Optimal control using pontryagin’s maximum principle: Tuberculosis spread case

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. This research aims to determine the results of the tuberculosis disease model and simulation without and with the use of optimal control. The mathematical model SEIR is a model that can analyze the spread of the disease tuberculosis. In this research, a variable treatment compartment to the SEIR model. It used 4 antibiotics in the intensive phase and added Isoniazid and Rifampicin 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 people infected with Tuberculosis.