Stability Analysis of SIR Model with Distributed Delay on Complex Networks

Chuangxia Huang, Jie Cao, Fenghua Wen and Xiaoguang Yang

PLOS ONE, 2016, vol. 11, issue 8, 1-22

Abstract: In this paper, by taking full consideration of distributed delay, demographics and contact heterogeneity of the individuals, we present a detailed analytical study of the Susceptible-Infected-Removed (SIR) epidemic model on complex population networks. The basic reproduction number R 0 of the model is dominated by the topology of the underlying network, the properties of individuals which include birth rate, death rate, removed rate and infected rate, and continuously distributed time delay. By constructing suitable Lyapunov functional and employing Kirchhoff’s matrix tree theorem, we investigate the globally asymptotical stability of the disease-free and endemic equilibrium points. Specifically, the system shows threshold behaviors: if R 0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally asymptotically stable. Furthermore, the obtained results show that SIR models with different types of delays have different converge time in the process of contagion: if R 0 > 1, then the system with distributed time delay stabilizes fastest; while R 0 ≤ 1, the system with distributed time delay converges most slowly. The validness and effectiveness of these results are demonstrated through numerical simulations.

Date: 2016
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0158813

DOI: 10.1371/journal.pone.0158813

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