Introduction: HIV continues to be a major global public health problem, with ongoing transmission across all countries. At the end of 2024, around 40.8 million people were living with HIV worldwide, while an estimated 630,000 people died from HIV-related causes. In Indonesia, an estimated 570,000 individuals are living with HIV. Despite the absence of a cure, effective prevention, diagnosis, treatment, and care have made HIV a manageable chronic disease, enabling people living with HIV to maintain long and healthy lives. In Indonesia, treatment coverage among people living with HIV is low, with only 31% accessing antiretroviral therapy (ART) and 14% attaining viral suppression. Addressing the treatment gap is among the most critical challenges facing the country’s HIV response. Thus, the objective of this study is to assess the optimal strategy required to contain HIV/AIDS transmission in Indonesia using optimal testing (or diagnosis) and ART.

Methods: An optimal control framework based on a non-autonomous deterministic HIV/AIDS transmission model was developed. The model incorporates time-dependent ART use and testing strategies. Pontryagin’s maximum principle was used for the qualitative analysis of the model. The associated optimality system was simulated to demonstrate the effects of separate and combined use of the optimal controls on HIV/AIDS dynamics in Indonesia.

Results: With optimal ART, more people become treated while fewer people become acute and chronic HIV-infected and full-blown AIDS patients. Activation of optimal testing only leads to fewer acute HIV-infected people, and fewer people progress to AIDS as more people are aware of their status and are receiving ART. Simultaneous implementation of the two optimal control shows fewer number of acute and chronic HIV-infected people, while fewer people progress to AIDS as more people receive ART.

Conclusion: Optimal implementation of testing (or diagnosis) and ART can significantly help in stemming the spread of HIV/AIDS in Indonesia.