One-Step Hybrid Block Method for the Numerical Solution of Malthus and SIR Epidemic Models equations

The Malthusian population model and Susceptible-Infectious-Recovered (SIR) epidemic model are described by systems of first order ordinary differential equations (ODEs) that model the dynamics of population growth and infectious disease spread respectively. Efficient numerical methods to solve these models play an integral role across mathematical biology disciplines. This study presents the formulation, analysis and application of a novel one-step hybrid block method for the direct integration of the Malthus and SIR models ODE systems. Consistency, zero-stability and convergence tests prove the method is numerically satisfactory. The technique is implemented in solving benchmark problems for the Malthusian quadratic and SIR epidemic models. Numerical results demonstrated that the new solver is more accurate and computationally efficient when compared to existing one-step and linear multistep methods widely used for population dynamics models. The hybrid block method provides an accurate and fast approach for simulating the dynamics of these biological systems