(622a) Stochastic Modeling and Monte Carlo Simulation of the Temporal Evolution of Phenotypes R5, R5X4, and X4 of Human Immunodeficiency Virus Type 1
The temporal evolution of phenotypes R5, R5X4, and X4 of Human Immunodeficiency Virus Type 1, HIV-1, is modeled as a stochastic process. Viral populations, such as HIV-1, comprise discrete and mesoscopic organisms that behave erratically in time and/or space; moreover, the three strains or phenotypes of HIV-1, i.e., R5, R5X4, and X4, transform into one another according to a biological mechanism that can be regarded as random. This gives rise to incessant fluctuations in the HIV-1 phenotypes' characteristics, e.g., their number concentrations in a fluid medium. Such is especially the case at the onset of infection where the populations of HIV-1 phenotypes are minute, thereby appreciably magnifying the concomitant fluctuations. Thus, it is appropriate that the temporal evolution of HIV-1 phenotypes be treated as a stochastic process. Specifically, the temporal evolution of HIV-1 phenotypes is modeled as a birth-death process, the most typical subclass of Markov processes, with its intensity of transition characterized by a non-linear, time-dependent rate law. The resultant model, in turn, leads to the governing, i.e., master, equation of the birth-death process whose solution renders it possible to evaluate the means and higher moments about the process' means, e.g., the variances, of the random variables characterizing the temporal evolution of HIV-1 phenotypes. These higher moments are of special significance: They are collectively a manifestation of the process' inherent fluctuations. Moreover, the master equation of the birth-death process is simulated by means of the Monte Carlo method by resorting to the event-driven and time-driven approaches. The analytical solutions from the master equation as well as the numerical results from Monte Carlo simulation are compared with the available or simulated experimental data.