  Introduction. Can the infection due to the human immunodeficiency virus type
1 induce a change in the differentiation status or process in T cells?.
Methods. We will consider two stochastic Markov chain models, one which will
describe the T-helper cell differentiation process, and another one describing
that process of infection of the T-helper cell by the virus; in these Markov
chains, we will consider a set of states $\{X_t \}$ comprised of those proteins
involved in each of the processes and their interactions (either
differentiation or infection of the cell), such that we will obtain two
stochastic transition matrices ($A,B$), one for each process; afterwards, the
computation of their eigenvalues shall be performed, in which, should the
eigenvalue $\lambda_i=1$ exist, the computation for the equilibrium
distribution $\pi^n$ will be obtained for each of the matrices, which will
inform us on the trends of interactions amongst the proteins in the long-term.
Results. The stochastic processes considered possess an equilibrium
distribution, when reaching their equilibrium distribution, there exists an
increase in their informational entropy, and their log-rank distributions can
be modeled as discrete beta generalized distributions (DGBD). Discussion. The
equilibrium distributions of both process can be regarded as states in which
the cell is well-differentiated, ergo there exists an induction of a novel
HIV-dependent differentiated state in the T-cell; these processes due to their
DGBD distribution can be considered complex processes; due to the increasing
entropy, the equilibrium states are stable ones. Conclusion. The HIV virus can
promote a novel differentiated state in the T-cell, which can give account for
clinical features seen in patients; this model, notwithstanding does not give
account of YES/NO logical switches involved in the regulatory networks.
