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The effect of stochastic perturbation on a nonlinear delay malaria epidemic model

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  • Krstić, Marija

Abstract

The subject of this paper is the stochastic epidemic malaria model with time delay, described by the system of the It oˆ stochastic functional delay equations. We center such a system around the endemic equilibrium state and, by the Lyapunov functional method, we obtain sufficient conditions for model parameters, as well as for time delays within which we can claim the asymptotical mean square stability and stability in probability. Finally, we present an example to show the compatibility of our mathematical results with the stochastic delay malaria model with quantities which are reliable data, as well as an example which shows that introduction of environmental noise annuls Hopf Bifurcation of the corresponding deterministic model.

Suggested Citation

  • Krstić, Marija, 2011. "The effect of stochastic perturbation on a nonlinear delay malaria epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 558-569.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:4:p:558-569
    DOI: 10.1016/j.matcom.2011.09.003
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    1. Beretta, Edoardo & Kolmanovskii, Vladimir & Shaikhet, Leonid, 1998. "Stability of epidemic model with time delays influenced by stochastic perturbations1This paper was written during a visit of V. Kolmanovskii and L. Shaikhet in Italy (Napoli, Urbino).1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(3), pages 269-277.
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    Cited by:

    1. Teng, Zhidong & Wang, Lei, 2016. "Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 507-518.

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