Part 1: Deterministic Models

This pathway gives every lesson one main purpose. Begin with biological meaning, then learn numerical solution, and finish with reusable analysis and scientific communication.

Stage A: Represent the biological model

Learn what the compartments mean, how people transfer between them, how flows become equations and how a valid starting state is defined.

01Python quantities, variables and parametersStore biological counts and model parameters in Python. 02SIR compartments and biological transfersRepresent infection and recovery as coordinated integer movements, without rates or differential equations. 03Writing the deterministic SIR equationsTurn flows in and out into differential equations and Python expressions. 04Initial conditions and population conservationValidate starting states, counts, proportions and invariants.

Stage B: Construct numerical solutions

Prepare numerical storage, learn Euler’s method carefully, apply it to SIR and SEIR, then use an adaptive scientific solver.

05Time grids, lists and NumPy arraysPrepare matched time points and compartment storage. 06Forward Euler method from scratchUnderstand one numerical method using a recovery-only equation. 07Programming the SIR model with Euler’s methodCombine three coupled equations into one complete trajectory. 08Programming the SEIR model with Euler’s methodAdd exposure, progression and a fourth simultaneous update. 09Solving SIR and SEIR with solve_ivpUse adaptive library solvers, tolerances and returned solution objects.

Stage C: Analyse and communicate results

Organise reusable code, define outcomes precisely, represent interventions, test parameter response and communicate evidence responsibly.

10Functions for reusable epidemic modelsSeparate equations, simulation and summary responsibilities. 11Peak size, peak time and final epidemic sizeDefine and calculate epidemiological outcomes without confusing related quantities. 12Vaccination and time-dependent interventionsChange initial immunity and program a piecewise transmission parameter. 13Parameter comparisons and sensitivity experimentsStudy exact, local, range-based, interaction and timing sensitivity. 14Graphs, flow diagrams, tables and interpretationChoose evidence displays and write biologically meaningful, qualified conclusions.