Abstract
The phenomena of disease spread are unpredictable in nature due to random mixing of individuals in a population. It is of more significance to include this randomness while modeling infectious diseases. Modeling epidemics including their stochastic behavior could be a more realistic approach in many situations. In this paper, a stochastic gonorrhea epidemic model with treatment effect has been analyzed numerically. Numerical solution of stochastic model is presented in comparison with its deterministic part. The dynamics of the gonorrhea disease is governed by a threshold quantity A(1) called basic reproductive number. If A(1) < 1, then disease eventually dies out while A(1) > 1 shows the persistence of disease in population. The standard numerical schemes like Euler Maruyama, stochastic Euler and stochastic Runge-Kutta are highly dependent on step size and do not behave well in certain scenarios. A competitive non-standard finite difference numerical scheme in stochastic setting is proposed, which is independent of step size and remains consistent with the corresponding deterministic model.