Global stability analysis of an SVEIR epidemic model with general incidence rate
Abstract In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function f(S,I)...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-03-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-018-0961-7 |
| _version_ | 1818847754412097536 |
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| author | Da-peng Gao Nan-jing Huang Shin Min Kang Cong Zhang |
| author_facet | Da-peng Gao Nan-jing Huang Shin Min Kang Cong Zhang |
| author_sort | Da-peng Gao |
| collection | DOAJ |
| description | Abstract In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function f(S,I) $f(S,I)$. The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number R0 $\mathcal{R}_{0}$ is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on R0 $\mathcal{R}_{0}$ as well as on the treatment rate. If R0>1 $\mathcal{R}_{0}>1$, then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results. |
| first_indexed | 2024-12-19T06:06:28Z |
| format | Article |
| id | doaj.art-73b7a5f1e48d44b694090e9c74853f1f |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-19T06:06:28Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-73b7a5f1e48d44b694090e9c74853f1f2022-12-21T20:33:06ZengSpringerOpenBoundary Value Problems1687-27702018-03-012018112210.1186/s13661-018-0961-7Global stability analysis of an SVEIR epidemic model with general incidence rateDa-peng Gao0Nan-jing Huang1Shin Min Kang2Cong Zhang3School of Mathematics and Information, China West Normal UniversityDepartment of Mathematics, Sichuan UniversityDepartment of Mathematics and the RINS, Gyeongsang National UniversitySchool of Management, Sichuan University of Science and EngineeringAbstract In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function f(S,I) $f(S,I)$. The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number R0 $\mathcal{R}_{0}$ is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on R0 $\mathcal{R}_{0}$ as well as on the treatment rate. If R0>1 $\mathcal{R}_{0}>1$, then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results.http://link.springer.com/article/10.1186/s13661-018-0961-7Epidemic modelReproduction numberLyapunov functionGeometric approachGlobal stabilitySusceptible–Vaccinated–Exposed–Infectious–Recovered |
| spellingShingle | Da-peng Gao Nan-jing Huang Shin Min Kang Cong Zhang Global stability analysis of an SVEIR epidemic model with general incidence rate Boundary Value Problems Epidemic model Reproduction number Lyapunov function Geometric approach Global stability Susceptible–Vaccinated–Exposed–Infectious–Recovered |
| title | Global stability analysis of an SVEIR epidemic model with general incidence rate |
| title_full | Global stability analysis of an SVEIR epidemic model with general incidence rate |
| title_fullStr | Global stability analysis of an SVEIR epidemic model with general incidence rate |
| title_full_unstemmed | Global stability analysis of an SVEIR epidemic model with general incidence rate |
| title_short | Global stability analysis of an SVEIR epidemic model with general incidence rate |
| title_sort | global stability analysis of an sveir epidemic model with general incidence rate |
| topic | Epidemic model Reproduction number Lyapunov function Geometric approach Global stability Susceptible–Vaccinated–Exposed–Infectious–Recovered |
| url | http://link.springer.com/article/10.1186/s13661-018-0961-7 |
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