
Mathematical Biosciences and Engineering, 2017, 14(4): 901931. doi: 10.3934/mbe.2017048.
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Competitive exclusion in an infectionage structured vectorhost epidemic model
1. Department of Public Education, Zhumadian Vocational and Technical College, Zhumadian 463000, China
2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
3. Department of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China
Received: , Accepted: , Published:
The competitive exclusion principle means that the strain with the largest reproduction number persists while eliminating all other strains with suboptimal reproduction numbers. In this paper, we extend the competitive exclusion principle to a multistrain vectorborne epidemic model with agesinceinfection. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts, both of which describe the different removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The formulas for the reproduction numbers $\mathcal R^j_0$ of strain $j,j=1,2,···, n$, are obtained from the biological meanings of the model. The strain $j$ can not invade the system if $\mathcal R^j_0<1$, and the disease free equilibrium is globally asymptotically stable if $\max_j\{\mathcal R^j_0\}<1 if="" mathcal="" r="" j_0="" _0="">1$, then a singlestrain equilibrium $\mathcal{E}_{j_0}$ exists, and the single strain equilibrium is locally asymptotically stable when $\mathcal R^{j_0}_0>1$ and $\mathcal R^{j_0}_0>\mathcal R^{j}_0,j≠ j_0$. Finally, by using a Lyapunov function, sufficient conditions are further established for the global asymptotical stability of the singlestrain equilibrium corresponding to strain $j_0$, which means strain $j_0$ eliminates all other stains as long as $\mathcal R^{j}_0/\mathcal R^{j_0}_0<b_j/b_{j_0}<1,j≠ j_0$, where $b_j$ denotes the probability of a given susceptible vector being transmitted by an infected host with strain $j$.
Keywords: Agestructure; competitive exclusion; global stability; vectorborne disease; Lyapunov function
Citation: Yanxia Dang, Zhipeng Qiu, Xuezhi Li. Competitive exclusion in an infectionage structured vectorhost epidemic model. Mathematical Biosciences and Engineering, 2017, 14(4): 901931. doi: 10.3934/mbe.2017048
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Copyright Info: 2017, Zhipeng Qiu, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
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