An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate
An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I) and G(I), respectively. By constructing Lyapunov...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/131257 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560946304778240 |
|---|---|
| author | Mingming Li Xianning Liu |
| author_facet | Mingming Li Xianning Liu |
| author_sort | Mingming Li |
| collection | DOAJ |
| description | An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I) and G(I), respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0. |
| format | Article |
| id | doaj-art-5fb88472cda04dc984c15f7368ff4e1d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5fb88472cda04dc984c15f7368ff4e1d2025-02-03T01:26:19ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/131257131257An SIR Epidemic Model with Time Delay and General Nonlinear Incidence RateMingming Li0Xianning Liu1Key Laboratory of Eco-Environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaKey Laboratory of Eco-Environments in Three Gorges Reservoir Region (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaAn SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I) and G(I), respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0.http://dx.doi.org/10.1155/2014/131257 |
| spellingShingle | Mingming Li Xianning Liu An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate Abstract and Applied Analysis |
| title | An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate |
| title_full | An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate |
| title_fullStr | An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate |
| title_full_unstemmed | An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate |
| title_short | An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate |
| title_sort | sir epidemic model with time delay and general nonlinear incidence rate |
| url | http://dx.doi.org/10.1155/2014/131257 |
| work_keys_str_mv | AT mingmingli ansirepidemicmodelwithtimedelayandgeneralnonlinearincidencerate AT xianningliu ansirepidemicmodelwithtimedelayandgeneralnonlinearincidencerate AT mingmingli sirepidemicmodelwithtimedelayandgeneralnonlinearincidencerate AT xianningliu sirepidemicmodelwithtimedelayandgeneralnonlinearincidencerate |