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The primary objective of this paper is to conduct an in-depth analysis of the intricacies inherent in a gender-structured model depicting the dynamics of HIV–TB coinfection. The model is articulated through a set of nonlinear fractional-order differential equations. Our focus is on elucidating the stability characteristics around equilibrium points, employing advanced fractional stability techniques. We leverage sensitivity analysis as a powerful tool to discern the specific model parameters exerting significant influence on the transmission and control of the coinfection, as gauged by the basic reproduction number. Through this, we aim to identify key factors that drive the spread or containment of the dual affliction. Furthermore, we delve into the realm of optimization by formulating a fractional optimal control problem. The objective is to design and implement two control strategies that effectively mitigate the prevalence of coinfection, demonstrating a state of perfect protection. Notably, our findings reveal that the implementation of control measures at a rate exceeding 80% suffices to eliminate the infection entirely. We anticipate that the insights garnered from this research will prove instrumental for policymakers in crafting strategic interventions to curtail the tragic impact of HIV–TB coinfection. Our scientifically grounded study serves as a foundation upon which comprehensive plans can be devised to stem the devastating consequences of this dual health challenge. [ABSTRACT FROM AUTHOR]

Reverse transcriptase (RT) and integrase (IN) are two pivotal enzymes in HIV-1 replication. RT converts the single-stranded viral RNA genome into double-stranded DNA and IN catalyzes the integration of viral double-stranded DNA into host DNA. Currently, dual inhibitors of HIV-1 RT and IN have become a hotspot in new anti-HIV drug research and development. A dual inhibitor of HIV-1 RT/IN does the same thing as the two independent drugs would do. In this paper, we develop a mathematical model comprising a system of nonlinear differential equations describing HIV-1 RT/IN catalyzed biochemical reactions based on Michaelis–Menten enzyme kinetic reaction. In the formulated model we incorporate HIV-1 RT/IN dual inhibitor which simultaneously works as a non-nucleoside RT inhibitor and IN inhibitor. To examine the efficacy of HIV-1 RT/IN dual inhibitor in the treatment of HIV-1 infection, we have introduced a one-dimensional impulsive differential equation model and determined an effective dosing regimen for applying the inhibitor numerically. Furthermore, the exact closed form solution of the impulsive differential equation model is carried out by using the Lambert W function and the local stability of the periodic solution is also obtained analytically. The results obtained from analytical as well as numerical studies provide a basic idea to investigate the minimum dose with the highest efficacy for administering HIV-1 RT/IN dual inhibitors to prevent HIV-1 infection. [ABSTRACT FROM AUTHOR]

In this paper, an HIV infection model with eclipse phase, humoral immune response and immunological delay has been discussed. By studying the characteristic equations of the model, the local stability analysis of various equilibrium points has been explored. Treating the delay as the bifurcation parameter, it has been shown that the delay can destabilize the stability of the infected steady-state leading to Hopf bifurcation and periodic solutions. By using Lyapunov functionals and LaSalle's invariance principle, the global stability analysis of the boundary equilibrium points has also been explored. It has also been shown numerically that the inclusion of the drug therapy in the model generates sporadic outbursts of virus called viral blips. In the end, numerical simulations have been employed to justify the analytical results proved in the paper. Biologically, the proposed model can explain the presence of viral blips in the system, during the introduction of HAART, as observed in the HIV-infected patient. These blips could mark the viral advancement in the system, thus resulting in complete immunological failure. One of the reasons for these viral blips can be the presence of delay in the activation of immunological response. But the development of drug-resistive virus could also be the reason for this sudden rise in viral loads. Moreover, the incorporation of the delay in the model generates oscillations and periodicity in the model, thus validating the long latency period seen in most HIV-infected patients. Also, a longer delay in the activation of immune response marks a viral advancement in the viral timeline resulting in viral blips, which signify the evolution of the virus. [ABSTRACT FROM AUTHOR]

In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two equilibria, whose existence is characterized by means of the basic reproduction number R 0 . The global stability of each equilibrium is proven by using the Lyapunov method. The effects of impairment of B-cell functions and of antiviral treatment on the human immunodeficiency virus (HIV) dynamics are studied. We have shown that if the functions of B-cell are impaired, then the concentration of HIV increases in the plasma. Moreover, we have determined the minimal drug efficacy which is required to reduce the concentration of HIV particles to a lower level. We have shown that a more accurate computation of drug efficacy can be performed by using our proposed model. Our theoretical results are illustrated by means of numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study the application of a pulse vaccination strategy to eradicate hepatitis B and C modeled by SIV epidemic model. Since infection age is an important factor of hepatitis progression, we incorporate the infection age into the model. In this model, we consider the infectiousness of latent individuals. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p and interpulse time T. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of hepatitis B and C. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV. [ABSTRACT FROM AUTHOR]

