# American Institute of Mathematical Sciences

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

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

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

Received  April 2012 Revised  May 2013 Published  January 2014

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