Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology
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 d...
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AIMS Press
2013-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.403 |
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| author | Edward J. Allen |
| author_facet | Edward J. Allen |
| author_sort | Edward J. Allen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-76a82e3aa0d94dc19062c7452ad9e4a7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-76a82e3aa0d94dc19062c7452ad9e4a72025-01-24T02:28:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-12-0111340342510.3934/mbe.2014.11.403Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biologyEdward J. Allen0Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042Stochastic 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.403stochastic differential equationstochastic delay differential equationdelay differential equationmathematical biologystochastic model.population biology |
| spellingShingle | Edward J. Allen Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology Mathematical Biosciences and Engineering stochastic differential equation stochastic delay differential equation delay differential equation mathematical biology stochastic model. population biology |
| title | Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology |
| title_full | Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology |
| title_fullStr | Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology |
| title_full_unstemmed | Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology |
| title_short | Derivation and computation of discrete-delayand continuous-delay SDEs in mathematical biology |
| title_sort | derivation and computation of discrete delayand continuous delay sdes in mathematical biology |
| topic | stochastic differential equation stochastic delay differential equation delay differential equation mathematical biology stochastic model. population biology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.403 |
| work_keys_str_mv | AT edwardjallen derivationandcomputationofdiscretedelayandcontinuousdelaysdesinmathematicalbiology |