Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate
In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold $R_0$ which completely governs the disease dynamics: when $R_0<1 the=&...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016016 |
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| _version_ | 1832590081761738752 |
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| author | Shouying Huang Jifa Jiang |
| author_facet | Shouying Huang Jifa Jiang |
| author_sort | Shouying Huang |
| collection | DOAJ |
| description | In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold $R_0$ which completely governs the disease dynamics: when $R_0<1 the="" disease-free="" equilibrium="" is="" globally="" asymptotically="" stable="" i="" e="" the="" disease="" will="" die="" out="" when="" r_0="">1$, the disease is permanent. It is interesting that the threshold value $R_0$ bears no relation to the functional form of the nonlinear incidence rate and degree-dependent birth. Furthermore, by applying an iteration scheme and the theory of cooperative system respectively, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. Our results improve and generalize some known results. To illustrate the theoretical results, the corresponding numerical simulations are also given. |
| format | Article |
| id | doaj-art-d99e95f568b840739db5946c39b9a298 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d99e95f568b840739db5946c39b9a2982025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113472373910.3934/mbe.2016016Global stability of a network-based SIS epidemic model with a general nonlinear incidence rateShouying Huang0Jifa Jiang1Mathematics and Science College, Shanghai Normal University, Shanghai, 200234Mathematics and Science College, Shanghai Normal University, Shanghai 200234In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold $R_0$ which completely governs the disease dynamics: when $R_0<1 the="" disease-free="" equilibrium="" is="" globally="" asymptotically="" stable="" i="" e="" the="" disease="" will="" die="" out="" when="" r_0="">1$, the disease is permanent. It is interesting that the threshold value $R_0$ bears no relation to the functional form of the nonlinear incidence rate and degree-dependent birth. Furthermore, by applying an iteration scheme and the theory of cooperative system respectively, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. Our results improve and generalize some known results. To illustrate the theoretical results, the corresponding numerical simulations are also given.https://www.aimspress.com/article/doi/10.3934/mbe.2016016heterogeneous networknonlinear incidenceepidemic spreadingequilibriumglobal stability. |
| spellingShingle | Shouying Huang Jifa Jiang Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate Mathematical Biosciences and Engineering heterogeneous network nonlinear incidence epidemic spreading equilibrium global stability. |
| title | Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate |
| title_full | Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate |
| title_fullStr | Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate |
| title_full_unstemmed | Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate |
| title_short | Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate |
| title_sort | global stability of a network based sis epidemic model with a general nonlinear incidence rate |
| topic | heterogeneous network nonlinear incidence epidemic spreading equilibrium global stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016016 |
| work_keys_str_mv | AT shouyinghuang globalstabilityofanetworkbasedsisepidemicmodelwithageneralnonlinearincidencerate AT jifajiang globalstabilityofanetworkbasedsisepidemicmodelwithageneralnonlinearincidencerate |