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A class of stochastic vector-borne infectious disease models is derived andstudied. The class type is determined by a general nonlinear incidence rate ofthe disease. The disease spreads in a highly random environment withvariability from the disease transmission and natural death rates. Othersources of variability include the random delays of disease incubation insidethe vector and the human being, and also the random delay due to the period ofeffective acquired immunity against the disease. The basic reproduction numberand other threshold conditions for disease eradication are computed. Thequalitative behaviors of the disease dynamics are examined under the differentsources of variability in the system. A technique to classify the differentlevels of the intensities of the noises in the system is presented, and used toinvestigate the qualitative behaviors of the disease dynamics in theinfection-free steady state population under the different intensity levels ofthe white noises in the system. Moreover, the possibility of populationextinction, whenever the intensities of the white noises in the system are highis examined. Numerical simulation results are presented to elucidate thetheoretical results.

Analyzing the qualitative properties of white noise on a family of infectious disease models in a highly random environment