Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function
The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/910421 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552638234755072 |
|---|---|
| author | Jinhong Zhang Jianwen Jia Xinyu Song |
| author_facet | Jinhong Zhang Jianwen Jia Xinyu Song |
| author_sort | Jinhong Zhang |
| collection | DOAJ |
| description | The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings. |
| format | Article |
| id | doaj-art-4e0c4b32ea954985a368fb04ce0d6087 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4e0c4b32ea954985a368fb04ce0d60872025-02-03T05:58:15ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/910421910421Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment FunctionJinhong Zhang0Jianwen Jia1Xinyu Song2School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, ChinaSchool of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, ChinaDepartment of Mathematics, Xinyang Normal University, Xinyang, Henan 464000, ChinaThe dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.http://dx.doi.org/10.1155/2014/910421 |
| spellingShingle | Jinhong Zhang Jianwen Jia Xinyu Song Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function The Scientific World Journal |
| title | Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function |
| title_full | Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function |
| title_fullStr | Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function |
| title_full_unstemmed | Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function |
| title_short | Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function |
| title_sort | analysis of an seir epidemic model with saturated incidence and saturated treatment function |
| url | http://dx.doi.org/10.1155/2014/910421 |
| work_keys_str_mv | AT jinhongzhang analysisofanseirepidemicmodelwithsaturatedincidenceandsaturatedtreatmentfunction AT jianwenjia analysisofanseirepidemicmodelwithsaturatedincidenceandsaturatedtreatmentfunction AT xinyusong analysisofanseirepidemicmodelwithsaturatedincidenceandsaturatedtreatmentfunction |