Acta Scientific Medical Sciences (ASMS)(ISSN: 2582-0931)

Research Article Volume 8 Issue 6

ODE Versus Petri Net Implementation of Identical SEIRS Model

Kayden KM Low and Maurice HT Ling*

School of Applied Science, Temasek Polytechnic, Singapore

*Corresponding Author: Maurice HT Ling, School of Applied Science, Temasek Polytechnic, Singapore.

Received: May 02, 2024; Published: May 24, 2024


Differential equation; more commonly, ordinary differential equation (ODE); and Petri Net are complementary methods commonly used in dynamic systems modelling. However, the differences between ODE models and Petri Net models have not been adequately studied. In this study, we implement a closed 4-compartment SEIRS infectious disease model in both ODE and Petri Net, to examine the differences by comparing their simulation results. Our simulation results suggest that although there are differences between the simulation results across various ODE solvers, the differences between ODE or Petri Net implementations are significant differences (t ≥ 15.34, p-value ≤ 1.59E-12) as a whole; but these differences may not be significant across all compartments. This suggests that ODE model and Petri Net model may reveal different insights into the same problem; hence, supporting the view that ODE model and Petri Net model are complementary.

 Keywords: Dynamic Systems Modelling (DSM); Ordinary Differential Equation (ODE); Petri Net; Epidemiological Model


  1. Dundar S., et al. “Mathematical Modelling at a Glance: A Theoretical Study”. Procedia - Social and Behavioral Sciences 46 (2012): 3465-3470.
  2. Li Y. “Mathematical Modeling Methods and Their Application in the Analysis of Complex Signal Systems”. Advances in Mathematical Physics (2022): 1-10.
  3. Irwin M and Wang Z. “Dynamic Systems Modeling”. The International Encyclopedia of Communication Research Methods, eds Matthes J, Davis CS, Potter RF (Wiley), 1st Ed (2017).
  4. Varshney G. “Advancement in Mathematical Modelling of Economic Systems: A Review”. International Journal of Engineering, Science and Mathematics7 (2023): 62-81.
  5. Crawshaw JR., et al. “Mathematical Models of Developmental Vascular Remodelling: A Review”. PLoS Computational Biology8 (2023): e1011130.
  6. Walker JG., et al. “The impact of Policing and Homelessness on Violence Experienced by Women who Sell Sex in London: A Modelling Study”. Scientific Reports1 (2024): 8191.
  7. Mousavi S., et al. “Hybrid Mathematical and Simulation Model for Designing a Hierarchical Network of Temporary Medical Centers in a Disaster”. Journal of Simulation2 (2024): 119-135.
  8. Fulford GR. “Mathematical Modelling Using Scenarios, Case Studies and Projects in Early Undergraduate Classes”. International Journal of Mathematical Education in Science and Technology2 (2024): 468-479.
  9. Cifuentes-Faura J., et al. “Mathematical Modeling and the Use of Network Models as Epidemiological Tools”. Mathematics18 (2022): 3347.
  10. Kretzschmar M and Wallinga J. “Mathematical Models in Infectious Disease Epidemiology”. Modern Infectious Disease Epidemiology, Statistics for Biology and Health., eds Krämer A, Kretzschmar M, Krickeberg K (Springer New York, New York, NY) (2009): 209-221.
  11. White PJ. “Mathematical Models in Infectious Disease Epidemiology”. Infectious Diseases (Elsevier) (2017): 49-53.e1.
  12. Wang W., et al. “A Scoping Review of Drug Epidemic Models”. International Journal of Environmental Research and Public Health4(2022): 2017.
  13. Tang AY and Ling MH. “Relapse Processes are Important in Modelling Drug Epidemic”. Acta Scientific Medical Sciences6 (2022): 177-182.
  14. Yap SS., et al. “Assembly of Single Substance Use Epidemiological Models”. Acta Scientific Medical Sciences1 (2024): 43-50.
  15. Ling M. “Of (Biological) Models and Simulations”. MOJ Proteomics and Bioinformatics 3 (2016): 00093.
  16. Gutowska K., et al. “Petri Nets and ODEs as Complementary Methods for Comprehensive Analysis on an Example of the ATM-p53-NF-kB Signaling Pathways”. Scientific Reports1 (2022): 1135.
  17. Zhao Y-B and Krishnan J. “mRNA Translation and Protein Synthesis: An Analysis of Different Modelling Methodologies and a New PBN Based Approach’. BMC Systems Biology1 (2014): 25.
  18. Chung NN and Chew LY. “Modelling Singapore COVID-19 Pandemic with a SEIR Multiplex Network Model”. Scientific Reports1 (2021): 10122.
  19. Trawicki M. “Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity”. Mathematics1 (2017): 7.
  20. Ochieng FO. “SEIRS Model for Malaria Transmission Dynamics Incorporating Seasonality and Awareness Campaign”. Infectious Disease Modelling1 (2024): 84-102.
  21. Bjørnstad ON., et al. “The SEIRS Model for Infectious Disease Dynamics”. Nature Methods6 (2020): 557-558.
  22. Soliman S and Heiner M. “A Unique Transformation from Ordinary Differential Equations to Reaction Networks”. PloS One12 (2010): e14284.
  23. Ling MH. “COPADS IV: Fixed Time-Step ODE Solvers for a System of Equations Implemented as a Set of Python Functions”. Advances in Computer Science: an International Journal3 (2016): 5-11.
  24. Chay ZE., et al. “PNet: A Python Library for Petri Net Modeling and Simulation”. Advances in Computer Science: an International Journal4 (2016): 24-30.
  25. Hodson TO. “Root-Mean-Square Error (RMSE) or Mean Absolute Error (MAE): When to Use Them or Not”. Geoscientific Model Development14 (2022): 5481-5487.
  26. Liu J., et al. “Correlation and Agreement: Overview and Clarification of Competing Concepts and Measures”. Shanghai Archives of Psychiatry2 (2016): 115-120.
  27. Peric R., et al. “A Systematic Review and Meta-Analysis on the Association and Differences between Aerobic Threshold and Point of Optimal Fat Oxidation”. International Journal of Environmental Research and Public Health11 (2022): 6479.
  28. Hopkins M and Furber S. “Accuracy and Efficiency in Fixed-Point Neural ODE Solvers”. Neural Computation10 (2015): 2148-2182.
  29. Watts HA. “Starting Step Size for an ODE Solver”. Journal of Computational and Applied Mathematics2 (1983): 177-191.
  30. Steyer AJ and Van Vleck ES. “A Step-Size Selection Strategy for Explicit Runge-Kutta Methods Based on Lyapunov Exponent Theory”. Journal of Computational and Applied Mathematics 292 (2016): 703-719.
  31. Green KR., et al. “On Theoretical Upper Limits for Valid Timesteps of Implicit ODE Methods”. AIMS Mathematics6 (2019): 1841-1853.
  32. Söderlind G. “Time-Step Selection Algorithms: Adaptivity, Control, and Signal Processing”. Applied Numerical Mathematics3-4 (2006): 488-502.


Citation: Kayden KM Low and Maurice HT Ling. “ODE Versus Petri Net Implementation of Identical SEIRS Model”.Acta Scientific Medical Sciences 8.6 (2024): 100-104.


Copyright: © 2024 Kayden KM Low and Maurice HT Ling. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


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