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Erschienen in:
Short Introduction to Stability Theory of Deterministic Functional Differential Equations Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

11. Stability of SIR Epidemic Model Equilibrium Points

verfasst von : Leonid Shaikhet

Erschienen in: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Verlag: Springer International Publishing

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Abstract

Chapter 11 deals with a mathematical model of the spread of infectious diseases, so called SIR epidemic model. Sufficient conditions for stability in probability of the degenerated equilibrium point \(E_{0}=(b\mu_{1}^{-1},0,0)\) and the positive equilibrium point E ∗=(S ∗,I ∗,R ∗) of SIR epidemic model with distributed delays and stochastic perturbations are obtained. Results of numerical simulations of stability regions and trajectories of stable solutions are shown in 3 figures. Similarly to the previous chapters numerical simulations of the processes S(t), I(t) and R(t) were obtained via the Euler–Maruyama scheme for stochastic differential equations.

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Vorheriges Kapitel Stability of Positive Equilibrium Point of Nonlinear System of Type of Predator–Prey with Aftereffect and Stochastic Perturbations
Nächstes Kapitel Stability of Some Social Mathematical Models with Delay Under Stochastic Perturbations
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Metadaten
Titel
Stability of SIR Epidemic Model Equilibrium Points
verfasst von
Leonid Shaikhet
Copyright-Jahr
2013
Verlag
Springer International Publishing
Buch
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

Print ISBN: 978-3-319-00100-5

Electronic ISBN: 978-3-319-00101-2

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-3-319-00101-2_11

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