Dynamics of Tuberculosis (TB) Population Distribution Using the Pontryagin Maximum Principle

EasyChair Preprint 10487

Abstract

Tuberculosis is one of the deadliest infectious diseases in the world. In 2020, 9.9 million people were infected and 1.5 million died. East Java province ranks third with 43,268 tuberculosis cases. The purpose of this research is to see the condition of the spread of TB without and given optimal control. The mathematical model SEIR is a model that can analyze the spread of the disease tuberculosis. In this study, we added a variable treatment compartment to the SEIR model. We used 4 antibiotics in the intensive phase and added isoniazid and rifampin in the advanced phase as the optimal control parameters. Optimal control uses Pontriagin's maximum principle as the derivative to modify the SEIR model and is described by a Runge-Kutta order 4 scheme. It shows both the useful parameters in the optimal control with a maximum value of 1 and plots where the effect of optimal control exists further constrained—the number of people infected the Tuberculosis.

Keyphrases: Tuberculosis, mathematics model, optimal control

@booklet{EasyChair:10487,
  author    = {Muhammad Iqbal Widiaputra and Ahmad Hanif Asyhar and Wika Dianita Utami and Putroue Keumala Intan and Dian Yuliati and Muhamma Fahrur Rozi},
  title     = {Dynamics of Tuberculosis (TB) Population Distribution Using the Pontryagin Maximum Principle},
  howpublished = {EasyChair Preprint 10487},
  year      = {EasyChair, 2023}}