Model Analysis of Diphtheria Disease Transmission with Vaccination, Quarantine, and Hand-Washing Behavior

Nur Rahmi; Muh. Isbar Pratama

doi:10.31764/jtam.v7i2.13466

Model Analysis of Diphtheria Disease Transmission with Vaccination, Quarantine, and Hand-Washing Behavior

Nur Rahmi, Muh. Isbar Pratama

Abstract

Recently, diphtheria outbreaks occur in many countries. According to the latest data from the World Health Organization, the number of registered cases and incidence of diphtheria in 2021 will be 8,638 cases worldwide. Diphtheria is generally an acute respiratory infection with most infections being asymptomatic or having a relatively slight clinical course. However, many sufferers are afflicted by breathing obstruction. In this study, we developed and analyzed the diphtheria spread model by considering transmission by contact with an exposed and infected individual, progression for vaccinated exposed individuals becoming infected, quarantine for both exposed and infected people, and hand-washing behavior. Besides that, we proved the stability analysis around the equilibrium points and did the numerical simulations of models. The results of this study show that the model system has two steady states, namely disease-free equilibrium and endemic equilibrium. The disease-free equilibrium is stable if the basic reproduction number is less than one, either is unstable. The endemic equilibrium exists and is stable if the basic reproduction number is greater than one. The numerical simulations show that there is a significant effect of vaccination, quarantine, and hand-washing behavior for infected numbers, respectively. Vaccination, quarantine, and hand-washing behavior could significantly reduce the basic reproductive and the infected number. Whereas vaccination for exposed people could increase the basic reproductive and the infected number.

Keywords

Mathematical model; Diphtheria; Stability; Dynamic- analysis.

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References

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DOI: https://doi.org/10.31764/jtam.v7i2.13466