Journal ArticleDOI
Global dynamics of a time delayed SIR model with varying population size
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In this article, a disease transmission model of susceptible-infective-recovered type with a constant latent period is analyzed, and the global dynamics of the disease-free equilibrium is investigated.Abstract:
A disease transmission model of susceptible-infective-recovered type with a constant latent period is analysed. The global dynamics of the disease-free equilibrium is investigated. If the basic reproduction number is greater than unity, a unique endemic equilibrium exists. Using Lyapunov functional approach, this endemic equilibrium is globally stable in the feasible region. The disease will persist (and is permanent) at the endemic equilibrium if it is initially present. The effects of loss of immunity on the dynamics of the model are analysed, and the parameters that drive the disease dynamics are obtained. Numerical simulations support our analytical results and illustrate possible behavioural scenarios of the model.read more
Citations
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Book
Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Journal ArticleDOI
The effect of time delay in plant--pathogen interactions with host demography.
Bruno Buonomo,Marianna Cerasuolo +1 more
TL;DR: Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are obtained through qualitative analysis, and it is proved that the onset of oscillations may occur through Hopf bifurcation.
Journal ArticleDOI
SIRS model of passengers' panic propagation under self-organization circumstance in the subway emergency
TL;DR: Wang et al. as discussed by the authors built an improved SIRS model of passengers' panic spread in subway emergency with consideration of passengers density, the characteristic of subway car with the confined space, and passengers' psychological factors.
Permanence of an SIR Epidemic Model with Distributed Time Delays (関数方程式の定性的理論とその現象解析への応用 短期研究報告集)
万彪 馬,康博 竹内,惟行 原,Edoardo Beretta +3 more
Proceedings ArticleDOI
Stability and Hopf bifurcation for an epidemic disease model with time delay
TL;DR: In this paper, the conditions for stability and Hopf bifurcation of a SIR disease model with survival probability and time delay are analyzed, and the conditions of the existence and local stability of disease-free and endemic equilibrium are investigated.
References
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Infectious Diseases of Humans: Dynamics and Control
Roy M. Anderson,Robert M. May +1 more
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Journal ArticleDOI
On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations
TL;DR: It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.
On the definition and the computation of the basic reproduction ratio : $R_ 0$ in models for infectious diseases in heterogeneous populations
TL;DR: In this paper, the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is defined as the dominant eigenvalue of a positive linear operator.
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