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Zbl 1245.60058
Krstić, Marija
The effect of stochastic perturbation on a nonlinear delay malaria epidemic model. (English)
[J] Math. Comput. Simul. 82, No. 4, 558-569 (2011). ISSN 0378-4754

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.

MSC 2000:: *60H10 Stochastic ordinary differential equations
92D25 Population dynamics
93E15 Stochastic stability

Keywords: endemic equilibrium; human population; incubation period; mosquito population; stability

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