Dynamical analysis of a multi-strain model of HIV in the presence of anti-retroviral drugs

One major drawback associated with the use of anti-retroviral drugs in curtailing HIV spread in a population is the emergence and transmission of HIV strains that are resistant to these drugs. This paper presents a deterministic HIV treatment model, which incorporates a wild (drug sensitive) and a drug-resistant strain, for gaining insights into the dynamical features of the two strains, and determining effective ways to control HIV spread under this situation. Rigorous qualitative analysis of the model reveals that it has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold (R t 0) is less than unity and that the disease will persist in the population when this threshold exceeds unity. Further, for the case where R t 0 > 1, it is shown that the model can have two co-existing endemic equilibria, and competitive exclusion phenomenon occurs whenever the associated reproduction number of the resistant strain (R t r) is greater than that of the wild strain (R t w). Unlike in the treatment model, it is shown that the model without treatment can have a family of infinitely many endemic equilibria when its associated epidemiological threshold (R(0)) exceeds unity. For the case when [Formula in text], it is shown that the widespread use of treatment against the wild strain can lead to its elimination from the community if the associated reduction in infectiousness of infected individuals (treated for the wild strain) does not exceed a certain threshold value (in this case, the use of treatment is expected to make R t w < R t r.     

On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population

In this paper, we examine an HIV/AIDS transmission model which has been widely used for studying the spread of HIV/AIDS through sexual contact. Some sufficient conditions are obtained for the uniqueness of endemic equilibrium. We also present a two-group model whose no-disease equilibrium is unstable but it has at least three positive endemic equilibria.     

Oscillatory viral dynamics in a delayed HIV pathogenesis model

We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that time delay has no effect on the local asymptotic stability of the uninfected steady state, but can destabilize the infected steady state, leading to a Hopf bifurcation to periodic solutions in the realistic parameter ranges.     

HIV RNA and proviral HIV DNA can be detected in semen after 6 months of antiretroviral therapy although HIV RNA is undetectable in blood

The risk of sexual transmission of HIV is strongly correlated with amounts of genital HIV RNA. Few studies have reported amounts of HIV RNA and HIV DNA in semen in HIV‐infected Chinese patients undergoing antiviral treatment (ART). In this observational study, the amounts of HIV RNA and HIV DNA in semen were assessed after six months of ART in HIV‐infected Chinese individuals, when HIV RNA was undetectable in blood . This study included 19 HIV‐infected Chinese men undergoing ART for six months. Amounts of HIV in paired semen and blood samples were assessed using real‐time PCR. The C2‐V5 region of the HIV envelope (env) genes was cloned and sequenced and genotype and co‐receptor usage predicted based on the sequence. It was found that HIV RNA was undetectable in the plasma of most patients (17/19), whereas HIV RNA could be detected in the semen of most patients (16/19). HIV DNA could be detected in both semen and blood. Genetic diversity of HIV between the seminal and blood compartments was identified. Thus, amounts of HIV RNA and HIV DNA remain high in semen of HIV‐infected Chinese patients after six months of ART treatment, even when HIV RNA was undetectable in blood.     

Modelling HIV/AIDS in the presence of an HIV testing and screening campaign

Preventing and managing the HIV/AIDS epidemic in South Africa will dominate the next decade and beyond. Reduction of new HIV infections by implementing a comprehensive national HIV prevention programme at a sufficient scale to have real impact remains a priority. In this paper, a deterministic HIV/AIDS model that incorporates condom use, screening through HIV counseling and testing (HCT), regular testing and treatment as control strategies is proposed with the objective of quantifying the effectiveness of HCT in preventing new infections and predicting the long-term dynamics of the epidemic. It is found that a backward bifurcation occurs if the rate of screening is below a certain threshold, suggesting that the classical requirement for the basic reproduction number to be below unity though necessary, is not sufficient for disease control in this case. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number R₀. Numerical simulations are performed and the model is fitted to data on HIV prevalence in South Africa. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long-term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed.     

