
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