| Abstract | Within host viral-immune system population dynamics are often studied through a deterministic dynamical systems approach. However, viral and immune system evolution involves many underlying stochastic processes, and it is a subject of debate whether one needs to model viral-immune system population dynamics with a stochastic dynamical system. An important aspect of this debate is the difficulty of analyzing stochastic predator-prey systems, and indeed such systems are not well understood. Within host viral dynamics often occurs on a faster time scale than immune system dynamics. An important example of such time scale separation is HIV, which evolves on a time scale of hours to days while being targeted by a CTL population that evolves on a time scale of days to weeks. In this talk we consider a stochastic dynamical system model of HIV-CTL interaction assuming such scale separation. The scale separation allows us to employ asymptotic techniques to analyze a stochastic predator-prey system. We consider a case in which two viral types are competing. In the deterministic case, the viral types coexist, but we show that in the stochastic setting either one of the viral types may be lost with a significant probability and on a time scale that would affect within host viral dynamics. |
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