Modeling and predicting the spread of diphtheria in guinea using delayed stochastic differential equations

Abstract

Diphtheria is a highly infectious and life-threatening disease caused by Corynebacterium diphtheriae, continues to be a significant public health threat, particularly in regions with insufficient vaccination coverage. Despite the progress made in vaccination programs globally, recent outbreaks, such as those in Thailand in 2019 and Guinea in 2023, have highlighted the resurgence of the disease, especially among populations with waning immunity. In this study, we extend the classic Susceptible-Infectious-Recovered (SIR) model to incorporate both deterministic and stochastic time-delayed models, aiming to predict the epidemiological trend of diphtheria and evaluate the impact of multiple control strategies, including vaccination and public awareness campaigns. The main contributions of this work include establishing the well-posedness of the proposed models and identifying conditions under which diphtheria may either persist or be eradicated within a population. Parameters for the models were estimated using real-world outbreak data, and numerical simulations were conducted to both forecast the future spread of diphtheria and verify the theoretical findings. Our results emphasize the critical role of maintaining high vaccination coverage and the need for timely public health interventions to effectively control the spread of diphtheria.