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Intermediate4 equations~5 hours

Medicine and Epidemiology

Models that save lives — from SIR to pharmacokinetics.

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  1. 1

    SIR Model

    Intermediate
    dSdt=−βSI,dIdt=βSI−γI,dRdt=γI\frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I, \quad \frac{dR}{dt} = \gamma I

    Susceptible become Infected at rate βSI; Infected Recover at rate γI.

    Medical Sciences
    Epidemiology
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  2. 2

    Body Mass Index

    Beginner
    BMI=mh2BMI = \frac{m}{h^2}

    Weight divided by height squared—a screening metric for body composition.

    Medical Sciences
    Medicine
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  3. 3

    Hill Equation (Dose-Response)

    Advanced
    E=Emax⁡[L]nKdn+[L]nE = E_{\max} \frac{[L]^n}{K_d^n + [L]^n}

    Drug effect saturates sigmoidally with ligand concentration—cooperativity via Hill coefficient n.

    Medical Sciences
    Pharmacology
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  4. 4

    Poiseuille's Law

    Intermediate
    Q=πr4ΔP8μLQ = \frac{\pi r^4 \Delta P}{8 \mu L}

    Blood or fluid flow through a tube depends strongly on radius to the fourth power.

    Medical Sciences
    Medicine
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