- Course overview
- Search within this course
- What is a mathematical model?
- Introduction to networks and graphs
- How to get from biology to mathematics
- Introduction to three mathematical model formalisms
- Case study – Infectious diseases (SIR Models)
- Other modelling approaches
- Sustainable modelling and sharing
- Summary
- Check your learning
- Your feedback
- References
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Summary
Mathematical models don’t care whether the entity being modelled is a protein, a cell, or a population—what matters is how interactions between the components influence the system over time. Models for very different biological entities (from enzymes to pandemics) can look strikingly similar and the model building follows essentially the same principles.
How to get from biology to mathematics
- Define the question you want to answer with the model
- Identify the biological players involved
- Identify the interactions and assign directionality
Mathematical model formalisms
Mathematical model formalisms differ in the way they treat time, how time is updated, what values variables can take and how variables interact.
We have introduced three different model formalisms in this tutorial:
| Model formalism | Variables | Time |
| Boolean network models | Binary (zero or one) | Qualitative progress (step-based) |
| Difference equation models | Continuous (any number) | Discrete (any whole number) |
| Ordinary differential equation models | Continuous (any number) | Continuous (any number) |
Choosing between model formalisms
Which model formalism you choose should depend on the biological question you want to answer and the data you have available (more complex model – more parameters – more data needed). The choice of model formalism can also depend on your or your collaborators’ experience.
Move on to check your learning with the final quiz of this tutorial.