Journal of the Indonesian Mathematical Society
Vol. 31 No. 4 (2025): DECEMBER

Optimal Control of HIV/AIDS Epidemics: Integrating Media Awareness and Antiviral Treatment

Ayu, Regina Wahyudyah Sonata (Unknown)
Wilda, Robiatul Witari (Unknown)
Rizka, Sailah Ar (Unknown)
Yumia, Mega (Unknown)
Afli, Febrianto (Unknown)



Article Info

Publish Date
12 Nov 2025

Abstract

This paper investigates an optimal control strategy to mitigate the spread of HIV/AIDS by integrating media awareness campaigns and antiviral treatment efforts. A modified SI-type model is developed, dividing the population into five subgroups: unaware susceptible individuals, aware susceptible individuals, unaware infected individuals, aware infected individuals, and individuals undergoing treatment. Additionally, a separate compartment representing the level of media awareness is included to model the dynamics of awareness campaigns over time. Three control variables are introduced: the success of media awareness programs aimed at reducing contact between susceptible and infected individuals and encouraging infected individuals to seek and receive treatment; the effort to provide antiretroviral treatment; and the effort to strengthen the intensity of media awareness programs. The objective is to minimize the number of unaware susceptible and infected individuals while maximizing the number of individuals receiving treatment, and to reduce implementation costs. The model employs optimal control theory to identify the best combination of strategies by minimizing a cost functional. Numerical simulations explore seven control strategy combinations, ranging from single to multiple controls. The results indicate that combining all control variables yields the most significant reduction in unaware and infected individuals, a substantial increase in the number of individuals receiving treatment, and effective minimization of costs.

Copyrights © 2025






Journal Info

Abbrev

JIMS

Publisher

Subject

Mathematics

Description

Journal of the Indonesian Mathematical Society disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and their ...