Abstract
In this paper, we construct SEIPA model for the acute period of HIV-AIDS with delay time, stability analysis and numerical simulation of the SEIPA model on the spread of HIV-AIDS. The method used to build the model is a model of the acute time delay of HIV-AIDS using psychological therapy as a parameter of the time delay model, the analysis of the model using the mathematical graph method to obtain the basic reproduction number and the global stability of the HIV-AIDS spread model with time delay. The numerical model simulation uses secondary data on the number of HIV-AIDS cases in South Sulawesi. The results obtained are SEIPA model of acute time delay in the spread of HIV-AIDS; Model analysis produces global stability and information on the status of the spread of HIV-AIDS in South Sulawesi, which depends on parameter values. Then the simulation results provide an overview of the prediction of the number of HIV-AIDS cases and also shown that psychological therapy can delay the acute period of the spread of HIV-AIDS in South Sulawesi. The results obtained can be used as a reference for early prevention of the spread of HIV-AIDS in South Sulawesi
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