Stochastic model, measles, epidemiology, Wiener process, Euler scheme.
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of susceptible individuals. Using the best currently available parameter values, the intrinsic variability in response to a given initial infection is examined by solving the stochastic system numerically. The results of the simulation seem to agree with the historical pattern of measles in Nigeria.
Keywords: Stochastic model, measles, epidemiology, Wiener process, Euler scheme.