Search

Understanding HIV-1 replication and latency in different reservoirs is an ongoing challenge in the care of patients with HIV/AIDS. A mathematical model was created to describe and predict the viral dynamics of HIV-1 and SIV infection within the brain during effective combination antiretroviral therapy (cART). The mathematical model was formulated based on the biology of lentiviral infection of brain macrophages and used to describe the dynamics of transmission and progression of lentiviral infection in brain. Based on previous reports quantifying total viral DNA levels in brain from HIV-1 and SIV infections, estimates of integrated proviral DNA burden were made, which were used to calibrate the mathematical model predicting viral accrual in brain macrophages from primary infection. The annual rate at which susceptible brain macrophages become HIV-1 infected was estimated to be 2.90×10-4.87×10 per year for cART-treated HIV/AIDS patients without comorbid neurological disorders. The transmission rate for SIV infection among untreated macaques was estimated to be 5.30×10-1.37×10 per year. An improvement in cART effectiveness (1.6-48%) would suppress HIV-1 infection in patients without neurological disorders. Among patients with advanced disease, a substantial improvement in cART effectiveness (70%) would eradicate HIV-1 provirus from the brain within 3-32 (interquartile range 3-9) years in patients without neurological disorders, whereas 4-51 (interquartile range 4-16) years of efficacious cART would be required for HIV/AIDS patients with comorbid neurological disorders. HIV-1 and SIV provirus burdens in the brain increase over time. A moderately efficacious antiretroviral therapy regimen could eradicate HIV-1 infection in the brain that was dependent on brain macrophage lifespan and the presence of neurological comorbidity. [ABSTRACT FROM AUTHOR]

Abstract: Anti-retroviral treatments (ART) such as HAART have been used to control the replication of HIV virus in HIV-positive patients. In this paper, we study an in-host model of HIV infection with ART and carry out mathematical analysis of the global dynamics and bifurcations of the model in different parameter regimes. Among our discoveries is a parameter region for which backward bifurcation can occur. Biologically, the catastrophic behaviors associated with backward bifurcations may explain the sudden rebound of HIV viral load when ART is stopped, and possibly provide an explanation for the viral blips during ART suppression of HIV. [Copyright &y& Elsevier]

The cytotoxic T lymphocyte (CTL) response to the infection of CD4 T cells by human T cell leukemia virus type I (HTLV-I) has previously been modelled using standard response functions, with relatively simple dynamical outcomes. In this paper, we investigate the consequences of a more general CTL response and show that a sigmoidal response function gives rise to complex behaviours previously unobserved. Multiple equilibria are shown to exist and none of the equilibria is a global attractor during the chronic infection phase. Coexistence of local attractors with their own basin of attractions is the norm. In addition, both stable and unstable periodic oscillations can be created through Hopf bifurcations. We show that transient periodic oscillations occur when a saddle-type periodic solution exists. As a consequence, transient periodic oscillations can be robust and observable. Implications of our findings to the dynamics of CTL response to HTLV-I infections in vivo and pathogenesis of HAM/TSP are discussed. [ABSTRACT FROM AUTHOR]

Abstract: Human T-cell leukaemia virus type I (HTLV-I) preferentially infects the CD4+ T cells. The HTLV-I infection causes a strong HTLV-I specific immune response from CD8+ cytotoxic T cells (CTLs). The persistent cytotoxicity of the CTL is believed to contribute to the development of a progressive neurologic disease, HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP). We investigate the global dynamics of a mathematical model for the CTL response to HTLV-I infection in vivo. To account for a series of immunological events leading to the CTL response, we incorporate a time delay in the response term. Our mathematical analysis establishes that the global dynamics are determined by two threshold parameters and , basic reproduction numbers for viral infection and for CTL response, respectively. If , the infection-free equilibrium is globally asymptotically stable, and the HTLV-I viruses are cleared. If , the asymptomatic-carrier equilibrium is globally asymptotically stable, and the HTLV-I infection becomes chronic but with no persistent CTL response. If , a unique HAM/TSP equilibrium exists, at which the HTLV-I infection is chronic with a persistent CTL response. We show that the time delay can destabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and stable periodic oscillations. Implications of our results to the pathogenesis of HTLV-I infection and HAM/TSP development are discussed. [Copyright &y& Elsevier]

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease, and adult T-cell leukemia (ATL). Chronically infected individuals often harbor high proviral loads despite maintaining a persistently activated immune response. Based on a new hypothesis for the persistence of HTLV-I infection, a three-dimensional compartmental model is constructed that describes the dynamic interactions among latently infected target cells, target-cell activation, and immune responses to HTLV-I, with an emphasis on understanding the role of Tax expression in the persistence of HTLV-I. [ABSTRACT FROM AUTHOR]

Abstract: We consider a mathematical model for HIV/AIDS that incorporates staged progression and amelioration. Amelioration as a result of HAART treatment is allowed to occur across any number of stages. The global dynamics are completely determined by the basic reproduction number . If , then the disease-free equilibrium (DFE) is globally asymptotically stable and the disease always dies out. If , DFE is unstable and a unique endemic equilibrium (EE) is globally asymptotically stable, and the disease persists at the endemic equilibrium. The proof of global stability utilizes a global Lyapunov function. [Copyright &y& Elsevier]

Abstract: We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number . More specifically, we prove that, if , then the disease-free equilibrium is globally asymptotically stable; if , then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals. [Copyright &y& Elsevier]

Mesenchymal motion denotes a form of cell movement through tissue which can be observed for certain cancer metastases. In [T. Hillen, J. Math. Biol., 53 (2006), pp. 585-616], a mathematical model for this form of movement was introduced. In the current paper we present a comprehensive analysis of the one-dimensional mesenchymal motion model. We establish the global existence of classical solutions and rigorously carry out the parabolic limit of the model. We discuss the stationary solutions, prove the existence of traveling wave solutions, and use numerical simulations to illustrate the results. Finally, we discuss the biological implications of the results. [ABSTRACT FROM AUTHOR]