An efficient numerical approach to simulate NPZ and SIR biological models with diffusion

Abstract

Abstract The two mathematical models of Nitrogen, Phytoplankton and Zooplankton (NPZ) and whooping cough SIR model that concerns with the susceptible, infected and recovered cases of the population are considered in this paper. To incorporate with the unidimensional movements of the three species in each of the NPZ and SIR models, the models are considered with diffusion terms. A numerical scheme based on the collocation of cubic B-splines is proposed to estimate the solutions of the considered NPZ and SIR models. The numerical results obtained are compared and found in good agreement with those already available in the literature. Due to unavailability of the analytic solutions of these models, such a numerical scheme can be of prime interest for biologists to interpret the results theoretically.