A mathematical model on Acquired Immunodeficiency Syndrome

Mahato, Buddhadeo; Mishra, Bimal Kumar; Jayswal, Anurag; Chandra, Ramesh

doi:10.1016/j.joems.2013.12.001

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…AIDS is labeled by its rapid transmission, slow onset, and high fatality rate. There are three main ways of transmission, that is, sexual intercourse, blood transfusion, and mother‐to‐child transmission [1]. When a person is infected by HIV virus, his initial clinical manifestation is not clear.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behaviors of a stochastic HIV/AIDS epidemic model with treatment

Zhao

Dong

2023

Math Methods in App Sciences

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In this paper, by using Itô's formula, we study the dynamic behaviors of a stochastic human immune deficiency virus (HIV) model, which describes Acquired Immune Deficiency Syndrome (AIDS) with the effect of treatment. First, we discuss the global positivity of the solution to such a model with positive initial value. Then, we consider the limiting behavior of the solution. Moreover, we obtain the sufficient condition to guarantee the extinction of AIDS. Meanwhile, by constructing an appropriate Lyapunov function, we prove that the solution has a unique ergodic stationary distribution under a certain assumptions. Finally, we illustrate the validity of our results by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Dynamical behaviors of a stochastic HIV/AIDS epidemic model with treatment

Zhao

Dong

2023

Math Methods in App Sciences

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“…AIDS, acquired immunodeficiency syndrome; HIV, human immunodeficiency virus. Source: Hollingsworth et al (2008) (SEIR) have been widely used to study the HIV/AIDS transmission dynamics (Mahato et al, 2014). Besides, some mathematical models have incorporated the antiretroviral treatment of HIV/AIDS patients (see e.g., Baggaley et al, 2005;Cai et al, 2009;Granich et al, 2009;Okongo et al, 2013;Rong et al, 2007;Waziri et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Current forecast of HIV/AIDS using Bayesian inference

Prieto

Romero–Leiton

2021

Natural Resource Modeling

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In this study, we address the problem of fitting a mathematical model to the human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) data. We present a quantitative analysis of the formulated mathematical model by using Bayesian inference. The mathematical model consists of a suitable simple system of ordinary differential equations. We perform a local and global sensitivity analysis of parameters to determine which parameters of the model are the most relevant for the transmission and prevalence of the disease. We formulate the inverse problem associated to the parameter estimation of the model, and solve it using Bayesian statistics. Then, we estimate the basic reproductive number of the disease based on the estimation of the parameters of the model and its comparison with one is tested through hypothesis tests. The data set consist of HIV and AIDS data from Luxembourg, Czech Republic,

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“…Each compartment states the subpopulation of susceptible individuals , exposed , infected , and AIDS infectious . In 2014, Mahato [6] analyzed the mathematical model of HIV/AIDS with vertical transmission. In this study, the disease epidemic model are expressed in four compartments, i.e , with the spread of the disease affected by verti-…”

Section: Introduction mentioning

confidence: 99%

Dynamical Analysis of HIV/AIDS Epidemic Model with Treatment

Ulfa

Trisilowati

Wuryansari

2018

JELS

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In this article, an epidemic model of HIV/AIDS with treatment is observed. This model consists of five populations: susceptible, educated susceptible, exposed, HIV infected, and AIDS infected. Antiretroviral therapy (ART) is one type of treatment that can be given to individual that is infected by HIV. This medication can prevent the growth of the virus. Exposed individuals are given short term antiretroviral treatment called Post Exposure Profilaxis (PPP), while for infected individuals are given treatment by combining two or three types of antiretroviral drugs. Dynamical analysis is performed by determining equilibrium points and local stability analysis. Based on the analysis results, two equilibrium points are obtained, namely disease free equilibrium point and endemic equilibrium points. The stability analysis shows that the free equilibrium point is locally asymptotically stable if and the endemic equilibrium point is locally asymptotically stable under certain conditions. Numerical simulations show that giving two medications together has a greater effect in reducing the spread of the disease.

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A mathematical model on Acquired Immunodeficiency Syndrome

Cited by 5 publications

References 14 publications

Dynamical behaviors of a stochastic HIV/AIDS epidemic model with treatment

Dynamical behaviors of a stochastic HIV/AIDS epidemic model with treatment

Current forecast of HIV/AIDS using Bayesian inference

Dynamical Analysis of HIV/AIDS Epidemic Model with Treatment

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