Estimating White Noise Intensity Regions for Comparable Properties of a Class of Seirs Stochastic and Deterministic Epidemic Models

A comparative stochastic and deterministic study of a family of epidemic models for vector-borne diseases e.g. malaria and dengue fever etc. is presented. The family type is determined by a general nonlinear incidence rate of the disease. Two major sources of environmental white noises are considered: disease transmission and natural death rates. The impacts of each source of noise on the disease dynamics are examined. The basic reproduction numbers and other threshold values for the disease in the stochastic and deterministic settings are determined and compared to determine the impacts of the noises on the dynamics. The question about the extend that stability conditions for steady states in the noise-free disease dynamics, remain valid for the stochastic stability of the steady state is answered in this paper. Moreover, noise intensity regions are computed, within which all stability conditions for both systems are the same, and both systems behave similarly.