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

Junyuan Yang; Yuming  Chen; Jiming  Liu

doi:10.3934/dcdsb.2016076

Article Contents

2016, Volume 21, Issue 8: 2851-2866. Doi: 10.3934/dcdsb.2016076

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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

Received: August 31, 2015

Revised: February 29, 2016

Published: September 2016

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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.

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Mathematics Subject Classification: 92D30, 92D25, 90B10.

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