Biomedical subjects
Publications and source records attributed to David Wick.
Simulating strongly-interacting biological populations over many orders-of-magnitude can be challenging even on fast modern computers. Here we describe a regime-switching technique that can speed up simulations from stochastic models by large factors, while retaining third-order accuracy at each time-step. We apply it to an elementary model of the immune response to an infectious organism.
In Wick and Stelf [Math. Biosci. 187 (2004) 1], we showed how to simulate a pair of strongly interacting biological populations evolving stochastically over many orders-of-magnitude. Here we generalize the method to any (finite) number of compartments; transitions including births, deaths, progression through life-stages, and mitoses; and arbitrary rate functions. We illustrate the technique for a seven-compartment model of the cellular immune response to a viral infection.
That HIV-specific cytotoxic T-lymphocytes (CTLs) might be defective in some way has stimulated much controversy and research. We use mathematical models to explore the predictions of two competing CTL-defect theories: "defective memory" and "defective activation". We discuss whether these models are consistent with adoptive-transfer experiments in HIV-infected patients and vaccine trials in simian immunodeficiency virus (SIV)-infected monkeys. Finally, we describe experimental tests that could decide among these two theories and a competitor: CTL exhaustion.
Early in HIV infection, a million virions per milliliter appear in the blood; yet over the next few weeks, this number drops by two orders-of-magnitude. Symptoms resolve and a quasi-steady-state forms. What halts the viremic outburst? In 1996, Phillips proposed a simple explanation: HIV depletes its target cells. Here, we combine observations of primary disease with mathematical analysis to argue that target-cell scarcity cannot explain the virus's decline, indirectly shoring up the chief alternative theory: control by the immune system.