Several lines of evidence suggest that HIV-1 is present in the thymus during HIV-1 infection. Precursors to mature CD4+ T lymphocytes develop in the thymus, which suggests that thymic infection may play a role in the CD4+ T-cell decline observed during the course of pediatric HIV-1 infection. We illustrate, through mathematical modeling, the potential effects of thymic infection on the course of pediatric AIDS disease progression. We find that infection in the thymus not only can supplement peripheral infection but can help explain the faster progression in pediatric cases, as well as the early and high viral burden.
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"Mathematical modelling has been introduced as a crucial tool to reveal underlying mechanisms for different viral infections. A huge amount of work has been invested to HIV, for which several models were proposed to understand the relation between HIV and the immune system [Kirschner et al., 1998, Perelson and Nelson, 1999, Nowak and May, 2000, Yates et al., 2007, Hernandez-Vargas and Middleton, 2013, Hernandez-Vargas et al., 2013]. Furthermore, many works have been attempting to quantify the dynamics of influenza virus infection [Möhler et al., 2005, Baccam et al., 2006, Beauchemin and Handel, 2011, Hernandez-Vargas et al., 2014, Pawelek et al., 2012] and Ebola virus infection [Nguyen et al., 2015]. "
[Show abstract][Hide abstract] ABSTRACT: Nowadays, infections by viral pathogens are one of the biggest health threats to mankind. The development of new avenues of thinking to integrate the complexity of infectious diseases and the immune system is urgently needed. Recently mathematical modelling has emerged as a tool to interpret experimental results on quantitative grounds providing relevant insights to understand several infectious diseases. Nevertheless, modelling the complex mechanisms between viruses and the immune system can result in models with a large number of parameters to be estimated. Furthermore, experimental measurements have the problem to be sparse (in time) and highly noisy. Therefore, structural and practical identifiability are key obstacles to overcome towards mathematical models with predictive value. This paper addresses the identifiability limitations in the most common mathematical model to represent viral infections. Additionally, numerical simulations reveal how initial conditions of differential equations and fixing parameter values can alter the profile likelihood.
"Significant efforts have been made in order to understand and to characterize the underlying mechanism of the disease. Earlier mathematical framework has been considered to model HIV/AIDS dynamics focusing on the viral and CD4 T-cells dynamics [3–11]and the references therein. Recently, there has been some work to explore the impact of the immune response in the HIV dynamics [12–15]. "
[Show abstract][Hide abstract] ABSTRACT: Objectives
Mathematical models can be helpful to understand the complex dynamics of human immunodeficiency virus infection within a host. Most of work has studied the interactions of host responses and virus in the presence of active cytotoxic immune cells, which decay to zero when there is no virus. However, recent research highlights that cytotoxic immune cells can be inactive but never be depleted.
We propose a mathematical model to investigate the human immunodeficiency virus dynamics in the presence of both active and inactive cytotoxic immune cells within a host. We explore the impact of the immune responses on the dynamics of human immunodeficiency virus infection under different disease stages.
Standard mathematical and numerical analyses are presented for this new model. Specifically, the basic reproduction number is computed and local and global stability analyses are discussed.
Our results can give helpful insights when designing more effective drug schedules in the presence of active and inactive immune responses.
"A number of previous works have examined some aspects of HIV infection, for example (Hazenberg et al., 2003; Ye et al., 2004; Wang, 1997; Turville et al., 2002; Letvin and Walker, 2003; Chun et al., 1997; Cloyd et al., 2000; Kirschner et al., 1998; Grossman et al., 2002; Yates et al., 2007; Hougue et al., 2008; Ferreira et al., 2011). These and other works present a basic relation between CD4þT cells, infected CD4 þT cells and viral load (Kirschner et al., 1998; Hougue et al., 2008; Nowak and May, 2000; Kirschner, 1996; Callaway and Perelson, 2002; Kirschner and Perelson, 1995; Perelson and Nelson, 1999; Xia, 2007; Tan and Wu, 1998; Dalal et al., 2008; Zorzenon dos Santos, 2001; Burkheada et al., 2009). A significant effort has been made in understanding the interaction of the immune response with HIV (Campello, 1999; Adams et al., 2004; Stan et al., 2007; Wodarz, 2001; Zurakowski and Teel, 2006). "
[Show abstract][Hide abstract] ABSTRACT: A typical HIV infection response consists of three stages: an initial acute infection, a long asymptomatic period and a final increase in viral load with simultaneous collapse in healthy CD4+T cell counts. The majority of existing mathematical models give a good representation of either the first two stages or the last stage of the infection. Using macrophages as a long-term active reservoir, a deterministic model is proposed to explain the three stages of the infection including the progression to AIDS. Simulation results illustrate how chronic infected macrophages can explain the progression to AIDS provoking viral explosion. Further simulation studies suggest that the proposed model retains its key properties even under moderately large parameter variations. This model provides important insights on how macrophages might play a crucial role in the long term behaviour of HIV infection.
Full-text · Article · Dec 2012 · Journal of Theoretical Biology