Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity

Evidence-based modeling of combination control on Kenyan youth HIV/AIDS dynamics

We formulate a sex-structured deterministic model to study the effects of varying HIV testing rates, condom use rates and ART adherence rates among Adolescent Girls and Young Women (AGYW) and, Adolescent Boys and Young Men (ABYM) populations in Kenya. Attitudes influencing the Kenyan youth HIV/AIDS control measures both positively and negatively were considered. Using the 2012 Kenya AIDS Indicator Survey (KAIS) microdata we constructed our model, which we fitted to the UNAIDS-Kenya youth prevalence estimates to understand factors influencing Kenyan youth HIV/AIDS prevalence trends. While highly efficacious combination control approach significantly reduces HIV/AIDS prevalence rates among the youth, the disease remains endemic provided infected unaware sexual interactions persist. Disproportional gender-wise attitudes towards HIV/AIDS control measures play a key role in reducing the Kenyan youth HIV/AIDS prevalence trends. The female youth HIV/AIDS prevalence trend seems to be directly linked to increased male infectivity with decreased female infectivity while the male youth prevalence trend seems to be directly associated with increased female infectivity and reduced male infectivity.

Modeling the effects of contact tracing on COVID-19 transmission

In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The contact tracing-induced reproduction number R q and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The contact tracing-induced reproduction number R q is compared with the basic reproduction number R 0 for the model in the absence of any intervention to assess the possible benefits of the contact tracing strategy.

SIS and SIR Epidemic Models Under Virtual Dispersal

We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number [Formula: see text] is computed as a function of a patch residence-time matrix [Formula: see text]. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: There is a unique globally stable endemic equilibrium when [Formula: see text], while the disease-free equilibrium is globally stable when [Formula: see text]. Our further analysis indicates that the dispersal behavior described by the residence-time matrix [Formula: see text] has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence-time matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single-outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease-prevalence-driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state-dependent [Formula: see text] on disease dynamics.

Modelling Hepatotoxicity of Antiretroviral Therapy in the Liver during HIV Monoinfection

Liver related complications are currently the leading cause of morbidity and mortality among human immunodeficiency virus (HIV) infected individuals. In HIV monoinfected individuals on therapy, liver injury has been associated with the use of antiretroviral agents as most of them exhibit some degree of toxicity. In this study we proposed a mathematical model with the aim of investigating hepatotoxicity of combinational therapy of antiretroviral drugs. Therapy efficacy and toxicity were incorporated in the model as dose-response functions. With the parameter values used in the study, protease inhibitors-based regimens were found to be more toxic than nonnucleoside reverse transcriptase inhibitors-based regimens. In both regimens, the combination of stavudine and zidovudine was the most toxic baseline nucleoside reverse transcriptase inhibitors followed by didanosine with stavudine. However, the least toxic combinations were zidovudine and lamivudine followed by didanosine and lamivudine. The study proposed that, under the same second line regimens, the most toxic first line combination gives the highest viral load and vice versa.

THE EFFECTS OF VACCINATION AND TREATMENT ON THE SPREAD OF HIV/AIDS

This study investigates the effects of vaccination and treatment on the spread of HIV/AIDS. The objectives are (i) to derive conditions for the success of vaccination and treatment programs and (ii) to derive threshold conditions for the existence and stability of equilibria in terms of the effective reproduction number R. It is found, firstly, that the success of a vaccination and treatment program is achieved when R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α), where R0t and R0v are respectively the reproduction numbers for populations consisting entirely of treated and vaccinated individuals, R0 is the basic reproduction number in the absence of any intervention, RUT(α) and RVT(σ) are respectively the reproduction numbers in the presence of a treatment (α) and a combination of vaccination and treatment (σ) strategies. Secondly, that if R<1, there exists a unique disease free equilibrium point which is locally asymptotically stable, while if R>1 there exists a unique locally asymptotically stable endemic equilibrium point, and that the two equilibrium points coalesce at R=1. Lastly, it is concluded heuristically that the stable disease free equilibrium point exists when the conditions R0t<R0, R0t<R0v and γeRVT(σ)<RUT(α) are satisfied.

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.

HIV/AIDS MODEL ASSESSING THE EFFECTS OF GENDER-INEQUALITY AFFECTING WOMEN IN AFRICAN HETEROSEXUAL SETTINGS

A sex-structured model for heterosexual transmission of HIV/AIDS for addressing the epidemic as a gender-based issue in African heterosexual settings is presented. The epidemic threshold and equilibria for the model are determined and stabilities are investigated. Comprehensive qualitative analysis of the model including positivity and boundedness of solutions, as well as persistence are carried out. The epidemic threshold for the model is computed and used to assess the effects of gender-inequality affecting women in heterosexual settings. The obtained gender-inequality-induced reproductive number [Formula: see text] is greater than the reproductive number in the absence of gender-inequality [Formula: see text] suggesting that gender-inequality affecting women in heterosexual settings enlarges the HIV/AIDS epidemic. Numerical simulations are carried out using demographic and epidemiological parameters for Zimbabwe and the obtained results confirm that gender-inequality increases HIV/AIDS prevalence in heterosexual settings. We conclude from the study that gender-inequality affecting women among heterosexuals should be properly addressed for the effective control of the HIV/AIDS epidemic.

