M. Kamrujjaman, Md. Saiful Islam, Md. Shahidul Islam
{"title":"一类非线性时空流行病模型的Lyapunov映射与分析","authors":"M. Kamrujjaman, Md. Saiful Islam, Md. Shahidul Islam","doi":"10.3329/dujs.v69i3.60026","DOIUrl":null,"url":null,"abstract":"This paper focuses on the global asymptotic properties of the SIR diffusive model for infectious diseases. Using the analytic technique with Lyapunov functions, we developed conditions for the global attractor of a unique disease steady-state and the disease free equilibrium. The most eminent refuge to the model is the direct Lyapunov mapping. We investigate the global well-posedness of the mathematical model, determine conditions on Ro for which non-trivial equilibrium states exist, and examine their global stability. We are interested in finding the model’s basic reproductive number, which determines whether the disease dies out or persists in the population. Finally, we consider a series of computational results to verify the theoretical results. The extensive numerical simulations show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail. The findings allude that the dynamics of the system are entirely estimated by the deterministic value Ro.\nDhaka Univ. J. Sci. 69(3): 161-170, 2022 (June)","PeriodicalId":11280,"journal":{"name":"Dhaka University Journal of Science","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lyapunov Mappings and Analysis of a Nonlinear Spatio-temporal Epidemic Model\",\"authors\":\"M. Kamrujjaman, Md. Saiful Islam, Md. Shahidul Islam\",\"doi\":\"10.3329/dujs.v69i3.60026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper focuses on the global asymptotic properties of the SIR diffusive model for infectious diseases. Using the analytic technique with Lyapunov functions, we developed conditions for the global attractor of a unique disease steady-state and the disease free equilibrium. The most eminent refuge to the model is the direct Lyapunov mapping. We investigate the global well-posedness of the mathematical model, determine conditions on Ro for which non-trivial equilibrium states exist, and examine their global stability. We are interested in finding the model’s basic reproductive number, which determines whether the disease dies out or persists in the population. Finally, we consider a series of computational results to verify the theoretical results. The extensive numerical simulations show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail. The findings allude that the dynamics of the system are entirely estimated by the deterministic value Ro.\\nDhaka Univ. J. Sci. 69(3): 161-170, 2022 (June)\",\"PeriodicalId\":11280,\"journal\":{\"name\":\"Dhaka University Journal of Science\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dhaka University Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/dujs.v69i3.60026\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dhaka University Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/dujs.v69i3.60026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lyapunov Mappings and Analysis of a Nonlinear Spatio-temporal Epidemic Model
This paper focuses on the global asymptotic properties of the SIR diffusive model for infectious diseases. Using the analytic technique with Lyapunov functions, we developed conditions for the global attractor of a unique disease steady-state and the disease free equilibrium. The most eminent refuge to the model is the direct Lyapunov mapping. We investigate the global well-posedness of the mathematical model, determine conditions on Ro for which non-trivial equilibrium states exist, and examine their global stability. We are interested in finding the model’s basic reproductive number, which determines whether the disease dies out or persists in the population. Finally, we consider a series of computational results to verify the theoretical results. The extensive numerical simulations show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail. The findings allude that the dynamics of the system are entirely estimated by the deterministic value Ro.
Dhaka Univ. J. Sci. 69(3): 161-170, 2022 (June)