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.

Optimal Control of HIV-1 Spread in Combination with Nutritional Status and ARV-Treatment

“…Compartment diagram of HIV-1 spread is shown in Figure 1. from Figure 1, the following equation is obtained [7].…”

“…A nonlinear HIV/AIDS dynamics model based on HIV-infected populations is presented by Dutta et HIV/AIDS transmission [6]. The analysis of the S-I-P-A model in the case of the spread of HIV/AIDS shows that there is a very significant effect the difference between the number of the AIDS population when free of disease and during endemic conditions [7].…”

Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

“…Abueldahab et al studied an epidemic model to observe the spread of Human Immunodeficiency Virus (HIV) in Khartoum [11]. Sanusi et al developed a epidemic model to study and predict the spread of HIV/AIDS [12]. Shaikh et al proposed the model of the dynamics of HIV/AIDS transmission in the existence of a conscious community using a fractional differential operator [13].…”