# Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

## TL;DR

This paper formulates a multiobjective optimal control problem for TB-HIV/AIDS coinfection, balancing infection minimization and treatment costs, and analyzes the resulting population dynamics through numerical simulations.

## Contribution

It introduces a multiobjective control framework for TB-HIV/AIDS coinfection, overcoming limitations of prior models and providing detailed insights into optimal treatment strategies.

## Key findings

- Optimal control policies reduce infection prevalence.
- Some treatment strategies yield nonintuitive results.
- Numerical simulations validate the approach's effectiveness.

## Abstract

We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome (AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663]. We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are: minimization of the number of HIV infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.