{"title":"A heterogeneous continuous age-structured model of mumps with vaccine","authors":"","doi":"10.1016/j.idm.2024.09.004","DOIUrl":null,"url":null,"abstract":"<div><p>In classical mumps models, individuals are generally assumed to be uniformly mixed (homogeneous), ignoring population heterogeneity (preference, activity, etc.). Age is the key to catching mixed patterns in developing mathematical models for mumps. A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper. The stability of age-structured models is a difficult question. An explicit formula of <em>R</em><sub>0</sub> was defined for the various mixing modes (isolation, proportional and heterogeneous mixing) with or without the vaccine. The results show that the endemic steady state is unique and locally stable if <em>R</em><sub>0</sub> > 1 without any additional conditions. A number of numerical examples are given to support the theory.</p></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":null,"pages":null},"PeriodicalIF":8.8000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468042724001039/pdfft?md5=cc9d975dffe62e46b221b254e4d36443&pid=1-s2.0-S2468042724001039-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infectious Disease Modelling","FirstCategoryId":"3","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468042724001039","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Medicine","Score":null,"Total":0}
引用次数: 0
Abstract
In classical mumps models, individuals are generally assumed to be uniformly mixed (homogeneous), ignoring population heterogeneity (preference, activity, etc.). Age is the key to catching mixed patterns in developing mathematical models for mumps. A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper. The stability of age-structured models is a difficult question. An explicit formula of R0 was defined for the various mixing modes (isolation, proportional and heterogeneous mixing) with or without the vaccine. The results show that the endemic steady state is unique and locally stable if R0 > 1 without any additional conditions. A number of numerical examples are given to support the theory.
期刊介绍：
Infectious Disease Modelling is an open access journal that undergoes peer-review. Its main objective is to facilitate research that combines mathematical modelling, retrieval and analysis of infection disease data, and public health decision support. The journal actively encourages original research that improves this interface, as well as review articles that highlight innovative methodologies relevant to data collection, informatics, and policy making in the field of public health.
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