Global stability of infectious disease models with contact rate as a function of prevalence index
In this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played...
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| Language: | English |
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AIMS Press
2017-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017053 |
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| author | Cruz Vargas-De-León Alberto d'Onofrio |
| author_facet | Cruz Vargas-De-León Alberto d'Onofrio |
| author_sort | Cruz Vargas-De-León |
| collection | DOAJ |
| description | In this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease-free equilibrium point. Our approach is applicable to global stability of the endemic equilibrium of the previously defined SIR and SIS models with feedback on behavior of susceptible subjects. |
| format | Article |
| id | doaj-art-79bcec568be744dbbd5fa219a961743e |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-79bcec568be744dbbd5fa219a961743e2025-01-24T02:39:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-07-011441019103310.3934/mbe.2017053Global stability of infectious disease models with contact rate as a function of prevalence indexCruz Vargas-De-León0Alberto d'Onofrio1Maestría en Ciencias de la Salud, Escuela Superior de Medicina, Instituto Politécnico Nacional, Plan de San Luis y Díaz Mirón s/n, Col. Casco de Santo Tomas, Del. Miguel Hidalgo, 11340, Ciudad de México, MexicoInternational Prevention Research Institute, 96 Cours Lafayette, 69006 Lyon, FranceIn this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease-free equilibrium point. Our approach is applicable to global stability of the endemic equilibrium of the previously defined SIR and SIS models with feedback on behavior of susceptible subjects.https://www.aimspress.com/article/doi/10.3934/mbe.2017053behavioral epidemiologyinformation variablenegative feedbacklyapunov functionglobal stability |
| spellingShingle | Cruz Vargas-De-León Alberto d'Onofrio Global stability of infectious disease models with contact rate as a function of prevalence index Mathematical Biosciences and Engineering behavioral epidemiology information variable negative feedback lyapunov function global stability |
| title | Global stability of infectious disease models with contact rate as a function of prevalence index |
| title_full | Global stability of infectious disease models with contact rate as a function of prevalence index |
| title_fullStr | Global stability of infectious disease models with contact rate as a function of prevalence index |
| title_full_unstemmed | Global stability of infectious disease models with contact rate as a function of prevalence index |
| title_short | Global stability of infectious disease models with contact rate as a function of prevalence index |
| title_sort | global stability of infectious disease models with contact rate as a function of prevalence index |
| topic | behavioral epidemiology information variable negative feedback lyapunov function global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017053 |
| work_keys_str_mv | AT cruzvargasdeleon globalstabilityofinfectiousdiseasemodelswithcontactrateasafunctionofprevalenceindex AT albertodonofrio globalstabilityofinfectiousdiseasemodelswithcontactrateasafunctionofprevalenceindex |