This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+ T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for the effect of drug therapy on the in-host dynamics of HIV is considered and analyzed. As the process of reverse transcription is highly error prone, it causes mutation of virus which results in the emergence of drug resistant virus. This is also accounted in the model and corresponding model with both drug resistant and drug sensitive viral strains is studied. We found that, if reproductive ratios for both the strains are less than one, the virus population goes to extinction. If the reproductive ratio of either strain is greater than one and the reproductive ratio of drug resistant virus is smaller than that of drug sensitive virus then both the virus strains persist and infection is not cleared. However if reproductive ratio of drug resistant virus is greater than that of drug sensitive virus then the drug resistant virus out-competes the drug sensitive virus and only drug resistant virus survives. Hence the ratio of two reproduction ratios works as invading capacity threshold value for drug resistant strain. We also noted that by increasing the effective efficacy of the drug, virus may be cleared. Numerical simulations are performed to support and elaborate the analytical findings. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the global dynamics of a simple SI model with two explicit age groups and apply the findings to the HIV dynamics in the United States. Specifically, we would like to explore the long term HIV dynamics to answer questions such as what will happen to human population level if all the demographical and epidemiological parameters stay constant. We also wonder if treatment alone will actually slow the spread of HIV or not. We divide the population into juvenile and adult groups. Only adults are assumed to be sexually active and we implicitly assume that the sex ratio is constant. We also assume that infected adults may produce both susceptible newborns and infected newborns. The model is fit with parameters from the HIV epidemic in the US. It produces an optimistic outcome: if nothing changes, the USA infected population may be halved in about 20 years. However, if treatment is found to extend the life expectance of infected individuals to 30 years or more, then the number of infected adults may actually increase in the next 20 years or so. This creates a dilemma: to treat or not to treat? [ABSTRACT FROM AUTHOR]

We present a review and comparison of several recent differential equations models of treatment of HIV-1 infection. We seek to clarify the role of the natural anti-HIV immune response and determine its effect upon optimal treatment schemes. In this paper, we consider systems in which treatment is expressed as a forcing function, as well as those in which we determine optimal treatment via control theoretic techniques. The primary goal of this study is to compare treatment schemes for systems in which a natural nonconstant immune response of the patient is considered explicitly with those that consider implicitly a constant non-specific immune response. We find that when the natural immune response can be boosted sufficiently, drug levels may not need to be as high as previously supposed. This implies that a treatment scenario in which intervals of drug treatment are alternated with some form of immune-boosting therapy may be highly beneficial in terms of reducing toxicity to the patient. Additionally, in developing countries where HIV infection is widespread and sufficient funds are not available to supply rigourous drug regimens, the implications of these models are profound, as they suggest methods of treating HIV at a minimal cost. [ABSTRACT FROM AUTHOR]

In this paper, neglecting the effects of free virus, we consider a simple model of cell-to-cell spread of HIV-1. We discuss the impact of the CD8+ cell non-cytotoxic anti-viral response (CNAR) and cytotoxic T lymphocyte (CTL) activity on infection by HIV-1. Two types of models are considered: the ordinary differential equation (ODE) model and the discrete time delay differential equation (DDE) system. The steady states of the ODE model are globally asymptotically stable respectively under two threshold criteria. In the DDE model, the global stability of the infected steady state of the ODE model becomes only ultimately stable. Moreover, at a certain interval of the time delay, the DDE model will produce Hopf bifurcation or periodic solutions. The introduction of CTL and CNAR will change the values of these steady states and induce fluctuations in the cell concentration. It also affects the critical value of the time delay and is of utility in the interpretation of typical HIV-dynamics data resulting from clinical trials. The DDE model produces sustained infective oscillations in some real parameter values, which is different from the result of the similar cell-free viral spread model with delay. [ABSTRACT FROM AUTHOR]

A model for assessing the impact of key population at risk in spreading HIV/ AIDS is designed. The model is shown to have a globally asymptotically stable (GAS) disease-free equilibrium whenever the associated reproduction number is less than unity. It has a unique GAS endemic equilibrium whenever reproduction number exceeds unity, if there is no back and forth movement in susceptible classes. It is shown that if infected individuals with high risk abandon their risky behavioral practices, then the disease burden will reduce. Furthermore, if infected individuals with low risk do not adopt risky behaviors then the transmission of the disease will decrease. Partial Rank Correlation Coefficient (PRCC) indices are assessed using all the infection-related classes and basic reproduction number of the model. Uncertainty and sensitivity analysis results show that controlling the effective contact rate, disease-induced death rate in AIDS stage with low and high risk classes will help controlling the transmission of the disease. [ABSTRACT FROM AUTHOR]

