Stability Analysis of HIV/AIDS Model with Interaction Between Educated and Infected (Not Consuming ARV) Subpopulations

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-8
Year of Publication : 2021
Authors : Ummu Habibah, Trisilowati, Mohamad Hasyim Muzaqi
  10.14445/22315373/IJMTT-V67I8P512

MLA

MLA Style: Ummu Habibah, Trisilowati, Mohamad Hasyim Muzaqi "Stability Analysis of HIV/AIDS Model with Interaction Between Educated and Infected (Not Consuming ARV) Subpopulations" International Journal of Mathematics Trends and Technology 67.8 (2021):103-111. 

APA Style: Ummu Habibah, Trisilowati, Mohamad Hasyim Muzaqi(2021). Stability Analysis of HIV/AIDS Model with Interaction Between Educated and Infected (Not Consuming ARV) Subpopulations International Journal of Mathematics Trends and Technology, 67(8), 103-111.

Abstract
We study stability analysis of HIV/AIDS model. The mathematical model of HIV/AIDS is constructed with seven compartments, S, E, I1, I2, A, T, and R. S is susceptible/uneducated individuals; E is educated individuals; I1 is HIV-positive individuals consuming ARV; and I2 is HIV-positive individuals not consuming ARV; A is full-blown AIDS not receiving treatment; T is individuals receiving ARV treatment; and R is recovered individuals who change and maintain their sexual habits for the rest of their lives. We consider multi-interaction between educated (E), uneducated (S) and infected (I1 and I2) subpopulations. We investigate local stability of the equilibrium points according to the basic reproduction number (R0) as a threshold of disease transmission. The disease-free and endemic equilibrium points are locally asymptotically stable when R0 <1 and R0 > 1 respectively. We conduct numerical simulation to support the analytical results.

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Keywords : dynamical system, multi-interaction, local stability.