Mathematical Modeling, Optimal Control and Cost-Effectiveness Analysis of Diphtheria Transmission Dynamics

Diphtheria remains a serious public health concern in regions with low vaccination coverage and limited access to timely treatment, highlighting the urgent need for effective modeling and control strategies to guide intervention efforts. A nonlinear mathematical model is developed to describe the transmission dynamics of diphtheria. The well-posedness of the model is analyzed by investigating the positivity and boundedness of its solutions. The solutions of the disease-free equilibrium points are obtained analytically. The basic reproduction number () is determined using Diekmann-Heesterbeek-Metz Next Generation Matrix approach. The stability of the disease-free and endemic equilibrium points are rigorously analyzed. Sensitivity analysis of the model parameters with respect to is conducted to assess the relative impact of each parameter on the transmission dynamics of the disease. Based on the results of the sensitivity analysis, the proposed diphtheria model is extended into an optimal control problem by introducing four time-dependent control variables: personal protection, booster vaccine administration, detection/treatment of the asymptomatic infected humans and reduction of bacteria concentration. Four different scenarios with each involving at least three of the control variables are examined. We evaluated the cost-effectiveness of each control strategy using IAR, ACER and ICER methods in order to identify the most economically efficient strategy. The findings demonstrate that Strategy A is the most cost-effective startegy that can significantly reduce diphtheria transmission throught optimal personal protection, detection/treatment of the asymptomatic infected humans and reduction of bacteria concentration.