Mathematical model analysis on the significance of surveillance and awareness on the transmission dynamics of diphtheria

Abstract

Corynebacterium diphtheriae is a respiratory pathogen. Diphtheria was a major source of disease and mortality, particularly in children under five years of age and those over forty years of age. However, due to the lack of vaccinations, the disease is still widespread in several countries, particularly after the COVID-19 pandemic. In light of the above reason, we propose a deterministic mathematical model to characterize the dynamics of diphtheria transmission, evaluating the effects of awareness and surveillance that other authors have not considered. The boundedness and positivity of the solution have been established. In addition, it has been investigated that if Rc < 1, the model shows a diphtheria-free equilibrium that is stable both locally and globally. According to the theoretical study, there is a distinct positive endemic equilibrium, and the corresponding control reproduction number is greater than one. The endemic equilibrium has also been shown to be globally asymptotically stable when the disease induces mortality, vaccination, booster vaccination, and isolation are zero. Both the diphtheria-free and the endemic equilibrium global stability are numerically justified. Model fitting and parameter estimation are obtained using the least-squares method. Numerical simulation reveals that the development of surveillance and awareness is effective in curtailing the spread of diphtheria infection. Finally, the theoretical and numerical result shows that with surveillance and awareness, the disease can be eradicated in the population in less than ten years.