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The government and various authorized agencies are trying to reduce HIV population day by day. The proposed mathematical model may help to observe the patch of HIV infected or suspected population by nominated agencies. The proposed mathematical model supports the observability and asymptotic stability of the propagation of HIV epidemiology in a migrant heterosexual affected population.

This paper investigates the state estimation of a stochastic model for the spread of HIV in mobile heterosexual population. The transmission of HIV model with the force of infection in the multiple patches is investigated for the varying population. In this paper, we introduce a novel concept of the observer model like a transmission of HIV model to estimate the spread of HIV in mobile heterosexual population. The boundedness and the equilibrium points have been found for the error state of observer model and original model. The global stability properties are analyzed by the concept of Lyapunav function. The stochastic model is introduced for the examination of the stochastic stability of the positive equilibrium. The stochastic and deterministic models of the system are compared and analyzed. Finally numerical examples and corresponding diagrams are presented to support the results.