This paper presents a novel deterministic-stochastic modelling framework for investigating the transmission dynamics of the Oropouche virus, an emerging arbovirus in South America. A nonlinear SIR model is developed, and the basic reproduction number R0, equilibrium points, and their stability are obtained analytically. Bifurcation theory is employed to find the critical value that distinguishes the existence of disease-free and coexisting endemic equilibria. To incorporate stochastic variability in disease transmission, the deterministic model is generalised to a stochastic differential equation model using the Yuan-Allen approach. Moreover, optimal control strategies are developed for both deterministic and stochastic models via Pontryagins Maximum Principle and its stochastic counterpart. Numerical simulations are carried out to validate the influence of stochastic variability on the transmission dynamics and to evaluate the effectiveness of the proposed control strategies in controlling the disease spread in both deterministic and stochastic models.
Meyyappan et al. (Fri,) studied this question.