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

  • Received: 01 April 2012 Accepted: 29 June 2018 Published: 01 January 2014
  • MSC : Primary: 60H10, 92D25; Secondary: 60H20, 65C30, 92B05.

  • 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-delayand continuous-delay SDEs in mathematical biology[J]. Mathematical Biosciences and Engineering, 2014, 11(3): 403-425. doi: 10.3934/mbe.2014.11.403

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  • 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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