Mathematical modeling and strategy for optimal control of diphtheria

Abstract

This research introduces a novel approach to combating diphtheria by presenting a comprehensive optimal control strategy focused on awareness campaigns to avoid direct contact with infected individuals and promote vaccinations. These campaigns highlight the severe complications of diphtheria, such as acute respiratory issues, myocarditis, and neurological paralysis. Additionally, the campaigns emphasize the negative impacts of an unbalanced lifestyle and environmental factors, as well as the importance of timely treatment and psychological support. The model aims to improve control strategies by reducing the number of infected individuals $I\left(t\right)$ and exposed individuals $E\left(t\right)$, as well as asymptomatic carriers $A\left(t\right)$, which we have integrated into the model as an aspect that has been relatively unexplored in diphtheria transmission. The optimal controls are meticulously determined using Pontryagin’s maximum principle. The resulting optimality system is solved iteratively, ensuring precision and clarity in the results. Extensive numerical simulations rigorously support and confirm the theoretical analysis using MATLAB, providing concrete evidence of the strategy’s effectiveness. The broader implications and potential applications of this optimal control strategy extend to other infectious diseases, enhancing its relevance and utility in public health.