Mathematical Model of HIV/AIDS with Two Different Stages of Infection Subpopulation and Its Stability Analysis

被引：0

作者：

Habibah, Ummu ^{[1
,2
]}

Trisilowati ^{[1
,2
]}

Pradana, Yona Lotusia ^{[1
]}

Villadystian, Winadya ^{[1
]}

机构：

[1] Brawijaya Univ, Dept Math, Jl Vet Malang, Kota Malang, Jawa Timur, Indonesia

[2] Brawijaya Univ, Res Grp Biomath, Jl Vet Malang, Kota Malang, Jawa Timur, Indonesia

来源：

ENGINEERING LETTERS | 2021年 / 29卷 / 01期

关键词：

dynamical system; HIV/AIDS; different stages; stability analysis; EPIDEMIC MODEL;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We propose mathematical model of HIV/AIDS with two different stages of infection subpopulation. The proposed model is more realistic since it establishes the compartment diagram based on data from the Indonesian Ministry of Health. The model consists of six compartments (susceptible, infected with and without treatment, AIDS, treatment, and recovered sub populations). We analyzed the model by proving the positivity and boundedness of the models solutions. Furthermore, we analyzed local and global stability of the solutions determined by the basic reproduction number as a threshold of disease transmission. The disease-free and endemic equilibrium points are locally asymptotically stable when R-0 < 1 and R-0 > 1 respectively. For global stability, we constructed the Lyapunov function. The results indicate that the disease-free equilibrium point is globally asymptotically stable when R-0 < 1 and that the endemic equilibrium point is globally asymptotically stable when R-0 > 1. We conducted numerical simulation to support the analytical results.

引用

页码：1 / 9

页数：9