Dynamical behaviour of a two-predator model with prey refuge

A three-component model consisting on one-prey and two-predator populations is considered with a Holling type II response function incorporating a constant proportion of prey refuge. We also consider the competition among predators for their food (prey) and shelter. The essential mathematical features of the model have been analyzed thoroughly in terms of stability and bifurcations arising in some selected situations. Threshold values for some parameters indicating the feasibility and stability conditions of some equilibria are determined. The range of significant parameters under which the system admits different types of bifurcations is investigated. Numerical illustrations are performed in order to validate the applicability of the model under consideration.     

Glycoproteomic analysis identifies human glycoproteins secreted from HIV latently infected T cells and reveals their presence in HIV+ plasma

Glycoproteins secreted into plasma from T cells infected with human immunodeficiency virus (HIV) latent infection may provide insight into understanding the host response to HIV infection in vivo. Glycoproteomics, which evaluates the level of the glycoproteome, remains a novel approach to study this host response to HIV. In order to identify human glycoproteins secreted from T cells with latent HIV infection, the medium from cultured HIV replication-competent T cells was compared with the medium from cultured parental A3.01 cells via solid phase extraction of glycopeptides (SPEG) and high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). Using these methods, 59 human glycoproteins were identified as having significantly different abundance levels between the media from these two cell lines. The relevance of these 59 proteins to HIV infection in vivo was assessed in plasma from HIV⁺ and HIV^- subjects. Comparison between T cell and plasma revealed that six glycoproteins (galectin-3-binding protein, L-selectin, neogenin, adenosine deaminase CECR1, ICOS ligand and phospholipid transfer protein) were significantly elevated in the HIV⁺ T cells and plasma studies. These findings suggest that the response of T cells harboring latent HIV infection contributed, in part, to the glycoprotein changes in HIV⁺ plasma. These proteins, once validated, could provide insight into host-HIV interaction.     

The complete classification for dynamics in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population was proposed by Li et al. in (J Math Biol 10:1037–1052, 1986). The sufficient and necessary conditions for coexistence and the sufficient conditions for stability of the boundary equilibria were provided. This paper will present a thorough classification of dynamics for this model in terms of the first and second so called reproductive numbers of infection in strains I and J. This classification not only solves a conjecture proposed in (Li et al., J Math Biol 10:1037–1052, 1986) but also gives the sufficient and necessary conditions for the competitive exclusion. Supported by the NSF of China grants 10531030 and 10671143.     

HIV vaccine development in the nonhuman primate model of AIDS

Development of a prophylactic human immunodeficiency virus type 1 (HIV-1) vaccine is a leading priority in biomedical research. Much of this work has been done with the nonhuman primate model of AIDS. In a historical context, vaccine studies, which use this model, are summarized and discussed.     

Dynamical analysis of a diffusion plant-wrack model with delay

In this paper, in view of the senescence of plant and the decay of wrack, time delays are introduced into the plant-wrack model. The effects of wrack decay and time delay on the dynamical behaviors of the diffusive plant-wrack model are studied analytically and numerically. When the delay is zero, the wrack decay will induce the change of stability of the unique equilibrium point, further lead to the occurrence of the Hopf bifurcation and the Turing instability. When the delay is present, the conditions for the occurrence of the Hopf bifurcation are established. By comparing the results of the model without and with delay, it is found that the increases of delay may induce no stability switches, a single stability switch or multiple stability switches, when the value of wrack decay can stabilize model with zero delay. When the value of wrack decay can destabilize model with zero delay, numerical simulations show that the small delay may cause homogeneous distributions of vegetation, while the larger delay may cause the emergence of periodic oscillation of vegetation. The obtained results provide a basis for understanding the spatiotemporal evolution of such a plant-wrack model with delay.     

Mathematical Study of a Staged-Progression HIV Model with Imperfect Vaccine

A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with therapeutic effect could have a positive or negative effect at the community level.     

