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 › Journal article › peer-review

6 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 = max{Rs,Rr} < 1, then the disease-free equilibrium is globally asymptotically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion reproduction 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

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

User-Defined Keywords

Complex network
Drug-resistant strain
Drug-sensitive strain
Stability

Access to Document

10.3934/dcdsb.2016076

Cite this

@article{2760f7b625a449108d74ef78e5744694,

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 = max\{Rs,Rr\} < 1, then the disease-free equilibrium is globally asymptotically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion reproduction 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: JY is supported by NSF grant (61573016, 61203228, 11071283), China Scholarship Council (201308140016), Shanxi Scholarship Council of China (2015-094), the Young Sciences Foundation of Shanxi (2011021001-1), Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, “131” Talents of Shanxi University, and YC is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.",

year = "2016",

month = oct,

doi = "10.3934/dcdsb.2016076",

language = "English",

volume = "21",

pages = "2851--2866",

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

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "8",

}

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: JY is supported by NSF grant (61573016, 61203228, 11071283), China Scholarship Council (201308140016), Shanxi Scholarship Council of China (2015-094), the Young Sciences Foundation of Shanxi (2011021001-1), Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, “131” Talents of Shanxi University, and YC is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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 = max{Rs,Rr} < 1, then the disease-free equilibrium is globally asymptotically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion reproduction 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 = max{Rs,Rr} < 1, then the disease-free equilibrium is globally asymptotically stable. If Rr > 1, then there is a unique drug-resistant strain dominated equilibrium Er, which is locally asymptotically stable if the invasion reproduction 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

UR - https://www.scopus.com/pages/publications/84988851280

U2 - 10.3934/dcdsb.2016076

DO - 10.3934/dcdsb.2016076

M3 - Journal article

AN - SCOPUS:84988851280

SN - 1531-3492

VL - 21

SP - 2851

EP - 2866

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 8

ER -

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

Abstract

UN SDGs

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this