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The effect of stochastic perturbation on a nonlinear delay malaria epidemic model. (English) Zbl 1245.60058
Summary: The subject of this paper is the stochastic epidemic malaria model with time delay, described by the system of the Itô 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.
60H10Stochastic ordinary differential equations
92D25Population dynamics (general)
93E15Stochastic stability
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