Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling
Mathematical models have been of great importance in various fields, especially for understanding the dynamical behaviour of biosystems. Several models, based on classical ordinary differential equations, delay differential equations, and stochastic processes are commonly employed to gain insights i...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/3/4/37 |
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| author | Oluwatosin Babasola Evans Otieno Omondi Kayode Oshinubi Nancy Matendechere Imbusi |
| author_facet | Oluwatosin Babasola Evans Otieno Omondi Kayode Oshinubi Nancy Matendechere Imbusi |
| author_sort | Oluwatosin Babasola |
| collection | DOAJ |
| description | Mathematical models have been of great importance in various fields, especially for understanding the dynamical behaviour of biosystems. Several models, based on classical ordinary differential equations, delay differential equations, and stochastic processes are commonly employed to gain insights into these systems. However, there is potential to extend such models further by combining the features from the classical approaches. This work investigates stochastic delay differential equations (SDDEs)-based models to understand the behaviour of biosystems. Numerical techniques for solving these models that demonstrate a more robust representation of real-life scenarios are presented. Additionally, quantitative roles of delay and noise to gain a deeper understanding of their influence on the system’s overall behaviour are analysed. Subsequently, numerical simulations that illustrate the model’s robustness are provided and the results suggest that SDDEs provide a more comprehensive representation of many biological systems, effectively accounting for the uncertainties that arise in real-life situations. |
| first_indexed | 2024-03-08T21:02:48Z |
| format | Article |
| id | doaj.art-a4a1f0ca7dee48878a9d84496ff117ad |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-08T21:02:48Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-a4a1f0ca7dee48878a9d84496ff117ad2023-12-22T13:48:45ZengMDPI AGAppliedMath2673-99092023-10-013470272110.3390/appliedmath3040037Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease ModellingOluwatosin Babasola0Evans Otieno Omondi1Kayode Oshinubi2Nancy Matendechere Imbusi3Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UKInstitute of Mathematical Sciences, Strathmore University, Nairobi P.O. Box 59857-00200, KenyaSchool of Informatics, Computing, and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USASchool of Mathematics and Actuarial Sciences, Technical University of Kenya, Nairobi P.O. Box 52428-00200, KenyaMathematical models have been of great importance in various fields, especially for understanding the dynamical behaviour of biosystems. Several models, based on classical ordinary differential equations, delay differential equations, and stochastic processes are commonly employed to gain insights into these systems. However, there is potential to extend such models further by combining the features from the classical approaches. This work investigates stochastic delay differential equations (SDDEs)-based models to understand the behaviour of biosystems. Numerical techniques for solving these models that demonstrate a more robust representation of real-life scenarios are presented. Additionally, quantitative roles of delay and noise to gain a deeper understanding of their influence on the system’s overall behaviour are analysed. Subsequently, numerical simulations that illustrate the model’s robustness are provided and the results suggest that SDDEs provide a more comprehensive representation of many biological systems, effectively accounting for the uncertainties that arise in real-life situations.https://www.mdpi.com/2673-9909/3/4/37stochastic delay differential equationbiosystemsdisease modellingEuler–MaruyamaMilsteinnumerical techniques and simulations |
| spellingShingle | Oluwatosin Babasola Evans Otieno Omondi Kayode Oshinubi Nancy Matendechere Imbusi Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling AppliedMath stochastic delay differential equation biosystems disease modelling Euler–Maruyama Milstein numerical techniques and simulations |
| title | Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling |
| title_full | Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling |
| title_fullStr | Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling |
| title_full_unstemmed | Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling |
| title_short | Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling |
| title_sort | stochastic delay differential equations a comprehensive approach for understanding biosystems with application to disease modelling |
| topic | stochastic delay differential equation biosystems disease modelling Euler–Maruyama Milstein numerical techniques and simulations |
| url | https://www.mdpi.com/2673-9909/3/4/37 |
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