GLOBAL ANALYSIS OF AN AGE-STRUCTURED SEIR MODEL WITH IMMIGRATION OF POPULATION AND NONLINEAR INCIDENCE RATE

Ran Zhang; Dan Li; Shengqiang Liu

doi:10.11948/2156-907X.20180281

2019 Volume 9 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2019 > 9(4): 1470-1492

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Ran Zhang, Dan Li, Shengqiang Liu. GLOBAL ANALYSIS OF AN AGE-STRUCTURED SEIR MODEL WITH IMMIGRATION OF POPULATION AND NONLINEAR INCIDENCE RATE[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1470-1492. doi: 10.11948/2156-907X.20180281

Citation:

Ran Zhang, Dan Li, Shengqiang Liu. GLOBAL ANALYSIS OF AN AGE-STRUCTURED SEIR MODEL WITH IMMIGRATION OF POPULATION AND NONLINEAR INCIDENCE RATE[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1470-1492. doi: 10.11948/2156-907X.20180281

GLOBAL ANALYSIS OF AN AGE-STRUCTURED SEIR MODEL WITH IMMIGRATION OF POPULATION AND NONLINEAR INCIDENCE RATE

1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

Corresponding author: Email address: sqliu@hit.edu.cn(S. Liu)
Fund Project: The authors were supported by National Natural Science Foundation of China(Nos.11801209, 11871179 and 11771374), and Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No. 18KJB110004)

Abstract

Abstract

Epidemic models with infection age of infectious individuals have been extensively studied, however, most of the existing works ignore the combined effects of immigration and nonlinear incidence. In this paper, we incorporate both the effects of immigration and nonlinear incidence, based on which we formulate an SEIR epidemic model. We give a rigorous mathematical analysis on some necessary technical materials. Then, by constructing a Lyapunov functional, we show that the endemic equilibrium is globally asymptotically stable. Numerical simulations of an application are given to support our theoretical results.
- Lyapunov functional /
- global stability /
- infection age /
- immigration /
- nonlinear incidence
MSC: 35Q92, 37N25, 92D30

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References

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