Characterizing the symmetric equilibrium of multi-strain host-pathogen systems in the presence of cross immunity

We investigate the population dynamics of host-pathogen systems in which the pathogen has a potentially arbitrary number of antigenically distinct strains interacting via cross-immunity. The interior equilibrium configuration of the symmetric multiple strain SIR model with cross-immunity is characterized. We develop an efficient iterative method for numerically solving the equilibrium equation together with a number of informative analytical approximations to the full solution. Equilibrium properties are studied as a function of the number of strains, reproduction number, infectious period, and cross immunity profile. We establish that the prevalence in the system increases monotonically with the number of strains and the reduction in cross immunity. Moreover, we demonstrate the existence of a phase transition separating high prevalence and low prevalence parameter regions, with the critical point being defined by R₀1, where is the level of cross-immunity and R₀ is the reproduction number. Above the threshold, prevalence saturates with increasing numbers of strains as a result of the inclusion of prohibition of co-infection in the model. Below the threshold, prevalence saturates much more rapidly as the number of strains increases - indicating that when cross-protection is sufficiently intense, the selective advantage for a pathogen to increase its diversity is substantially less than in the threshold region. Similarly, there is limited benefit to increased transmissibility (or decreased cross-immunity) both for the high and low diversity pathogen systems compared with systems at the threshold R₀1 where small increase in transmissibility can result in significant increase in prevalence.     

Dynamical analysis of density-dependent selection in a discrete one-island migration model

A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus. Results for the existence and stability of polymorphic equilibria are established. Properties for a genetically important class of equilibria associated with complete dominance in fitness are described. The birth of an unusual chaotic attractor is also illustrated. This attractor is produced when migration causes chaotic dynamics on a boundary of phase space to bifurcate into the interior of phase space, resulting in bistable genetic polymorphic behavior.     

Dynamical behavior of a hepatitis B virus transmission model with vaccination

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R₀≤1, and a globally asymptotically stable endemic equilibrium when R₀>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.     

Paradoxical suppression of poly-specific broadly neutralizing antibodies in the presence of strain-specific neutralizing antibodies following HIV infection

One of the first immunologic responses against HIV infection is the presence of neutralizing antibodies that seem able to inactivate several HIV strains. Moreover, in vitro studies have shown the existence of monoclonal antibodies that exhibit broad crossclade neutralizing potential. Yet their number is low and slow to develop in vivo. In this paper, we investigate the potential benefits of inducing poly-specific neutralizing antibodies in vivo throughout immunization. We develop a mathematical model that considers the activation of families of B lymphocytes producing poly-specific and strain-specific antibodies and use it to demonstrate that, even if such families are successful in producing neutralizing antibodies, the competition between them may limit the poly-specific response allowing the virus to escape. We modify this model to account for viral evolution under the pressure of antibody responses in natural HIV infection. The model can reproduce viral escape under certain conditions of B lymphocyte competition. Using these models we provide explanations for the observed antibody failure in controlling natural infection and predict quantitative measures that need to be satisfied for long-term control of HIV infection.     

Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells

A mathematical model that describes HIV infection of CD4(+) T cells is analyzed. Global dynamics of the model is rigorously established. We prove that, if the basic reproduction number R(0) < or = 1, the HIV infection is cleared from the T-cell population; if R(0) > 1, the HIV infection persists. For an open set of parameter values, the chronic-infection equilibrium P* can be unstable and periodic solutions may exist. We establish parameter regions for which P* is globally stable.     

Considerations for a Human Rights Impact Assessment of a Population Wide Treatment for HIV Prevention Intervention

Increasing attention is being paid to the potential of anti‐retroviral treatment (ART) for HIV prevention. The possibility of eliminating HIV from a population through a universal test and treat intervention, where all people within a population are tested for HIV and all positive people immediately initiated on ART, as part of a wider prevention intervention, was first proposed in 2009. Several clinical trials testing this idea are now in inception phase. An intervention which relies on universally testing the entire population for HIV will pose challenges to human rights, including obtaining genuine consent to testing and treatment. It also requires a context in which people can live free from fear of stigma, discrimination and violence, and can access services they require. These challenges are distinct from the field of medical ethics which has traditionally governed clinical trials and focuses primarily on patient researcher relationship. This paper sets out the potential impact of a population wide treatment as prevention intervention on human rights. It identifies five human right principles of particular relevance: participation, accountability, the right to health, non‐discrimination and equality, and consent and confidentiality. The paper proposes that explicit attention to human rights can strengthen a treatment as prevention intervention, contribute to mediating likely health systems challenges and offer insights on how to reach all sections of the population.