Stability Analysis of SIR Model with Distributed Delay on Complex Networks

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 [Formula: see tex...

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Bibliographic Details
Published in:PloS one 2016-08, Vol.11 (8), p.e0158813-e0158813
Main Authors: Huang, Chuangxia, Cao, Jie, Wen, Fenghua, Yang, Xiaoguang
Format: Article
Language:English
Subjects:
Applied mathematics
Asymptotic properties
Biology and Life Sciences
Birth rate
Communicable Diseases - epidemiology
Complex systems
Computer and Information Sciences
Computer simulation
Convergence
Delay
Demographics
Demography
Disease transmission
Distribution
Epidemics
Epidemiology
Equilibrium
Heterogeneity
Humans
Infections
Infectious diseases
Interdisciplinary aspects
Mathematical models
Medicine and Health Sciences
Models, Theoretical
Neural networks
Numerical simulations
Ordinary differential equations
People and Places
Physical Sciences
Population
Research and analysis methods
Social networks
Stability analysis
Statistical mechanics
Statistics
Systems science
Time lag
Topology
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Summary: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 [Formula: see text] 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 [Formula: see text], 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 [Formula: see text], then the system with distributed time delay stabilizes fastest; while [Formula: see text], the system with distributed time delay converges most slowly. The validness and effectiveness of these results are demonstrated through numerical simulations.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0158813