A Multi-Intervention Framework for Diphtheria Eradication: Optimizing Public Health Via Vaccination, Early Diagnosis, Isolation and Community-Driven Infection Control

Abstract

This study develops and analyzes a mathematical model for diphtheria transmission incorporating vaccination, exposure prevention, and treatment interventions. Analytical results include the disease-free and endemic equilibria, the basic reproduction number , and a sensitivity analysis showing that transmission rate, vaccination coverage, and treatment effort have the greatest influence on disease spread. A Hopf bifurcation analysis identifies threshold parameter values where the system may transition to oscillatory behavior, highlighting the potential for periodic outbreaks under specific conditions. Using the Pontryagin Maximum Principle, an optimal control framework is implemented via the forward-backward sweep method to minimize the number of infected individuals while optimizing public health resource allocation. Numerical simulations demonstrate that combined interventions significantly reduce both asymptomatic and symptomatic infections, achieving disease elimination within approximately 60 days. These results provide quantitative guidance for public health strategies, emphasizing the importance of early, sustained, and integrated control measures for effective diphtheria management