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.Web of Scienc

A model of HIV/AIDS population dynamics including ARV treatment and pre-exposure prophylaxis

Antiretroviral treatment (ART) and oral pre-exposure prophylaxis (PrEP) have recently been used efficiently in management of HIV infection. Pre-exposure prophylaxis consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals. We propose a new model for the transmission of HIV/AIDS including ART and PrEP. Our model can be used to test the effects of ART and of the uptake of PrEP in a given population, as we demonstrate through simulations. The model can also be used to estimate future projections of HIV prevalence. We prove global stability of the disease-free equilibrium. We also prove global stability of the endemic equilibrium for the most general case of the model, i.e., which allows for PrEP individuals to default. We include insightful simulations based on recently published South-African data

On the probability of extinction of the Haiti cholera epidemic

More than three years after its appearance in Haiti, cholera has already caused more than 8,500 deaths and 695,000 infections and it is feared to become endemic. However, no clear evidence of a stable environmental reservoir of pathogenic Vibrio cholerae, the infective agent of the disease, has emerged so far, suggesting the possibility that the transmission cycle of the disease is being maintained by bacteria freshly shed by infected individuals. Should this be the case, cholera could in principle be eradicated from Haiti. Here, we develop a framework for the estimation of the probability of extinction of the epidemic based on current information on epidemiological dynamics and health-care practice. Cholera spreading is modeled by an individual-based spatially-explicit stochastic model that accounts for the dynamics of susceptible, infected and recovered individuals hosted in different local communities connected through hydrologic and human mobility networks. Our results indicate that the probability that the epidemic goes extinct before the end of 2016 is of the order of 1 %. This low probability of extinction highlights the need for more targeted and effective interventions to possibly stop cholera in Haiti

Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals.

This paper presents a sex-structured model for heterosexual transmission of HIV/AIDS in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number (R0), are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold R0, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces R0, thus can help slow or eradicate the epidemic

Age and sex structured model for assessing the demographic impact of mother-to-child transmission of HIV/AIDS.

Age and sex structured HIV/AIDS model with explicit incubation period is proposed as a system of delay differential equations. The model consists of two age groups that are children (0-14 years) and adults (15-49 years). Thus, the model considers both mother-to-child transmission (MTCT) and heterosexual transmission of HIV in a community. MTCT can occur prenatally, at labour and delivery or postnatally through breastfeeding. In the model, we consider the children age group as a one-sex formulation and divide the adult age group into a two-sex structure consisting of females and males. The important mathematical features of the model are analysed. The disease-free and endemic equilibria are found and their stabilities investigated. We use the Lyapunov functional approach to show the local stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The basic reproductive number ([Symbol: see text](0)) for the model shows that the adult population is responsible for the spread HIV/AIDS epidemic, thus up-to-date developed HIV/AIDS models to assess intervention strategies have focused much on heterosexual transmission by the adult population and the children population has received little attention. We numerically analyse the HIV/AIDS model to assess the community benefits of using antiretroviral drugs in reducing MTCT and the effects of breastfeeding in settings with high HIV/AIDS prevalence ratio using demographic and epidemiological parameters for Zimbabwe

Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe.

We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which are shown to be equivalent to delay differential equations with a time delay due to incubation period. The sex-structured HIV/AIDS model divides the population into a two sex-structure consisting of females and males. The threshold and equilibria for the model are determined and stabilities are examined. We extend the model to focus on the effects of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. Initially we model the use of male condoms and further extend the model to incorporate the use of both female and male condoms. The model includes two primary factors in condom use to control HIV that are condom efficacy and compliance. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. The models are numerically analysed to assess the effectiveness of condom use on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters for Zimbabwe. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of female and male condom use as a preventative strategy in a heterosexually active population

HIV/AIDS MODEL FOR ASSESSING THE EFFECTS OF PROPHYLACTIC STERILIZING VACCINES, CONDOMS AND TREATMENT WITH AMELIORATION

HIV/AIDS vaccination model for heterosexual transmission with explicit incubation period is presented as a system of delay differential equations. The model considers prophylactic vaccination of sexually immature (pre- and early-adolescents) and mature susceptibles in a community. We start by formulating and analyzing an HIV/AIDS vaccination model that we extend to incorporate condom use based on efficacy and compliance. Further, we extend HIV/AIDS vaccination model with condom use by incorporating treatment which allows AIDS patients to undergo amelioration. The thresholds and equilibria for the models are determined, and stabilities analyzed. The basic reproductive numbers for the models are computed and compared to assess the possible community benefits of using prophylactic vaccines, condoms and treatment with amelioration of AIDS patients. We conclude from the study that vaccination and condom use can reduce the basic reproductive number [Formula: see text] to values below unity but treatment with amelioration intended to lengthen the lives of AIDS patients may result in more numbers of HIV infections and fail to reduce [Formula: see text] to values less than unity as intended for disease control. </jats:p

Asymptotic properties of an HIV/AIDS model with a time delay

A mathematical model for HIV/AIDS with explicit incubation period is presented as a system of discrete time delay differential equations and its important mathematical features are analysed. The disease-free and endemic equilibria are found and their local stability investigated. We use the Lyapunov functional approach to show the global stability of the endemic equilibrium. Qualitative analysis of the model including positivity and boundedness of solutions, and persistence are also presented. The HIV/AIDS model is numerically analysed to asses the effects of incubation period on the dynamics of HIV/AIDS and the demographic impact of the epidemic using the demographic and epidemiological parameters for Zimbabwe. © 2006 Elsevier Inc. All rights reserved