Developing a computational framework for accurately solving a mathematical model of streptococcus pneumonia infection

Abstract

The paper aims to optimal existence and numerically examine a Susceptible-Vaccinated-Exposed-InfectedRecovered (SVEIR) epidemic model of pneumonia disease dynamics. Three different numerical methods are carried out to approximate the underlying model, including forward Euler, Runge-Kutta (RK-4), and the proposed non-standard finite difference (NSFD). The NSFD technique has been proven to be a more efficient and reliable numerical approximation method than the Euler and RK-4 approximations because it conserves all the necessary characteristics of a continuous SVEIR pneumonia epidemic model, which include positivity, boundedness, and equilibrium stability. The case is not the same for forward Euler and RK-4 approximations. Besides that, unlike forward Euler and RK-4, the NSFD scheme developed in the paper is independent of time step size. Numerical simulations with a numerical test are given to establish all properties of the proposed technique.