Mathematical models for the study of HIV spread and control amongst men who have sex with men

For a quarter of century, mathematical models have been used to study the spread and control of HIV amongst men who have sex with men (MSM). We searched MEDLINE and EMBASE databases up to the end of 2010 and reviewed this literature to summarise the methodologies used, key model developments, and the recommended strategies for HIV control amongst MSM. Of 742 studies identified, 127 studies met the inclusion criteria. Most studies employed deterministic modelling methods (80%). Over time we saw an increase in model complexity regarding antiretroviral therapy (ART), and a corresponding decrease in complexity regarding sexual behaviours. Formal estimation of model parameters was carried out in only a small proportion of the studies (22%) while model validation was considered by an even smaller proportion (17%), somewhat reducing confidence in the findings from the studies. Nonetheless, a number of common conclusions emerged, including (1) identification of the importance of assumptions regarding changes in infectivity and sexual contact rates on the impact of ART on HIV incidence, that subsequently led to empirical studies to gather these data, and (2) recommendation that multiple strategies would be required for effective HIV control amongst MSM. The role of mathematical models in studying epidemics is clear, and the lack of formal inference and validation highlights the need for further developments in this area. Improved methodologies for parameter estimation and systematic sensitivity analysis will help generate predictions that more fully express uncertainty, allowing better informed decision making in public health.

Mathematical analysis of a two strain HIV/AIDS model with antiretroviral treatment

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use.

Modeling HIV/AIDS and tuberculosis coinfection

An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for the AIDS cases and treatment of all forms of TB, i.e., latent and active forms of TB, is presented. We begin by presenting an HIV/AIDS-TB coinfection model and analyze the TB and HIV/AIDS submodels separately without any intervention strategy. The TB-only model is shown to exhibit backward bifurcation when its corresponding reproduction number is less than unity. On the other hand, the HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed to analyze the full HIV-TB coinfection model and extend the model to incorporate antiretroviral therapy for the AIDS cases and treatment of active and latent forms of TB. The thresholds and equilibria quantities for the models are determined and stabilities analyzed. From the study we conclude that treatment of AIDS cases results in a significant reductions of numbers of individuals progressing to active TB. Further, treatment of latent and active forms of TB results in delayed onset of the AIDS stage of HIV infection.

Modeling the population level effects of an HIV-1 vaccine in an era of highly active antiretroviral therapy

First generation HIV vaccines may have limited ability to prevent infection. Instead, they may delay the onset of AIDS or reduce the infectiousness of vaccinated individuals who become infected. To assess the population level effects of such a vaccine, we formulate a deterministic model for the spread of HIV in a homosexual population in which the use of highly active antiretroviral therapy (HAART) to treat HIV infection is incorporated. The basic reproduction number R(0) is obtained under this model. We then expand the model to include the potential effects of a prophylactic HIV vaccine. The reproduction number R(f) is derived for a population in which a fraction f of susceptible individuals is vaccinated and continues to benefit from vaccination. We define f(*) as the minimum vaccination fraction for which R(f )< or =1 and describe situations in which it equals the critical vaccination fraction necessary to eliminate disease. When R(0) is large or an HIV vaccine is only partially effective, the critical vaccination fraction may exceed one. HIV vaccination, however, may still reduce the prevalence of disease if the reduction in infectiousness is at least as great as the reduction in the rate of disease progression. In particular, a vaccine that reduces infectiousness during acute infection may have an important public health impact especially if coupled with counseling to reduce risky behavior.

Effects of treatment and drug resistance on the transmission dynamics of malaria in endemic areas

We present a mathematical model for malaria treatment and spread of drug resistance in an endemic population. The model considers treated humans that remain infectious for some time and partially immune humans who are also infectious to mosquitoes although their infectiousness is always less than their non immune counterparts. The model is formulated by considering delays in the latent periods in both mosquito and human populations and in the period within which partial immunity is lost. Qualitative analysis of the model including positivity and boundedness of solutions is performed. Analysis of the reproductive numbers shows that if the treated humans become immediately uninfectious to mosquitoes then treatment will always reduce the number of sensitive infections. If however treated humans are infectious then for treatment to effectively reduce the number of sensitive infections, the ratio of the infectious period of the treated humans to the infectious period of the untreated humans multiplied by the ratio of the transmission rate from a treated human to the transmission rate of an untreated human should be less than one. Our results show that the spread of drug resistance with treatment as a control strategy depends on the ratio of the infectious periods of treated and untreated humans and on the transmission rates from infectious humans with resistant and sensitive infections. Numerical analysis is performed to assess the effects of treatment on the spread of resistance and infection. The study provides insight into the possible intervention strategies to be employed in malaria endemic populations with resistant parasites by identifying important parameters.

