Analysis and Simulation of SIPA Model for HIV-AIDS Transmission

Abstract

The aims of this study are: to build a SIPA model on the spread of HIV/AIDS; analyse and simulation of SIPA model and to predict the spread of HIV/AIDS. An applied mathematics for Analysis of the SIPA model in case of HIV/AIDS spreading using the Jacobi matrix method to obtain eigenvalues in two conditions, namely endemic and disease-free, while the simulation model uses Maple with initial value data in the form of assumptions represented in research. The research result are the mathematical SIPA model of HIV/AIDS spreading which is a system of differential equations. The analysis of the model gives the value of the disease-free equilibrium point and the asymptotically stable endemic equilibrium point. The results also found that the basic reproduction number was R0=0.0067 for disease-free conditions and R0=2.7944 for endemic conditions indicating the condition of HIV/AIDS spreading cases in the population. The simulation results found that there is a very significant difference between the numbers of AIDS populations when free from disease and during endemic conditions, so that attention is needed for the government to be able to tackle the spread of HIV/AIDS.