Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 2851 - 2866, Volume 21, Issue 8, October 2016      doi:10.3934/dcdsb.2016076

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Junyuan Yang - Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China (email)
Yuming Chen - Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada (email)
Jiming Liu - Department of Computer Science, Hongkong Baptist University, Kowloon Tong, Hongkong, China (email)

Abstract: 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.

Keywords:  Drug-sensitive strain, drug-resistant strain, complex network, stability.
Mathematics Subject Classification:  92D30, 92D25, 90B10.

Received: September 2015;      Revised: March 2016;      Available Online: September 2016.