A stochastic modeling of recurrent measles epidemic

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

On some properties of the block linear multi-step methods

The convergence, stability and order of Block linear Multistep methods have been determined in the past based on individual members of the block. In this paper, methods are proposed to examine the properties of the entire block. Some Block Linear Multistep methods have been considered, their convergence, stability and order have been determined using these approaches. Keywords: Annuity, Amortisation, Sinking Fund, Present and Future Value Annuity, Maturity date and Redemption value