Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure
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Authors
Jinliang Wang
- School of Mathematical Science, Heilongjiang University, Harbin 150080, China.
Yoshiaki Muroya
- Department of Mathematics, Waseda University 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169- 8555, Japan.
Toshikazu Kuniya
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
Abstract
In this paper, we formulate and study a multi-group SIS epidemic model with time-delays, nonlinear incidence
rates and patch structure. Two types of delays are incorporated to concern the time-delay of infection
and that for population exchange among different groups. Taking into account both of the effects of crossregion
infection and the population exchange, we define the basic reproduction number \(\mathcal{R}_0\) by the spectral
radius of the next generation matrix and prove that it is a threshold value, which determines the global
stability of each equilibrium of the model. That is, it is shown that if \(\mathcal{R}_0\leq 1\), the disease-free equilibrium
is globally asymptotically stable, while if \(\mathcal{R}_0 > 1\), the system is permanent, an endemic equilibrium exists
and it is globally asymptotically stable. These global stability results are achieved by constructing Lyapunov
functionals and applying LaSalle's invariance principle to a reduced system. Numerical simulation is
performed to support our theoretical results.
Share and Cite
ISRP Style
Jinliang Wang, Yoshiaki Muroya, Toshikazu Kuniya, Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 578--599
AMA Style
Wang Jinliang, Muroya Yoshiaki, Kuniya Toshikazu, Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure. J. Nonlinear Sci. Appl. (2015); 8(5):578--599
Chicago/Turabian Style
Wang, Jinliang, Muroya, Yoshiaki, Kuniya, Toshikazu. "Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 578--599
Keywords
- SIS epidemic model
- time-delay
- nonlinear incidence rate
- patch structure.
MSC
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