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.

Potential Impact of Antiretroviral Therapy on HIV-1 Transmission and AIDS Mortality in Resource-Limited Settings

OBJECTIVE

To estimate the potential impact of antiretroviral therapy on the heterosexual spread of HIV-1 infection and AIDS mortality in resource-limited settings.

METHODS

A mathematic model of HIV-1 disease progression and transmission was used to assess epidemiologic outcomes under different scenarios of antiretroviral therapy, including implementation of World Health Organization guidelines.

RESULTS

Implementing antiretroviral therapy at 5% HIV-1 prevalence and administering it to 100% of AIDS cases are predicted to decrease new HIV-1 infections and cumulative deaths from AIDS after 10 years by 11.2% (inter-quartile range [IQR]: 1.8%-21.4%) and 33.4% (IQR: 26%-42.8%), respectively. Later implementation of therapy at endemic equilibrium (40% prevalence) is predicted to be less effective, decreasing new HIV-1 infections and cumulative deaths from AIDS by 10.5% (IQR: 2.6%-19.3%) and 27.6% (IQR: 20.8%-36.8%), respectively. Therapy is predicted to benefit the infected individual and the uninfected community by decreasing transmission and AIDS deaths. The community benefit is greater than the individual benefit after 25 years of treatment and increases with the proportion of AIDS cases treated.

CONCLUSIONS

Antiretroviral therapy is predicted to have individual and public health benefits that increase with time and the proportion of infected persons treated. The impact of therapy is greater when introduced earlier in an epidemic, but the benefit can be lost by residual infectivity or disease progression on treatment and by sexual disinhibition of the general population.

HIV treatment models with time delay

The present paper shows possible effects of antiretroviral treatment on the dynamics of the spread of the disease of human immunodeficiency virus infection in a population of varying size. By introducing time delays, we model the latency period and the delayed onset of positive treatment effects in the patients. The Hopf bifurcation and stability behaviour of the delay differential-equation model are analysed and simulations for different scenarios depending on the size of the treatment-induced delay are presented, and the results are discussed in detail.

Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity

Genetic studies report the existence of a mutant allele Delta32 of CCR5 chemokine receptor gene at high allele frequencies (approximately 10%) in Caucasian populations. The presence of this allele is believed to provide partial or full resistance to HIV. In this study, we look at the impact of education, temporarily effective vaccines and therapies on the dynamics of HIV in homosexually active populations. In our model, it is assumed that some individuals possess one or two mutant alleles (like Delta32 of CCR5) that prevent the successful invasion or replication of HIV. Our model therefore differentiates by genetic and epidemiological status and naturally ignores the reproduction process. Furthermore, HIV infected individuals are classified as rapid, normal or slow progressors. In this complex setting, the basic reproductive number R0 is derived in various situations. The separate or combined effects of therapies, education, vaccines, and genetic resistance are analyzed. Our results support the conclusions of Hsu Schmitz that some integrated intervention strategies are far superior to those based on a single approach. However, treatment programs may have effects which counteract each other, as may genetic resistance.

Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity

Several mutant genes in HIV co-receptors (e.g., CCR5, CCR2 and CXCR4) have been correlated with susceptibility to HIV or/and rate of progression to AIDS. Some of these genes have high allele frequencies in general populations. Their effects on the HIV/AIDS dynamics may be significant. To study such genetic heterogeneity, Hsu Schmitz [S.-F. Hsu Schmitz, A mathematical model of HIV transmission in homosexuals with genetic heterogeneity, J. Theoret. Med. (to appear)] proposed a one-sex model with susceptibles classified by genotype as having no, partial or full natural resistance to HIV infection and infecteds classified as rapid, normal or slow progressors. The example of CCR5-Delta32 mutation in San Francisco gay men indicated that the normal progressors are most responsible for disease spread. The per-partnership transmission rates of rapid and slow progressors are identified as key parameters. The present manuscript extends the previous one by considering the intervention of treatment or/and vaccination. Detailed investigations are illustrated by using the same example of CCR5-Delta32 mutation in San Francisco gay men. Treating only newly infected individuals or vaccinating only newly recruited susceptibles is not effective enough for disease control. When both measures are applied, the epidemic may be eradicated if the transmission rate of slow progressors is not too large, and treatments and vaccines in use are of decent quality.