an sirs epidemic model with vital dynamics and a ratio-dependent saturation incidence rate
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ID: 233873
2015
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Abstract
This paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemic equilibrium are first studied. Under the assumption of nonexistence of periodic solution, the global dynamics of the model is established: either the number of infective individuals tends to zero as time evolves or it produces bistability in which there is a region such that the disease will persist if the initial position lies in the region and disappears if the initial position lies outside this region. Computer simulation shows such results.
| Reference Key |
wang2015discretean
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|---|---|
| Authors | ;Xinli Wang |
| Journal | Journal of the American Heart Association |
| Year | 2015 |
| DOI |
10.1155/2015/720682
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