{"title":"提高认识方案对霍乱传播动态影响的理论评估","authors":"Daudel Tchatat, G. Kolaye, S. Bowong, A. Temgoua","doi":"10.1515/ijnsns-2021-0341","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we propose and analyse a mathematical model of the transmission dynamics of cholera incorporating awareness programs to study the impact of socio-media and education on cholera outbreaks. These programs induce behavioural changes in the population, which divide the susceptible class into two subclasses, aware individuals and unaware individuals. We first provide a basic study of the model. We compute the Disease-Free Equilibrium (DFE) and derive the basic reproduction number R 0 0 ${\\mathcal{R}}_{0}^{0}$ that determines the extinction and the persistence of the disease. We show that there exists a threshold parameter ξ such that when R 0 0 ≤ ξ < 1 ${\\mathcal{R}}_{0}^{0}\\le \\xi < 1$ , the DFE is globally asymptotically stable, but when ξ ≤ R 0 0 < 1 $\\xi \\le {\\mathcal{R}}_{0}^{0}< 1$ , the model exhibits the phenomenon of backward bifurcation on a feasible region. The model exhibits one endemic equilibrium locally stable when R 0 0 > 1 ${\\mathcal{R}}_{0}^{0} > 1$ and in that condition the DFE is unstable. Various cases for awareness proportions are performed using the critical awareness rate in order to measure the effect of awareness programs on the infected individuals over time. The results we obtained show that the higher implementation of strategies combining awareness programs and therapeutic treatments increase the efficacy of control measures. The numerical simulations of the model are used to illustrate analytical results and give more precision on critical values on the controls actions.","PeriodicalId":50304,"journal":{"name":"International Journal of Nonlinear Sciences and Numerical Simulation","volume":" ","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Theoretical assessment of the impact of awareness programs on cholera transmission dynamic\",\"authors\":\"Daudel Tchatat, G. Kolaye, S. Bowong, A. Temgoua\",\"doi\":\"10.1515/ijnsns-2021-0341\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, we propose and analyse a mathematical model of the transmission dynamics of cholera incorporating awareness programs to study the impact of socio-media and education on cholera outbreaks. These programs induce behavioural changes in the population, which divide the susceptible class into two subclasses, aware individuals and unaware individuals. We first provide a basic study of the model. We compute the Disease-Free Equilibrium (DFE) and derive the basic reproduction number R 0 0 ${\\\\mathcal{R}}_{0}^{0}$ that determines the extinction and the persistence of the disease. We show that there exists a threshold parameter ξ such that when R 0 0 ≤ ξ < 1 ${\\\\mathcal{R}}_{0}^{0}\\\\le \\\\xi < 1$ , the DFE is globally asymptotically stable, but when ξ ≤ R 0 0 < 1 $\\\\xi \\\\le {\\\\mathcal{R}}_{0}^{0}< 1$ , the model exhibits the phenomenon of backward bifurcation on a feasible region. The model exhibits one endemic equilibrium locally stable when R 0 0 > 1 ${\\\\mathcal{R}}_{0}^{0} > 1$ and in that condition the DFE is unstable. Various cases for awareness proportions are performed using the critical awareness rate in order to measure the effect of awareness programs on the infected individuals over time. The results we obtained show that the higher implementation of strategies combining awareness programs and therapeutic treatments increase the efficacy of control measures. The numerical simulations of the model are used to illustrate analytical results and give more precision on critical values on the controls actions.\",\"PeriodicalId\":50304,\"journal\":{\"name\":\"International Journal of Nonlinear Sciences and Numerical Simulation\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Nonlinear Sciences and Numerical Simulation\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1515/ijnsns-2021-0341\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Nonlinear Sciences and Numerical Simulation","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1515/ijnsns-2021-0341","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
Abstract In this paper, we propose and analyse a mathematical model of the transmission dynamics of cholera incorporating awareness programs to study the impact of socio-media and education on cholera outbreaks. These programs induce behavioural changes in the population, which divide the susceptible class into two subclasses, aware individuals and unaware individuals. We first provide a basic study of the model. We compute the Disease-Free Equilibrium (DFE) and derive the basic reproduction number R 0 0 ${\mathcal{R}}_{0}^{0}$ that determines the extinction and the persistence of the disease. We show that there exists a threshold parameter ξ such that when R 0 0 ≤ ξ < 1 ${\mathcal{R}}_{0}^{0}\le \xi < 1$ , the DFE is globally asymptotically stable, but when ξ ≤ R 0 0 < 1 $\xi \le {\mathcal{R}}_{0}^{0}< 1$ , the model exhibits the phenomenon of backward bifurcation on a feasible region. The model exhibits one endemic equilibrium locally stable when R 0 0 > 1 ${\mathcal{R}}_{0}^{0} > 1$ and in that condition the DFE is unstable. Various cases for awareness proportions are performed using the critical awareness rate in order to measure the effect of awareness programs on the infected individuals over time. The results we obtained show that the higher implementation of strategies combining awareness programs and therapeutic treatments increase the efficacy of control measures. The numerical simulations of the model are used to illustrate analytical results and give more precision on critical values on the controls actions.
期刊介绍:
The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at Researchers in Nonlinear Sciences, Engineers, and Computational Scientists, Economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.