Hernandez Vargas, Esteban Abelardo
A control theoretic approach to mitigate viral
escape in HIV.
PhD thesis, National University of Ireland Maynooth.
A very important scientific advance was the identification of HIV as a causative agent for AIDS.
HIV infection typically involves three main stages: a primary acute infection, a long asymptomatic
period and a final increase in viral load with a simultaneous collapse in healthy CD4+T cell count
during which AIDS appears. Motivated by the worldwide impact of HIV infection on health and
the difficulties to test in vivo or in vitro the different hypothesis which help us to understand the
infection, we study the problem from a control theoretic perspective. We present a deterministic
ordinary differential equation model that is able to represent the three main stages in HIV infection.
The mechanism behind this model suggests that macrophages could be long-term latent reservoirs
for HIV and may be important in the progression to AIDS. To avoid or slow this progression to
AIDS, antiretroviral drugs were introduce in the late eighties. However, these drugs are not always
successful causing a viral rebound in the patient. This rebound is associated with the emergence of
resistance mutations resulting in genotypes with reduced susceptibility to one or more of the drugs.
To explore antiretroviral effects in HIV, we extend the mathematical model to include the impact
of therapy and suggest different mutation models. Under some additional assumptions the model
can be seen to be a positive switched dynamic system. Consequently we test clinical treatments
and allow preliminary control analysis for switching treatments. After introducing the biological
background and models, we formulate the problem of treatment scheduling to mitigate viral escape
in HIV. The goal of this therapy schedule is to minimize the total viral load for the period
of treatment. Using optimal control theory a general solution in continuous time is presented for
a particular case of switched positive systems with a specific symmetry property. In this case the
optimal switching rule is on a sliding surface. For the discrete-time version several algorithms based
on linear programming are proposed to reduce the computational burden whilst still computing the
optimal sequence. Relaxing the demand of optimality, we provide a result on state-feedback stabilization
of autonomous positive switched systems through piecewise co-positive Lyapunov functions
in continuous and discrete time. The performance might not be optimal but provides a tractable
solution which guarantees some level of performance. Model predictive control (MPC) has been
considered as an important suboptimal technique for biological applications, therefore we explore
this technique to the viral escape mitigation problem.
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