Deterministic and stochastic models of virus dynamics

 Title: Deterministic and stochastic models of virus dynamics Author: Perera, Niranjala C Abstract: A variety of mathematical models ranging from very simple ones to complicated ones have been developed and analyzed in order to capture different phenomena associated with the spread of diseases . Even though none of these models behave exactly according to the observed clinical data , major features of disease dynamics can be captured merely by means of a simple model . The model introduced by Nowak and May [12] is such simple deterministic model of which a stability analysis has not been done . Our objectives in this endeavor are two -fold . The first objective of this thesis is to carry out a thorough analysis of the aforementioned deterministic model of virus dynamics while obtaining the related system of Ito stochastic differential equations which has not been obtained to date . The motivation for obtaining the related stochastic model is also two -fold . The first reason is the capability of stochastic models to capture the randomness associated with the disease dynamics . The second reason is while a deterministic model predicts a single outcome for a given set of parameter values , a stochastic model predicts an infinite set of possible outcomes weighed by their likelihoods and probabilities . Any mathematical model which describes virus dynamics , is not complete until it describes the immune response . With analogy to a predator -prey model , immune cells play the role of the predator while the virus plays the role of the prey . The immune response is triggered by encountering a foreign antigen . The role of the immune system is to fight off invasion by foreign pathogens . In this endeavor , our interest is a special kind of T cell , namely cytotoxic T lymphocyte (CTL ) which can also identify and eliminate infected cells . Then the immune response is incorporated with the aforementioned simple model of virus dynamics . This is done under three different assumptions on the CTL proliferation rate . This evidently results in three different models . The second objective of this thesis is to carry out a thorough stability analysis of the three deterministic models of virus dynamics with the CTL response while obtaining respective systems of Ito stochastic differential equations . URI: http : / /hdl .handle .net /2346 /22557 Date: 2003-12

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