J.Exp. Life Sci. Vol. 8 No. 1, 2018 ISSN. 2087-2852 E-ISSN. 2338-1655 23 HIV/AIDS Epidemic Model with Treatment (Ulfa et al.) Dynamical Analysis of HIV/AIDS Epidemic Model with Treatment Badria Ulfa 1 , Trisilowati 2* , Wuryansari Muharini Kusumawinahyu 2 1 Master Program of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia 2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia Abstract In this article, an epidemic model of HIV/AIDS with treatment is observed. This model consists of five populations: susceptible, educated susceptible, exposed, HIV infected, and AIDS infected. Antiretroviral therapy (ART) is one type of treatment that can be given to individual that is infected by HIV. This medication can prevent the growth of the virus. Exposed individuals are given short term antiretroviral treatment called Post Exposure Profilaxis (PPP), while for infect- ed individuals are given treatment by combining two or three types of antiretroviral drugs. Dynamical analysis is per- formed by determining equilibrium points and local stability analysis. Based on the analysis results, two equilibrium points are obtained, namely disease free equilibrium point and endemic equilibrium points. The stability analysis shows that the free equilibrium point is locally asymptotically stable if and the endemic equilibrium point is locally asymptotically stable under certain conditions. Numerical simulations show that giving two medications together has a greater effect in reducing the spread of the disease. Keywords: antiretroviral, dynamical analysis, HIV/AIDS. INTRODUCTION  In medical science, diseases are differentiated into infectious and non infectious diseases. Infectious diseases are diseases caused by bacteria, fungi, viruses, and parasites that can spread through various media. Infectious diseas- es are a big problem because they can lead to high relative mortality rates, as example is HIV/AIDS. AIDS (Acquired Immuno Deficiency Syndro- me) was first identified in 1981 in Los Angeles, USA. Furthermore, in 1983 has identified the virus that causes AIDS is HIV (Human Immuno- deficiency Virus), which is a virus that attacks and damage the human immune system [1]. The spread of HIV virus can occur through several media, such as sexual contact with HIV positive individuals, by sharing needles, by blood transfu- sions from HIV positive individuals, and through the vertical transmission process, which is mother to child HIV transmission [2]. Treatments that can be done to deal with the spread of HIV/AIDS is the treatment of post ex- posure prophylaxis (PPP) and antiretroviral (ART). Exposure is an event that causes the risk of transmission. PPP treatment is a short term an- tiretroviral treatment used to prevent infection  Correspondence address: Trisilowati Email : trisilowati@ub.ac.id Address : Dept. Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Veteran Malang, Malang 65145. after a risk incident. This treatment should be given as soon as possible after exposure, which is in the range of two to four hours. It is stated that the provision of PPP after seventy two hours is declared ineffective [3], so it is recommended to provide treatment by combining two or three types of antiretroviral drugs. ARV treatment works by inhibiting the progression of HIV in T-cells, so it can depress the course of the disease and improve the quality of life [2]. Some mathematical models related to the spread of HIV/AIDS have been studied by some researchers. In 2000, Culshaw [4] discussed a delay time differential equation model of HIV infection of T-cells. In his study, Culshaw proposed a model for the spread of HIV infection in three compartments, i.e and . In 2009, Cai [5] analyzed the model and sta- bility of the HIV/AIDS epidemic with treatment. The process of transmission of the disease occurs due to the presence of susceptible individuals who interact with individuals exposed and infect- ed with HIV. In this model, the HIV/AIDS epidem- ic is divided into four compartments, that is . Each compartment states the subpopulation of susceptible individuals , exposed , infected , and AIDS infectious . In 2014, Mahato [6] analyzed the mathemati- cal model of HIV/AIDS with vertical transmission. In this study, the disease epidemic model are expressed in four compartments, i.e , with the spread of the disease affected by verti-