Abstract

In this paper, we investigated on the stochastic epidemic model by incorporating viral load detectability. We derived HIV and AIDS stochastic model from the deterministic counterpart model and presented a stochastic threshold in terms of stochastic basic reproduction number. We showed that R_s^0 < 1 then the disease dies out exponentially and when R_s^0 > 1 the disease persists in the population. We further derived the existence and uniqueness, extinction and persistence properties of the stochastic model models, then the numerical simulation is done by using Milsten’s numerical scheme. The finding shows that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterparts which provide some useful control strategies to eradicate the disease

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