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

Junyuan Yang; Yuming Chen; Jiming LIU

doi:10.3934/dcdsb.2016076

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

Junyuan Yang^*, Yuming Chen, Jiming LIU

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 Rs and Rr are obtained. If R0 = maxfRs;Rrg < 1, then the disease-free equilibrium is globally asymptot-ically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion repro-duction number Rs r < 1. If Rs > 1 and Rs > Rr, then there is a unique coexistence equilibrium E. The persistence of the model is also proved. The theoretical results are supported with numerical simulations.

Original language	English
Pages (from-to)	2851-2866
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	21
Issue number	8
DOIs	https://doi.org/10.3934/dcdsb.2016076
Publication status	Published - Oct 2016

Scopus Subject Areas

Discrete Mathematics and Combinatorics
Applied Mathematics

User-Defined Keywords

Complex network
Drug-resistant strain
Drug-sensitive strain
Stability

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10.3934/dcdsb.2016076

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title = "Stability analysis of a two-strain epidemic model on complex networks with latency",

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 Rs and Rr are obtained. If R0 = maxfRs;Rrg < 1, then the disease-free equilibrium is globally asymptot-ically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion repro-duction number Rs r < 1. If Rs > 1 and Rs > Rr, 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 = "Complex network, Drug-resistant strain, Drug-sensitive strain, Stability",

author = "Junyuan Yang and Yuming Chen and Jiming LIU",

note = "Funding Information: NSF grant (61573016, 61203228, 11071283)",

year = "2016",

month = oct,

doi = "10.3934/dcdsb.2016076",

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journal = "Discrete and Continuous Dynamical Systems - Series B",

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publisher = "Southwest Missouri State University",

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TY - JOUR

T1 - Stability analysis of a two-strain epidemic model on complex networks with latency

AU - Yang, Junyuan

AU - Chen, Yuming

AU - LIU, Jiming

N1 - Funding Information: NSF grant (61573016, 61203228, 11071283)

PY - 2016/10

Y1 - 2016/10

N2 - 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 Rs and Rr are obtained. If R0 = maxfRs;Rrg < 1, then the disease-free equilibrium is globally asymptot-ically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion repro-duction number Rs r < 1. If Rs > 1 and Rs > Rr, then there is a unique coexistence equilibrium E. The persistence of the model is also proved. The theoretical results are supported with numerical simulations.

AB - 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 Rs and Rr are obtained. If R0 = maxfRs;Rrg < 1, then the disease-free equilibrium is globally asymptot-ically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion repro-duction number Rs r < 1. If Rs > 1 and Rs > Rr, then there is a unique coexistence equilibrium E. The persistence of the model is also proved. The theoretical results are supported with numerical simulations.

KW - Complex network

KW - Drug-resistant strain

KW - Drug-sensitive strain

KW - Stability

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DO - 10.3934/dcdsb.2016076

M3 - Article

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VL - 21

SP - 2851

EP - 2866

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 8

ER -

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

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