Stochastically perturbed vector-borne disease models with direct transmission

The subject of this paper is the stochastic epidemic malaria model with time delay, described by the system of the It ô 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. © 2011 Published by Elsevier B.V. on behalf of IMACS.