Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel
{"title":"治疗下具有细胞间传播和吸收效应的广义病毒感染时间模型的全局分析","authors":"Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel","doi":"10.5206/mase/14663","DOIUrl":null,"url":null,"abstract":"In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Global Analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy\",\"authors\":\"Alexis Nangue, Paulin Tiomo Lemofouet, Simon Ndouvatama, Kengne Emmanuel\",\"doi\":\"10.5206/mase/14663\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.\",\"PeriodicalId\":93797,\"journal\":{\"name\":\"Mathematics in applied sciences and engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in applied sciences and engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mase/14663\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/14663","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Global Analysis of a generalized viral infection temporal model with cell-to-cell transmission and absorption effect under therapy
In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in vivo models neglect this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitted. In this work, we propose a new virus dynamics model, which incorporates both modes and takes into account the absorption effect and treatment. First we show mathematically and biologically the well-posedness of our model preceded by the result on the existence and the uniqueness of the solutions. Also, an explicit formula for the basic reproduction number R0 of the model is determined. By analyzing the characteristic equations we establish the local stability of the uninfected equilibrium and the infected equilibrium in terms of R0. The global behavior of the model is investigated by constructing an appropriate Lyapunov functional for uninfected equilibrium and by applying a geometric approach to the study of the infected equilibrium. Numerical simulations are carried out, to confirm the obtained theoretical result in a particular case.