## Journal of Applied Mathematics

### Stability Results for an Age-Structured SIS Epidemic Model with Vector Population

#### Abstract

We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system.

#### Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 838312, 12 pages.

Dates
First available in Project Euclid: 15 April 2015

https://projecteuclid.org/euclid.jam/1429105042

Digital Object Identifier
doi:10.1155/2015/838312

Mathematical Reviews number (MathSciNet)
MR3319190

Zentralblatt MATH identifier
1344.92171

#### Citation

Liu, He-Long; Yu, Jing-Yuan; Zhu, Guang-Tian. Stability Results for an Age-Structured SIS Epidemic Model with Vector Population. J. Appl. Math. 2015 (2015), Article ID 838312, 12 pages. doi:10.1155/2015/838312. https://projecteuclid.org/euclid.jam/1429105042

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