# American Institute of Mathematical Sciences

October  2016, 21(8): 2851-2866. doi: 10.3934/dcdsb.2016076

## Stability analysis of a two-strain epidemic model on complex networks with latency

 1 Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi 2 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5 3 Department of Computer Science, Hongkong Baptist University, Kowloon Tong, Hongkong, China

Received  September 2015 Revised  March 2016 Published  September 2016

In this paper, a two-strain epidemic model on a complex network is proposed. The two strains are the drug-sensitive strain and the drug-resistant strain. The related basic reproduction numbers $R_s$ and $R_r$ are obtained. If $R_0=\max\{R_s,R_r\}<1$, then the disease-free equilibrium is globally asymptotically stable. If $R_r>1$, then there is a unique drug-resistant strain dominated equilibrium $E_r$, which is locally asymptotically stable if the invasion reproduction number $R_r^s<1$. If $R_s>1$ and $R_s>R_r$, then there is a unique coexistence equilibrium $E^*$. The persistence of the model is also proved. The theoretical results are supported with numerical simulations.
Citation: Junyuan Yang, Yuming Chen, Jiming Liu. Stability analysis of a two-strain epidemic model on complex networks with latency. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2851-2866. doi: 10.3934/dcdsb.2016076
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