A new stochastic compartmental epidemic model driven by a multidimensional stochastic differential equation under a voluntary and imperfect vaccination strategy

This work introduces a novel compartmental epidemic model that integrates both deterministic and stochastic components to capture the dynamics of disease transmission under a voluntary and imperfect vaccination strategy. The model features a nonlinear incidence rate and differentiates between two classes of susceptible individuals: those who opt for vaccination and those who decline it. The deterministic structure is formulated as a system of multidimensional ordinary differential equations. To incorporate environmental fluctuations, the model is extended by introducing stochastic perturbations into the transmission rate via a white noise term, yielding a system of multidimensional stochastic differential equations. The basic reproduction number is derived to establish the conditions under which the disease either dies out or persists. The effects of the vaccination strategy, as well as the model’s sensitivity to parameter variations, are thoroughly analyzed. Furthermore, the existence and uniqueness of solutions are proven, and the model’s equilibria are characterized. Finally, numerical simulations are conducted to illustrate and validate the analytical results.