Mathematical Biosciences and Engineering, 2014, 11(3): 403-425. doi: 10.3934/mbe.2014.11.403.

Primary: 60H10, 92D25; Secondary: 60H20, 65C30, 92B05.

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Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology

1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.
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Keywords stochastic differential equation; stochastic delay differential equation; delay differential equation; mathematical biology; stochastic model.; Population biology

Citation: Edward J. Allen. Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology. Mathematical Biosciences and Engineering, 2014, 11(3): 403-425. doi: 10.3934/mbe.2014.11.403

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