Abstract

APPLICATION OF ITERATION METHODS OF LINEAR AND NON-LINEAR DIFFERENTIAL EQUATIONS FOR INFECTIOUS DISEASES OF HUMANS

Mohemid Maddallah Al-Jebouri*, Mohammed Nokhas Murad Kaki

ABSTRACT

Background: This research investigates the dynamics of infectious disease transmission through a mathematical framework based on the classical Susceptible–Infected–Recovered (SIR) model. Both the full nonlinear system and a reduced linear formulation expressed in matrix form are considered to describe the evolution of the disease. Materials and Methods: Numerical simulations are carried out using the Euler discretization scheme to approximate the temporal behavior of the susceptible, infected, and recovered compartments over a specified time horizon. The analysis incorporates fundamental epidemiological parameters, including the infection rate (β) and the recovery rate (γ), under the assumption of a closed population with no demographic changes. Results: The simulations illustrate the progression of the outbreak, capturing the initial growth of infections, the attainment of a peak, and the subsequent decline as recovery dominates. These patterns reveal the influence of transmission mechanisms on the overall disease dynamics. Conclusions: The findings confirm that mathematical modeling, particularly when combined with matrix-based representations, provides an effective tool for analyzing infectious disease spread and supporting the development of informed public health interventions.

Keywords: Outbreak prediction, simulation analysis, epidemic threshold, and infection dynamics.