Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay
Articles
Hong Zhang
Jiangsu University, China
Juan Xia
Jiangsu University, China
Paul Georgescu
Technical University of Ia¸si, Romania
Published 2017-01-20
https://doi.org/10.15388/NA.2017.1.5
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Keywords

compartmental model
delay differential system
nonlinear incidence
disease relapse
global stability of equilibria
Lyapunov functional

How to Cite

Zhang, H., Xia, J. and Georgescu, P. (2017) “Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay”, Nonlinear Analysis: Modelling and Control, 22(1), pp. 64–83. doi:10.15388/NA.2017.1.5.

Abstract

In this paper, deterministic and stochastic SEIRI epidemic models featuring a distributed latent period and general, unspecified nonlinear incidence and growth rates for the susceptible class are proposed and investigated from a stability viewpoint. By applying Lyapunov–LaSalle invariance principle, we first obtain sufficient conditions for the global stability of equilibria of the deterministic model. On the basis of this result, we subsequently derive sufficient conditions for asymptotic stability of the stochastic model. Finally, numerical simulations are given to illustrate the previously obtained theoretical framework.

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