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Mathematical Modeling of Diphtheria: The Role of Antibiotics, Quarantine, and Healthcare Resource Allocation


Author: Eloho B. Akponana and Akindele Michael Okedoye
Department of Mathematics, Federal University of Petroleum Resources, Effurun, Nigeria.
Published Date: 2025-09-11
Keywords: Antibiotic treatment, Quarantine measures, Disease control, Recovery rates, Sensitivity analysis.
Abstract:
Diphtheria remains a significant public health concern, especially in resource-limited settings. This study presents a mathematical model to investigate the dynamics of diphtheria transmission, incorporating factors such as quarantine, antibiotic treatment, and healthcare resource allocation. The model consists of compartments for susceptible, exposed, infectious, quarantined, under antibiotic treatment, and recovered individuals, and analyzes how various parameters affect disease dynamics. Numerical simulations reveal that increasing the rate of entry into quarantine effectively reduces the susceptible population and increases the quarantined population, demonstrating the importance of quarantine in controlling disease spread. Higher recovery rates, both from general recovery and specific treatments, significantly reduce the peak and overall number of infectious individuals while increasing the recovered population. The rate of entry into antibiotic treatment and access to healthcare resources also plays a crucial role in managing the outbreak. This analysis underscores the need for balanced resource allocation and effective intervention strategies to mitigate diphtheria’s impact.