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Introduction to Stochastic Simulation with the Gillespie ...

Introduction to Stochastic Simulation with the Gillespie MethodDavid KarigApril 18, 2005 Stochastic Systems Many systems driven by random, discrete interactions Traditional deterministic models may not accurately describe such systems$Example: The Lambda SwitchVirus Decision Dictated by NoiseArkin, Ross, McAdams, Genetics(1998)Example: The Lambda SwitchVirus Decision Dictated by NoiseArkin, Ross, McAdams, Genetics(1998)Example: The Lambda SwitchVirus Decision Dictated by NoiseArkin, Ross, McAdams, Genetics(1998)Outline Deterministic rate reaction model Gillespie method Examples Lambda phage Epidemiology OptimizationsDeterministic ModelReactions:A + B C C A + BA BC ODE s:dA/dt = -k1*A*B + k2*C k3*AdB/dt = -k1*A*B + k2*C + k3*AdC/dt = k1*A*B k2*C - k4*C Given initial conditions, integrate the coupled equations for some period of timek1k4k2k3 Problem StatementIf we start with N species which can interact through one of M reactions at a given time,what will be the population levels of species after a gi

Introduction to Stochastic Simulation with the Gillespie Method David Karig April 18, 2005. Stochastic Systems • Many systems driven by random, discrete interactions • Traditional deterministic models may not accurately describe such systems $ Example: The Lambda Switch

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