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

Ummu Habibah; Trisilowati; Mohamad Hasyim Muzaqi

doi:https://doi.org/10.14445/22315373/IJMTT-V67I8P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P512

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

Ummu Habibah, Trisilowati, Mohamad Hasyim Muzaqi

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.

Keywords

dynamical system, multi-interaction, local stability.

References

[1] L. Cai, X. Li, M. Ghosh, and B. Guo., Stability analysis of an HIV/AIDS epidemic model with treatment., J. Comput. Appl. Math., 229 (1) (2009) 313–323.
[2] L. Cai, S. Guo, and S. Wang., Analysis of an extended HIV/AIDS epidemic model with treatment., Appl. Math. Comput., 236 (2014) 621–627.
[3] H. F. Huo, R. Chen, and X.-Y. Wang., Modelling and stability of HIV/AIDS epidemic model with treatment., Appl. Math. Model., 40 (13–14) (2016) 6550–6559.
[4] H.F. Huo and R. Chen., Stability of an HIV/AIDS Treatment Model with Different Stages., Discrete Dyn. Nat. Soc., 2015 (2015) 1–9.
[5] Dept. Mathematics, University of Brawijaya, B. Ulfa, T. Trisilowati, and W. M. K., Dynamical Analysis of HIV/AIDS Epidemic Model with Treatment., J. Exp. Life Sci., 8 (1) (2018) 23–29.
[6] U. Habibah, T. Trisilowati, Y. L. Pradana, and W. Villadistyan., Mathematical Model of HIV/AIDS with Two Different Stages of Infection Subpopulation and Its Stability Analysis., Engl. Lett., 29 (1) (2021) 1-9.
[7] H.F. Huo and L.-X. Feng., Global stability for an HIV/AIDS epidemic model with different latent stages and treatment., Appl. Math. Model., 37 (3) (2013) 1480–1489.
[8] U. Habibah and R. A. Sari., The effectiveness of an antiretroviral treatment (ARV) and a highly active antiretroviral therapy (HAART) on HIV/AIDS epidemic model., AIP Conference Proceedings, 2021 (2018) 060030.
[9] H. Miao, X. Abdurahman, Z. Teng, and C. Kang., Global Dynamics of a Fractional Order HIV Model with Both Virus-to-Cell and Cell-to-Cell Transmissions and Therapy Effect., IAENG Inter. J. Appl. Math., 47 (1) (2017) 75-81.
[10] S. Saha and G. P. Samanta., Modelling and optimal control of HIV/AIDS prevention through PrEP and limited treatment., Phys. Stat. Mech. Its Appl., 516 (2019) 280–307.
[11] J. M. Heffernan, R. J. Smith, and L. M. Wahl., Perspectives on the basic reproductive ratio., J. R. Soc. Interface, 2 (4) (2005) 281–293.
[12] U. Habibah, Trisilowati, I. Darti, M. H. Muzaqi, T. R. Tania and L.U. AlFaruq., Stability Analysis of HIV/AIDS Model with Educated Subpopulation., Cauchy, 6 (4) (2021) 189-199.

Citation :

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 (IJMTT), vol. 67, no. 8, pp. 103-111, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P512