Global Stability of a Vector-Borne Epidemic Model With Distributed Delay and Nonlinear Incidence

YANG Ya-li; LI Jian-quan; LIU Wan-meng; TANG San-yi

doi:10.3879/j.issn.1000-0887.2013.12.008

Volume 34 Issue 12

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YANG Ya-li, LI Jian-quan, LIU Wan-meng, TANG San-yi. Global Stability of a Vector-Borne Epidemic Model With Distributed Delay and Nonlinear Incidence[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1291-1299. doi: 10.3879/j.issn.1000-0887.2013.12.008

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Global Stability of a Vector-Borne Epidemic Model With Distributed Delay and Nonlinear Incidence

doi: 10.3879/j.issn.1000-0887.2013.12.008

¹College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P.R.China;²Science College, Air Force Engineering University, Xi’an 710051, P.R.China

Funds: The National Natural Science Foundation of China(11071256；11171267;11301320;11371369)；China Postdoctoral Science Foundation(2013M532016)

Received Date: 2013-08-14
Rev Recd Date: 2013-12-04
Publish Date: 2013-12-16

Abstract

Abstract

An SIR vector-borne epidemic model with distributed delay and nonlinear incidence was established, the basic reproduction number determining the uniform persistence of the disease was found. When the basic reproduction number was not greater than 1, the disease died out finally; when the basic reproduction number was greater than 1, the model had a unique endemic equilibrium, and the disease uniformly persisted in the population. By constructing Lyapunov functional, it was proved that, under certain conditions, the endemic equilibrium was globally stable in the feasible region only when it existed. In addition, the non-uniqueness of the suitable Lyapunov functionals was shown for proving the global stability of the endemic equilibrium.
- vector-borne epidemic model,
- the basic reproduction number,
- uniform persistence,
- equilibrium,
- global stability

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References(14)

References

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