Optimal Control of Mathematical Model of Diphtheria Spreading

Abstract

This article examines optimal control model for the spread of diphtheria disease. Diphtheria is an infectious disease caused by the bacterium Corynebacterium diphtheriae. This model is divided into six compartments, namely population of susceptibles (𝑆), population of latent (L), population of infected with symptoms (Is), population of infected without symptoms (Ia), population of recovered with full immunity (Rf) and population of recovered with partial immunity (Rp). Two optimal controls are applied in the model, namely vaccination and treatment. The problem of optimal control is solved by using Pontryagin's minimal principle, which consists in solving a set of necessary conditions that must be satisfied by the optimal control and its associated state. The numerical method used to solve the optimal control problem is the forward-backward sweep method. Based on the results of numerical simulations, both controls should be administered in large numbers and continuously since the beginning of observation in order to reduce the number of diphtheria infected population and to control the spread of diphtheria.

Mathematical Analysis of Spread and Control of Diphtheria with Emphasis on Diphtheria Antitoxin Efficiency

“…Mathematical models aid in understanding transmission dynamics and shaping public health strategies Oli et al (2006), Suggested Citation Sweileh (2022). Various authors have explored diphtheria dynamics, noting the role of contaminated environments and the necessity of booster vaccines Islam (2018), Husain (2019), Izzati et al (2020), Kanchanarat et al (2022), Ghani et al 2022, Akhi et al (2023, Amalia (2022), Rahmi & Pratama (2023), Djaafara (2020).…”

“…In the work of Amalia and Toaha (2022) diphtheria transmission dynamics in a particular region was examined, highlighting factors impacting disease spread. However, they do not delve into optimizing control strategies or incorporate multiple compartments and parameters in their model, while the mathematical model by Izzati (2020) addresses diphtheria transmission, emphasizing vaccination coverage and treatment effectiveness but neglects factors like partial immunity, progression rates, and compartment dynamics.…”