Successful immunologic control of HIV infection can be achieved in long-term non-progressors or HIV-1 controllers. Dendritic cells (DCs) are required for specific antigen presentation to naïve T lymphocytes and for antiviral, type I interferon secretion. To understand this mechanism, we develop a mathematical model that describes the role of direct presentation (replicating virus-infected DCs or other CD 4 + T cells directly) and cross presentation (DCs obtain antigen processed in other infected cells such as CD 4 + T lymphocytes) during HIV-1 infection. We find equilibria and determine stability in the case of no vaccination, and then, when vaccination is taken, we determine analytical thresholds for the strength and frequency of the vaccine to ensure the disease-free equilibrium remains stable. Our theoretical results suggest that the restoration of DC numbers may be predictive of immune restoration and may be a goal for immunotherapy to enhance viral control in a larger proportion of patients. [ABSTRACT FROM AUTHOR]

We formulate a mathematical model to study the dynamics of HIV-1 related Kaposi's Sarcoma (KS) pathogenesis. KS progression is modeled as a dual process involving the primary infection of B cells, which sustains HHV-8 replication and the secondary infection of progenitor cells by HHV-8, which sustains the KS cell replication. We incorporate the pharmacodynamics of highly active antiretroviral therapy (HAART), or combination therapy (HAART plus KS therapy) and consider how each treatment strategy alters the disease progression. Our results indicate that administration of HAART to individuals co-infected with the HIV-1 and HHV-8 viruses can greatly amplify the therapeutic response of low-dose KS therapies. We have found that adherence levels above 85% can significantly reduce the risk of KS and HIV for a treatment periods under 1 year. For longer treatment periods, however, at least 90% adherence level is recommended. [ABSTRACT FROM AUTHOR]

We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution. [ABSTRACT FROM AUTHOR]

Analysis of changes in viral load after initiation of treatment with potent antiretroviral agents has provided substantial insights into the dynamics of human immunodeficiency virus type 1. We built a simple mathematics model to study the effect of latent-infected resting memory CD4+ T cells during the HIV infection and highly active anti-retroviral therapy (HAART). Through analysis of eight patients who received HAART in China, we have an insight into the mechanisms of resting memory CD4+ T cells in HIV infection. Simulations show that new infections still exist in the eight patients even under the HAART. Also, because of the long half-life of resting infected memory CD4+ T cells, removal of HIV from patient could take considerably longer time or be unattainable. [ABSTRACT FROM AUTHOR]

A mathematical model for the effect of Reverse Transcriptase (RT) Inhibitor on the dynamics of HIV is proposed and analyzed. Further, with help of numerical simulations, the relation between efficacy of administered drug, the total number of virus particles emitted from the infected cell and the transition period is also discussed. [ABSTRACT FROM AUTHOR]

Human Immunodeficiency Virus type-1 (HIV-1) fuels the pathogenesis of Mycobacterium tuberculosis (Mtb) in humans. We develop a mathematical model in an attempt to understand the immune mechanisms that are involved during the co-infection of Mtb and HIV-1. Our study reveals that infection of an Mtb infected individual with HIV-1 results in fast development of active TB. The mathematical model analysis and simulations show that Mtb infection is linked to HIV infection through macrophages and CD4+ T cells. The study shows that depletion of macrophages and CD4+ T cells by HIV-1 worsens the picture of Mtb infection and in-turn Mtb infection affects the progression of HIV-1 infection since it is also capable of inducing rapid replication of HIV. Our analytical and numerical simulations show that macrophages are a potential reservoir of HIV particles during HIV-1 infection. Co-infection simulations reveal that co-infection exacerbates more the pathogen that caused the first infection. Simulations also show that co-infection disease progression patterns converge to a similar trend after a considerable time interval irrespective of which pathogen first caused infection and the second pathogen that caused co-infection. This work suggests directions for further studies and potential treatment strategies. [ABSTRACT FROM AUTHOR]

Cancer remains a significant burden in HIV-infected individuals. We present an HIV-1 dynamical model which incorporates the AIDS-related cancer cells in vivo. The model consists of four components: cancer cells, healthy CD4+ T-lymphocytes, infected CD4+ T-lymphocytes and free HIV-1 virus. We discuss the existence, the stability properties and the biological meanings of the model's steady states, in particular the positive cancer-HIV steady state. We find that Hopf bifurcation of the positive steady state can exist, which lead to periodic solutions, sequences of period doubling bifurcations and the appearance of chaos. We also prove theoretically that HIV-1 is of help in the growth of cancer. The result fits very well with the clinical observations that several different types of cancer are observed at an increased frequency in HIV-1 infection individuals. [ABSTRACT FROM AUTHOR]