Mathematical Analysis of Spread and Control of Diphtheria with Emphasis on Diphtheria Antitoxin Efficiency

Diphtheria, a bacterial infection caused by Corynebacterium diphtheriae, remains a significant public health concern worldwide. In this study, we employ mathematical modeling to analyze the spread and control of diphtheria, focusing on the efficacy of Diphtheria Antitoxin in mitigating the disease's impact. Through the development of compartmental models, system of differential equations governing the dynamics was formulated. Due to the complexity and non-linearity of the dynamics, a numerical solutions that utilizes Runge-Kutta Fehlberg order 4 and 5 method. The dynamics of diphtheria transmission and the potential impact of DAT administration on disease outcomes was investigate. Our findings highlight the critical role of Antitoxin efficiency in reducing disease burden, preventing severe cases, and containing epidemic spread. By exploring various scenarios and parameter sensitivities, we provide insights into optimal control strategies and intervention measures to combat diphtheria outbreaks effectively. This research contributes to a better understanding of diphtheria epidemiology and informs public health policies aimed at enhancing vaccination coverage and DAT availability to achieve sustainable disease control and prevention.