A Second Order NSFD Method for a Malaria Propagation Model

Standard numerical methods such as the implicit and explicit Euler and the Runge-Kutta methods have been used to approximate solutions of continuous-time transmission dynamics of many diseases. However, their convergence is conditional. Also, they do not always preserve the key features of the continuous-time model. Most times, they require a small time step which may increase the computational complexities especially for a long time horizon. In this paper we construct a nonstandard finite difference (NSFD) method to approximate the solution of a malaria propagation model. NSFD methods do not suffer from the drawback of time step restriction and preserve the physics of the problem under consideration. However their accuracy and rate of convergence remain a point of concern. In the construction of the NSFD scheme that we propose, we consider weights and denominator functions that depend not only on the time step but also iteratively on the state variables of the discrete model. This guarantees a second order convergence as opposed to earlier NSFD schemes which were independent of weights and their denominator functions were solely dependent of the time step. Numerical experiments confirm that the proposed scheme outperforms the first order NSFD in terms of accuracy and rate of convergence.