Stability Analysis and Optimal Control of the Dynamics Diphtheria Disease Spread with Education Campaign and Treatment

Abstract

Diphtheria is an infectious disease caused by the bacterium Corynebacterium diphtheriae and remains a public health problem, particularly in areas with low immunization coverage. This study develops and analyzes a mathematical model to describe the dynamics of diphtheria transmission in a population through equilibrium-point, stability analysis, and the determination of the basic reproduction number. This analysis identifies the conditions distinguishing between disease persistence and elimination. Given the disease’s complex transmission pathways, optimal control is required in the early stages, including educational campaign, treatment, and a combination of both interventions to reduce case numbers and lower patient care costs. Simulation results indicate that the simultaneous implementation of control measures is more effective in curbing disease spread than single-measure control. This model provides a structured quantitative basis for evaluating the impact of interventions and supports evidence-based decision-making in early intervention planning and resource allocation, thereby helping to prevent the resurgence of diphtheria.

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