A study on the transmission and dynamical behavior of an HIV/AIDS epidemic model with a cure rate

Attaullah; Sultan Alyobi; Mansour F. Yassen; Attaullah; Sultan Alyobi; Mansour F. Yassen

doi:10.3934/math.2022965

AIMS Mathematics

2022, Volume 7, Issue 9: 17507-17528. doi: 10.3934/math.2022965

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Research article

A study on the transmission and dynamical behavior of an HIV/AIDS epidemic model with a cure rate

1.
Department of Mathematics & Statistics, Bacha Khan University Charsadda 24461, Pakistan
2.
King Abdulaziz University, College of Science & Arts, Department of Mathematics, Rabigh, Saudi Arabia
3.
Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517 Damietta, Egypt

Received: 27 May 2022 Revised: 25 June 2022 Accepted: 30 June 2022 Published: 29 July 2022
MSC : 34A12, 34K28

In developing nations, the human immunodeficiency virus (HIV) infection, which can lead to acquired immunodeficiency syndrome (AIDS), has become a serious infectious disease. It destroys millions of people and costs incredible amounts of money to treat and control epidemics. In this research, we implemented a Legendre wavelet collocation scheme for the model of HIV infection and compared the new findings to previous findings in the literature. The findings demonstrate the precision and practicality of the suggested approach for approximating the solutions of HIV model. Additionally, establish an autonomous non-linear model for the transmission dynamics of healthy CD4⁺ T-cells, infected CD4⁺ T-cells and free particles HIV with a cure rate. Through increased human immunity, the cure rate contributes to a reduction in infected cells and viruses. Using the Routh-Hurwitz criterion, we determine the basic reproductive number and assess the stability of the disease-free equilibrium and unique endemic equilibrium of the model. Furthermore, numerical simulations of the novel model are presented using the suggested approach to demonstrate the efficiency of the key findings.
- HIV/AIDS,
- LWCM-method,
- Numerical comparison
Citation: Attaullah, Sultan Alyobi, Mansour F. Yassen. A study on the transmission and dynamical behavior of an HIV/AIDS epidemic model with a cure rate[J]. AIMS Mathematics, 2022, 7(9): 17507-17528. doi: 10.3934/math.2022965

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Abstract

In developing nations, the human immunodeficiency virus (HIV) infection, which can lead to acquired immunodeficiency syndrome (AIDS), has become a serious infectious disease. It destroys millions of people and costs incredible amounts of money to treat and control epidemics. In this research, we implemented a Legendre wavelet collocation scheme for the model of HIV infection and compared the new findings to previous findings in the literature. The findings demonstrate the precision and practicality of the suggested approach for approximating the solutions of HIV model. Additionally, establish an autonomous non-linear model for the transmission dynamics of healthy CD4⁺ T-cells, infected CD4⁺ T-cells and free particles HIV with a cure rate. Through increased human immunity, the cure rate contributes to a reduction in infected cells and viruses. Using the Routh-Hurwitz criterion, we determine the basic reproductive number and assess the stability of the disease-free equilibrium and unique endemic equilibrium of the model. Furthermore, numerical simulations of the novel model are presented using the suggested approach to demonstrate the efficiency of the key findings.

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