# Optimal Control and Cost-Effectiveness Analysis of HIV Model with Educational Campaigns and Therapy

## Authors

• . Marsudi Department of Mathematics University of Brawijaya Malang 65145, Indonesia
• Noor Hidayat Department of Mathematics University of Brawijaya Malang 65145, Indonesia
• Ratno Bagus Edy Wibowo Department of Mathematics University of Brawijaya Malang 65145, Indonesia

## Abstract

In this paper, we present a deterministic model for the transmission dynamics of HIV, in which educational campaigns and therapy are both important for disease management. We propose and analyze an optimal control problem to investigate the effectiveness and cost-effectiveness of three control measures (educational campaigns, therapy on infected individuals in the asymptomatic stage, and therapy on infected individuals in the pre-AIDS class). We formulate the appropriate optimal control problem and investigate the necessary conditions for disease control in order to determine the role of asymptomatic infection, pre-AIDS, and full-blown AIDS in the spread of HIV. Pontryagin’s Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. The fourth-order Runge-Kutta forward-backwards sweep numerical approximation method was used to solve the optimal control system. The Incremental Cost-Effectiveness Ratio (ICER) was calculated to investigate the cost-effectiveness of all possible combinations of the three control measures. Using cost-effectiveness analysis, we showed that control of therapy on pre-AIDS and a combination of control of educational campaigns and therapy on pre-AIDS provides the most cost-effective strategy to control the disease.

31-12-2019

## How to Cite

Marsudi, ., Hidayat, N., & Edy Wibowo, R. B. (2019). Optimal Control and Cost-Effectiveness Analysis of HIV Model with Educational Campaigns and Therapy. MATEMATIKA, 35(4), 123–138. https://doi.org/10.11113/matematika.v35.n4.1267

Mathematics