Mathematical modeling

Describing real-world systems with equations so we can analyse, predict and optimise them.

Mathematical modeling is the process of representing real-world systems, phenomena or problems through mathematical concepts, equations or structures — using math to describe and understand how a system behaves.

A model lets us analyse, predict and optimise outcomes by simulating the behaviour and relationships inside a well-defined framework. Machine learning is one way of building such models: instead of deriving the equations by hand, we learn them from data.

Formula to remember

SIR model

Slides

\frac{d S}{d t} \frac{d I}{d t} \frac{d R}{d t} = - β \frac{S I}{N} = β \frac{S I}{N} - γ I = γ I

Flow between Susceptible, Infected and Recovered compartments.

$β$: transmission rate
$γ$: recovery rate
$N$: population size

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