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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    [1] Mathematical Biosciences, 101 (1990), 139-153.
    [2] Stochastics and Stochastics Reports, 64 (1998), 117-142.
    [3] Springer, Dordrecht, 2007.
    [4] Stoch. Anal. Appl., 26 (2008), 274-297.
    [5] 2nd edition, CRC Press, Boca Raton, 2010.
    [6] Prentice Hall, Upper Saddle River, 2007.
    [7] Int. Journal of Math. Analysis, 1 (2007), 391-407.
    [8] Mathematical Biosciences, 149 (1998), 57-76.
    [9] Nonlinear Anal. Real World Appl., 2 (2001), 35-74.
    [10] Appl. Math. Modell., 34 (2010), 1405-1417.
    [11] Journal of Computational and Applied Mathematics, 125 (2000), 183-199.
    [12] Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 15 (1970), 111-130.
    [13] Archives of Microbiology, 157 (1992), 297-300.
    [14] Lecture Notes in Biomathematics 20, Springer, Berlin, Heidelberg, New York, 1977.
    [15] Proc. Nat. Acad. Sci., 102 (2005), 12471-12476.
    [16] Nature, 399 (1999), 541-548.
    [17] Marcel Decker, New York, 1987.
    [18] The Journal of Physical Chemistry, 81 (1977), 2340-2361.
    [19] Kluweer Academic Publishers, Dordrecht, The Netherlands, 1992.
    [20] Proceedings of the Royal Society of Edinburgh, 130 (2000), 1275-1291.
    [21] SIAM J. Appl. Math., 65 (2005), 550-566.
    [22] Nature, 287 (1980), 17-21.
    [23] Science Publishers, Enfield, New Hampshire, 2009.
    [24] Bulletin of Mathematical Biology, 52 (1990), 375-396.
    [25] Springer-Verlag, New York, 1992.
    [26] Springer, Berlin, 1994.
    [27] Academic Press, San Diego, 1993.
    [28] Journal of Applied Probability, 8 (1971), 344-356.
    [29] CRC Press, Boca Raton, Florida, 2004.
    [30] Comptes-rendus de l'Académie des Sciences, 146 (1908), 530-533.
    [31] J. Theor. Biol., 242 (2006), 722-735.
    [32] Applied Mathematics Letters, 20 (2007), 702-706.
    [33] in EOLSS encyclopedia, (eds. A. de Gaetano, P. Palumbo), 2011.
    [34] 2nd edition, Garland Science, Taylor and Francis Group, New York, 2011.
    [35] Journal of the American Collge of Nutrition, 12 (1993), 537-542.
    [36] Comparative Biochemistry and Physiology Part B, 133 (2002), 463-476.
    [37] in Delay Differential Equations and Applications, ( eds. O. Arino, M. Hbid and E. Ait Dads), Springer, Berlin, 2006, 477-517.
    [38] The Journal of Clinical Endocrinology & Metabolism, 67 (1988), 307-314.
    [39] The Journal of Clinical Endocrinology & Metabolism, 64 (1987), 669-674.
    [40] Am. J. of Physiol. Endocrinol. Metab., 260 (1991), E801-E809.
    [41] Nonlinear Analysis: Real World Applications, 11 (2010), 1692-1703.
    [42] Nature, 424 (2003), 1047-1051.
    [43] PLoS Biology, 3 (2005), 790-806.
    [44] Nature Reviews Microbiology, 5 (2007), 801-812.
    [45] J. Theor. Biol., 207 (2000), 361-375.
    [46] in Notes in Mathematics,, Volume 1180, (eds. A. Dold and B. Eckmann), Springer-Verlag, Berlin, 1986, 265-439.
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