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A mathematical model approach to control the spread of HIV and AIDS is needed to predict the future effect of HIV and AIDS on work productivity. In this paper, we consider the analysis of fractional-order mathematical models of the spread of HIV with productivity in the workplace. First, we estimate the epidemiological parameters of the HIV/AIDS model using the annual data of AIDS reported in Indonesia from 2006 to 2018. Based on the model analysis, two equilibria are determined, namely the HIV disease-free and endemic equilibrium's. The disease-free equilibrium of HIV is locally asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium is globally asymptotically stable if the reproduction number is greater than one. The sensitivity analysis and numerical simulations are then carried out with variations in fractional order values to determine the dynamics of HIV spread with on-site productivity. Based on numerical simulation results, it was found that the transition rate of HIV-productive workers to AIDS sufferers could reduce the labor population of people living with AIDS and increase the workforce population vulnerable to HIV infection. [ABSTRACT FROM AUTHOR]

The spreading of HIV or HTLV-I among the cells has received the great attention in recent modelling study to explore the virus infection dynamics. The co-infection of HIV and HTLV-I with the effect of Cytotoxic T-lymphocytes (CTLs) immune response is also important from epidemiological point of view. To identify the co-infection scenario of HIV and HTLV-I with the CTLs effect we proposed in this paper a six compartmental ODE-model with uninfected, HIV-infected, HTLV-I infected CD4+T cells and free HIV virus particles with HIV specific CTLs and HTLV-I specific CTLs. The rates of infection of the cases are considered here saturated type and proliferation rate of uninfected and HIV infected CD4+ T-cells are of logistic terms. To establish the well-posedness of the model we have shown that the solution of the proposed model is non-negative and bounded. We obtain the basic reproduction number which is the maximum of the HIV-related reproduction and the HTLV-I related reproduction number. Along with the disease free equilibrium point the system contains other seven endemic equilibrium points containing infection by single disease or both. Analytically, we establish the local and global stability conditions of the equilibrium points and also we establish that the system experiences transcritical bifurcation by the generation of only HIV or HTLV-I infected endemic equilibrium point. Using numerical simulations, we validate the theoretical results and found two infection paths, one initiating with HIV and other with HTLV-I, both cases ultimately become co-infected. Finally, using the optimal control analysis we found the optimal policy for treatment using AVR, RTI & PI for HIV or AZT for HTLV-I control and lastly concluded by some recommendations. • A co-infected HIV & HTLV-I infection model in vivo. • Proliferation of CD4+ T-cells are taken in logistic form. • Incidence rate is taken as saturated type. • Verified competitive exclusive principle. • Spreading path has been studied using Flow-diagram. • Three types of control strategies are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we study the global well-posedness and global dynamics of a reaction–diffusion HIV infection model with the chemotactic movement of CTLs (Cytotoxic T lymphocytes). We first show the global existence and uniform boundedness for solutions of the system with general functional incidences. Then, for the model with bilinear incidence rate, we discuss the existence conditions of the three equilibria (infection-free, chemokines-extinct, chemokines-acute equilibria) of the model and obtain the conclusion of the local asymptotic stability of these equilibria by analyzing the linearized system at these equilibria. Moreover, by constructing reasonable Lyapunov functionals, we investigate the global stability and attractivity of the equilibria. Applying the L p − L q estimate, Young's inequality, Gagiardo-Nirenberg inequality and the parabolic regularity theorem, we also discuss the convergence rates of the equilibria. Finally, some numerical simulations are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Antiretroviral (ART) drugs have been used to treat HIV patients over last two decades. But, the daily use of these drugs in order to control HIV load in patients' body results different side effects and high cost over long period of time. Motivated by these, researchers have been trying to find other treatment strategy whose combination with antiretroviral treatments can control HIV without use of large quantities of drugs. Immunotherapy is one of such treatment which assist natural immune system of patients in order to get control over viral infection. Administration of immunotherapy in combination with antiretroviral drugs has been found safe and effective after different clinical trials on humans and other animals. In this paper, we propose a mathematical model to describe HIV dynamics under antiretroviral treatment and immunotherapy combination. We find that our model is biologically feasible and the findings of the clinical trials support the dynamics of our model. The stability analyses of HIV-free equilibrium point are performed and found the basic reproduction number as a threshold parameter. Also, we calculate a critical efficacy for overall antiretroviral treatment such that when the efficacy of overall treatment exceeds this value HIV will be completely removed. Also, we have found that critical drug efficacy for antiretroviral drugs decreases with increasing immunotherapy, which indicates combination of immunotherapy with antiretroviral treatments minimize the quantity of antiretroviral drugs for HIV eradication, hence minimize the side effects and cost of antiretroviral drugs. Numerical simulations are carried out to substantiate the analytical results and to illustrate different drug administration scenarios. Moreover, an optimal combination of drugs which can control HIV with lower costs and side effects, is obtained by solving an optimal control problem numerically. [ABSTRACT FROM AUTHOR]

In this paper, an epidemic model with homogeneous Dirichlet boundary condition is formulated to study the joint impact of spatial diffusion, infection age and treatment adherence on the HIV/AIDS transmission among humans. It is an interesting problem to understand the threshold dynamics of HIV/AIDS model with the above three factors. Since the complexity of the model and specificity of the boundary condition, there are two main mathematical challenges: i). the compactness of the solution map is not guaranteed; ii). the explicit expression of the basic reproduction cannot be given even if the parameters are spatially independent. We first discuss the well-posedness of the system, then we identify the basic reproduction number R 0 as the spectral radius of the next generation operator, followed by the global attractivity of disease-free steady state when R 0 < 1 , the uniform persistence of the disease and the existence of the endemic steady state when R 0 > 1. Numerical simulations are carried out to illustrate our theoretical results, which suggest that the diffusion of individuals has an opposite effect on the disease outbreaks, and improving the treatment compliance of HIV infected individuals can control HIV transmission among the population effectively. [ABSTRACT FROM AUTHOR]

