{"title":"一类具有非线性发病率的延迟分数阶SIRS流行病模型的稳定性分析","authors":"M. Naim, F. Lahmidi, A. Namir","doi":"10.12732/ijam.v32i5.1","DOIUrl":null,"url":null,"abstract":"In this paper, we study the stability of a fractional order SIRS epidemic model with nonlinear incidence rate and time delay, where the fractional derivative is defined in the Caputo sense. The delay is introduced into the model in order to modeled the incubation period. Using the stability analysis of delayed fractional order systems, we prove that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number R0 < 1. Also, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. AMS Subject Classification: 34A08, 37C75, 92D30","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"121 1","pages":"733"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"STABILITY ANALYSIS OF A DELAYED FRACTIONAL ORDER SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE\",\"authors\":\"M. Naim, F. Lahmidi, A. Namir\",\"doi\":\"10.12732/ijam.v32i5.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the stability of a fractional order SIRS epidemic model with nonlinear incidence rate and time delay, where the fractional derivative is defined in the Caputo sense. The delay is introduced into the model in order to modeled the incubation period. Using the stability analysis of delayed fractional order systems, we prove that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number R0 < 1. Also, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. AMS Subject Classification: 34A08, 37C75, 92D30\",\"PeriodicalId\":14365,\"journal\":{\"name\":\"International journal of pure and applied mathematics\",\"volume\":\"121 1\",\"pages\":\"733\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of pure and applied mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/ijam.v32i5.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of pure and applied mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/ijam.v32i5.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
STABILITY ANALYSIS OF A DELAYED FRACTIONAL ORDER SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE
In this paper, we study the stability of a fractional order SIRS epidemic model with nonlinear incidence rate and time delay, where the fractional derivative is defined in the Caputo sense. The delay is introduced into the model in order to modeled the incubation period. Using the stability analysis of delayed fractional order systems, we prove that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number R0 < 1. Also, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. AMS Subject Classification: 34A08, 37C75, 92D30
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