Computational Solutions of a Delay-Driven Stochastic Model for Conjunctivitis Spread

This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations (SDDEs). A delayed stochastic model is formulated by dividing the population into five distinct compartments: susceptible, exposed, infected, environmental irritants, and recovered individuals. The model undergoes thorough analytical examination, addressing key dynamical properties including positivity, boundedness, existence, and uniqueness of solutions. Local and global stability around the equilibrium points is studied with respect to the basic reproduction number. The existence of a unique global positive solution for the stochastic delayed model is established. In addition, a stochastic nonstandard finite difference scheme is developed, which is shown to be dynamically consistent and convergent toward the equilibrium states. The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods. Finally, the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.