Researches have shown that in addition to direct virus-to-cell infection, viral particles can also be transferred from a productively-infected cell to an uninfected cell through the formation of virological synapses. In order to reduce the viral load in infected individuals, different classes of antiretroviral drugs have been developed, including reverse transcriptase inhibitor (RTI), integrase inhibitor (II), protease inhibitor (PI) and so on. In this paper, we incorporate the mitotic proliferation of target cells which is described by the logistic term, both virus-to-cell infection and cell-to-cell transmission, the intracellular delay and RTI-based therapy into an in-host HIV infection model. Through mathematical analysis, we find that the model undergoes a backward bifurcation when the turn-over rate coefficient of productively-infected cells is smaller than its mitotic proliferation rate coefficient. When the turn-over rate coefficient of productively-infected cells is greater than its mitotic proliferation rate coefficient, the existence of Hopf bifurcation at the chronic-infection equilibrium with and without the intracellular delay is established, respectively. Numerical simulations suggest that the dynamics of the model be sensitive to parameter values and initial conditions, which may be of great significance to control HIV infection. We also show numerical evidence to support the fact that the smaller the therapy efficacy, the higher the viral load in infected individuals. [ABSTRACT FROM AUTHOR]

This paper considers an impulsive switching human immunodeficiency virus (HIV) infection model incorporating the mean-reverting Ornstein–Uhlenbeck process. The model involve the virus-to-cell infection and cell-to-cell transmission and has an explicit age-dependent structure. Due to the exact solution of this system cannot be expressed explicitly, it is necessary to give a suitable numerical method to discuss the numerical solution. In this paper, we apply the truncated Euler–Maruyama (EM) method to investigate the explicit numerical approximation for the impulsive stochastic age-structured HIV infection model with Markovian switching. We study the p th moment boundedness of the numerical solution, and the corresponding strong convergence of such algorithm. Numerical simulations are presented to demonstrate the validity of our findings. [ABSTRACT FROM AUTHOR]

This paper deals with the study of a virus dynamics model in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). RTIs prevent viral replication/entry within the infected CD4 + T cells while PIs block the virus assembly and thus further propagation and production of new virions. The proliferation of uninfected CD4 + T cells has been assumed to be as full logistic growth term to capture the dynamics of HIV virus. The model also considers two important components of the acquired immune response, namely the cytotoxic T lymphocyte (CTL) immune response (self stimulation due to infection and stimulation due to infected cells have been considered) and antibody immune response. Critical threshold conditions for the existence of equilibrium points have been determined. We studied the analytical behavior of these equilibrium points locally as well as globally using Lasalle’s invariance principle and Lyapunov’s direct method. We explored the sensitivity of the therapeutic drugs on the model system. Further, the behavior of the proposed model system has been studied numerically through simulation tools. [ABSTRACT FROM AUTHOR]

In this paper, we consider the dynamical behavior of a HIV-1 infection model with logistic growth for target cells, time delay and two predominant infection modes, namely the classical cell-free infection and the direct cell-to-cell transfer. It is proved the existence of the positive equilibrium E 2 in different conditions. By analyzing the characteristic equations and using stability theory of delay differential equations, we establish the local stability of the two boundary equilibria and the infected equilibrium of the model. The time delay does not affect the stability of the boundary equilibrium, but can change the stability of E 2 and lead to the occurrence of Hopf bifurcations. The direction and stability of bifurcating periodic solutions is also studied. Finally, the numerical simulations are carried out to explain our theorems. [ABSTRACT FROM AUTHOR]

HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations. [ABSTRACT FROM AUTHOR]

This paper studies some HIV (Human Immunodeficiency Virus) models with switching parameters and pulse control. By taking into account of the effects of reverse transcriptase inhibitor (RTI) drugs, protease inhibitor (PI) drugs and the variable transmission rate, we propose a new HIV model with switching parameters and derive a general threshold value that measures the persistence of the disease. Furthermore, pulse vaccination is applied to the HIV model and some novel threshold conditions are established to ensure the existence and stability of the periodic infection-free solution. In contrast to the standard HIV models, it is shown that our proposed models are more practical and useful. Moreover, pulse vaccination strategies are proven to be more effective in determining whether or not the disease is eradicated. Numerical simulations are carried out to illustrate the effectiveness of the obtained results, and future research directions are suggested. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce fractional-order derivatives into a model of HIV infection of CD4+ T-cells with time delay. We deal with the stability of both the viral free equilibrium and the infected equilibrium. Criteria are given to ensure that both the equilibria are asymptotically stable for all delay under some conditions. Numerical simulations are carried out to illustrate the results. [Copyright &y& Elsevier]

Abstract: A simple deterministic model is proposed to represent the basic aspects concerning the effects of different antiretroviral treatment schedules on HIV incidence and prevalence of affected populations. The model mimics current treatment guidelines applied in Brazil. However, the model does not intend to fit the data with any acceptable degree of accuracy since uncertainties on the values of the parameters and on the precise effect of the treatment put some limits on the practical implications of our model from which only orders of magnitude and some qualitative effects can be deduced. So, this paper intends to provide a conceptual and mechanistic understanding of the possible long-term effects of treatment on the dynamics of HIV transmission. According to the model, the effect of the treatment depends on the level of sexual activity of the subpopulations considered, being more pronounced on the subpopulations with the highest sexual activity levels. Also, inefficient treatment can be prejudicial depending on the level of sexual activity and on the capacity to provide adequate treatment coverages to the population affected. [Copyright &y& Elsevier]