7 results
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2. Dynamical behavior and density function analysis of a stochastic HIV/AIDS model with general incidence rate.
- Author
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Zhang, Xinhong, Yang, Qing, and Wang, Yan
- Subjects
STOCHASTIC analysis ,HIV ,PROBABILITY density function ,AIDS ,WHITE noise ,STOCHASTIC models - Abstract
In this paper, we mainly present the dynamic properties of a stochastic SICA model with general incidence rate. Through rigorous analysis and reasoning of the stochastic model, we obtain that the solution of the model is global, positive, and unique. By constructing the threshold value R0s$$ {R}_0^s $$, which includes the influence of white noise, we obtain a sufficient condition for the ergodicity of this model. Furthermore, we show that the model has a unique ergodic stationary distribution while R0s>1$$ {R}_0^s>1 $$ by adopting a novel method. The extinction of the system is also established. Besides, the expression of probability density function of the stochastic model with bilinear incidence rate around the unique stable positive equilibrium of the deterministic model is derived. Finally, numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Dynamical behaviors of a stochastic HIV/AIDS epidemic model with treatment.
- Author
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Zhao, Xiaoqi and Dong, Lingzhen
- Subjects
- *
AIDS , *HIV , *TREATMENT effectiveness , *EPIDEMICS - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
4. Extinction and positive recurrence of a regime‐switching HIV/AIDS model with treatment and standard incidence.
- Author
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Gao, Miaomiao, Jiang, Daqing, Hayat, Tasawar, and Alsaedi, Ahmed
- Subjects
AIDS treatment ,AIDS ,MARKOV processes ,IMMUNOLOGICAL deficiency syndromes ,LYAPUNOV functions ,HIV - Abstract
In this paper, we investigate the dynamics of a high‐dimensional human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) model with treatment and standard incidence, which is perturbed by telegraph noise. The switching is formulated by a continuous time Markov chain. Firstly, we show the existence and uniqueness of the global positive solution. Then, conditions for extinction of the disease are established. Moreover, through constructing suitable Lyapunov functions, we derive sufficient conditions for the existence of positive recurrence of the solutions. Positive recurrence implies all the individuals can coexist and persist in the long term. Finally, numerical experiments are performed for supporting the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. Dynamics and optimal control of a spatial diffusion HIV/AIDS model with antiretrovial therapy and pre‐exposure prophylaxis treatments.
- Author
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Wang, Liping, Din, Anwarud, and Wu, Peng
- Subjects
HIV infection transmission ,HIV infections ,PRE-exposure prophylaxis ,AIDS ,BASIC reproduction number ,GLOBAL asymptotic stability ,DIFFUSION control - Abstract
In this paper, to investigate the synthetic effect of PrEP (pre‐exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, a realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, that is, CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number R0 is established and proved as a threshold parameter: The global asymptotic stability of the disease‐free steady state holds for R0<1, and the disease will be present if R0>1. Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART therapy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests the following: (1) Spatial factors cannot be ignored during the HIV intervention; (2)taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. A study on fractional HIV‐AIDs transmission model with awareness effect.
- Author
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Kumar, Sunil, Chauhan, Ram P., Osman, Mohamed S., and Mohiuddine, S. A.
- Subjects
AIDS ,HIV infection transmission ,HIV ,CAPUTO fractional derivatives ,AWARENESS ,BIOLOGICAL models - Abstract
The main aim of this work is to numerically investigate a mathematical model of the HIV/AIDS disease with awareness effect, as the fractional derivatives capture more the genetic and memory properties of the biological models in comparison to the classical derivative. Therefore, in this article, we utilize the generalized Caputo fractional derivative to extend the integer‐order model of HIV/AIDS transmission to fractional order. A novel fixed‐point approach is used to identify the existence and uniqueness of the FO model. We use a new numerical technique based on the Adams‐Bashforth predictor‐corrector method to solve the fractional‐order HIV/AIDS transmission model. We illustrated the obtained numerical results through graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
7. Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines.
- Author
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Estadilla, Carlo Delfin S. and Reyes, Aurelio A.
- Subjects
BASIC reproduction number ,AIDS ,HIV ,HIV infections ,OPTIMAL control theory ,EPIDEMICS - Abstract
The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease‐free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre‐exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP‐only scenario is shown to be the most cost‐effective, followed by other scenarios that combine PrEP with other controls. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
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