Assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of HIV/AIDS in heterosexual settings

Global stability for age-infection-structured human immunodeficiency virus model with heterogeneous transmission

In this paper, we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R 0 . If R 0 < 1 , disease-free equilibrium is globally asymptotically stable. If R 0 > 1 , it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for R 0 is performed by the method of partial rank correlation coefficient(PRCC).

HIV/AIDS Mathematical Model of Triangle Transmission

In this paper, a mathematical analysis of the HIV/AIDS deterministic model studied in the paper called Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a case study in the previous works preformed by Espitia is performed. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness; the calculus of the basic reproduction number; stationary points such as disease-free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE); and the local stability (LAS) of disease-free equilibrium. The findings allow us to conclude that the best way to reduce contagion and consequently reach a DFE is thought to be the reduction in the rate of homosexual partners, as they are the most affected population by the virus and are therefore the most likely to become infected and spread it. Increasing the departure rate of infected individuals leads to a decrease in untreated infected heterosexual men and untreated infected women.

Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia

While several studies on human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) in the homosexual and heterosexual population have demonstrated substantial advantages in controlling HIV transmission in these groups, the overall 2benefits of the models with a bisexual population and initiation of antiretroviral therapy have not had enough attention in dynamic modeling. Thus, we used a mathematical model based on studying the impacts of bisexual behavior in a global community developed in the PhD thesis work of Espitia (2021). The model is governed by a nonlinear ordinary differential equation system, the parameters of which are calibrated with data from the cumulative cases of HIV infection and AIDS reported in San Juan de Pasto in 2019. Our model estimations show which parameters are the most influential and how to modulate them to decrease the HIV infection.

Assessing the Impact of Optimal Health Education Programs on the Control of Zoonotic Diseases

To better understand the dynamics of zoonotic diseases, we propose a deterministic mathematical model to study the dynamics of zoonotic brucellosis with a focus on developing countries. The model contains all the relevant biological details, including indirect transmission by the environment. We analyze the essential dynamic behavior of the model and perform an optimal control study to design effective prevention and intervention strategies. The sensitivity analysis of the model parameters is performed. The aim of the controls is tied to reducing the number of infected humans, through health promotional programs within the affected communities. The Pontryagin's Maximum Principle is used to characterize the optimal level of the controls, and the resulting optimality system is solved numerically. Overall, the study demonstrates that through health promotional programs on zoonotic diseases among villagers, it is vital that they should be conducted with high efficacy.

Assessing the Potential Impact of Hormonal-Based Contraceptives on HIV Transmission Dynamics Among Heterosexuals

HIV susceptibility linked to hormonal contraception (HC) has been studied before, but with mixed results. Reports from some of the recent findings have prompted the World Health Organisation to encourage women who use HC to concurrently use condoms in order to prevent HIV infection in the light of possible increased HIV risk of infection associated with hormone-based contraceptives. A two-sex HIV model classifying women into three risk groups consisting of individuals who use condoms, natural methods, and hormone-based contraceptives is formulated and analysed to assess the possible effects of various birth control strategies on the transmission dynamics of the disease. Our model results showed that women who use HC could be key drivers of the epidemic and that their increased infectivity may be critical in driving the epidemic. Women who use hormone-based contraceptives potentially act as a core group from which men get infected and in turn transmit the disease to other population groups. We fitted the model to HIV prevalence data for Zimbabwe reported by UNAIDS and Zimbabwe Ministry of Health and Child Care and used the model fit to project HIV prevalence. Predictions using HIV data for Zimbabwe suggest that a hypothesised increase in susceptibility and infectivity of two-, three-, and fourfold would result in a 25, 50, and 100% increase in baseline HIV prevalence projection, respectively, thus suggesting possible increased disease burden even in countries reporting plausible HIV prevalence declines. Although a possible causal relationship between HIV susceptibility and HC use remains subject of continuing scientific probe, its inclusion as part of birth control strategy has been shown in this study, to possibly increase HIV transmission. If proven, HC use may potentially explain the inordinate spread of HIV within the sub-Saharan Africa region and therefore compel for urgent assessment with a view to reorienting birth control methods in use in settings with generalised epidemics.

Mathematical modeling of the HIV/Kaposi's sarcoma coinfection dynamics in areas of high HIV prevalence

We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛ _k < 1. A unique endemic equilibrium exists and is locally stable whenever ℛ _k > 1. Therefore, reducing ℛ _k to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.

A MODEL FOR CONTROL OF HIV/AIDS WITH PARENTAL CARE

In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.