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GP-MA-0X9O2POMathematicsOpen for request

Epidemic intervention modelling laboratory

A mathematical modelling laboratory for studying how assumptions and selected interventions change simulated epidemic trajectories.

  • Nuxt
  • Vue
  • FastAPI
  • PostgreSQL
  • Python
  • NumPy
  • SciPy
  • Docker

Project definition

Problem statement

Epidemic models simplify contact, transmission, recovery, reporting, immunity, and population structure. Different parameter combinations can fit the same observed curve but imply different futures.

The mathematical problem is to formulate model assumptions clearly, estimate which parameters are identifiable from available aggregate data, and propagate uncertainty through intervention comparisons.

Project objectives

  • Implement selected SIR, SEIR, age-structured, or metapopulation variants under documented assumptions.
  • Fit model parameters to synthetic or permitted aggregate time series with observation-error models.
  • Analyse parameter identifiability, correlation, sensitivity, and uncertainty.
  • Represent selected contact, detection, isolation, vaccination, or treatment scenarios mathematically.
  • Compare trajectories and resource proxies without presenting them as real public-health forecasts.

System design

System modules

01

Model builder

Defines compartments, flows, population groups, initial conditions, parameters, and conservation equations.

02

Numerical solver

Integrates deterministic differential equations and selected stochastic simulations under recorded settings.

03

Parameter estimator

Fits bounded parameters to prepared observations and displays residuals, correlation, and uncertainty.

04

Intervention laboratory

Applies time-dependent parameter changes and compares selected timing, coverage, and effectiveness assumptions.

05

Analysis dashboard

Shows compartments, incidence, uncertainty bands, fits, sensitivities, interventions, and assumption tables.

Methodology

System workflow

  1. 01
    Choose model

    The student selects a prepared population, compartment structure, observation process, and dataset.

  2. 02
    Verify equations

    Mass conservation, non-negativity, units, and analytical special cases are checked.

  3. 03
    Estimate parameters

    Selected parameters fit the training period with bounds, priors or penalties, and uncertainty.

  4. 04
    Run interventions

    Prepared scenarios change documented model parameters over selected periods.

  5. 05
    Compare sensitivity

    Trajectories are interpreted alongside parameter ranges, identifiability, and alternative assumptions.

Demonstration scenario

A synthetic outbreak is generated from a known SEIR model with incomplete reporting. The student fits several parameter sets that explain the observations similarly, then compares an earlier and later intervention. The dashboard shows how parameter uncertainty widens both scenario trajectories.

Engineering

Technical architecture

Web application
Nuxt and Vue for model diagrams, parameter controls, fit plots, scenario comparison, and exports.
Modelling API
FastAPI for equations, solver jobs, fitting, uncertainty, sensitivity, scenarios, and results.
Data layer
PostgreSQL for models, parameter sets, aggregate observations, fits, scenarios, and experiment records.
Numerical engine
Python, NumPy, and SciPy for differential equations, stochastic runs, constrained fitting, and sensitivity.
Verification
Conservation tests, known analytical cases, synthetic parameter recovery, solver tolerance, and repeated simulations.

Testing

Evaluation

Evaluation measures

  • Equation conservation, non-negativity, and solver convergence
  • Recovery of known parameters from synthetic observations
  • Fit error and residual behaviour on prepared aggregate data
  • Parameter confidence, correlation, practical identifiability, and sensitivity
  • Uncertainty coverage for held-out synthetic trajectories
  • Solver, fitting, and simulation time across structures and scenario counts

System boundaries

  • The laboratory is for mathematical education and does not predict a current outbreak or recommend public-health action.
  • Only synthetic, public aggregate, or explicitly permitted de-identified data is included.
  • Model outputs depend strongly on structure, reporting, behaviour, intervention, and parameter assumptions.
  • Real decisions require current surveillance, domain experts, ethical review, and responsible public-health authorities.

Included

  1. 01Population, model, parameter, and intervention interface
  2. 02Differential-equation, fitting, uncertainty, and sensitivity modules
  3. 03Compartment, incidence, parameter, scenario, and uncertainty views
  4. 04Prepared synthetic or aggregate public datasets and results
  5. 05Complete source code in a private GitHub repository
  6. 06Complete project documentation with synopsis, abstract, methodology, mathematical formulation, simulation results, screenshots, and conclusion
  7. 07Setup and usage guide

Project record

No buyer information is collected on this page.

Permanent project ID
GP-MA-0X9O2PO
Catalogued
21 Aug 2026
Completed
Pending
Verified
Pending
Demonstration
Added when ready

Handover

After purchase

  1. 01
    Payment is confirmed

    The project is marked unavailable and cannot be purchased again.

  2. 02
    Repository access is granted

    The buyer's submitted GitHub account receives access to the private repository.

  3. 03
    The purchase record is delivered

    The certification sheet is prepared from the reviewed buyer details and sent privately by email.