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A constrained optimisation framework for parameter identification of the SIRD model.

Andrés Miniguano-Trujillo1, John W Pearson2, Benjamin D Goddard2

  • 1Maxwell Institute for Mathematical Sciences, The University of Edinburgh and Heriot-Watt University, Bayes Centre, Edinburgh, Scotland, UK.

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Summary
This summary is machine-generated.

This study introduces a numerical framework for optimizing disease spread models, evaluating various algorithms to find the best parameters for accurate predictions. The research enhances disease modeling by providing reliable parameter tuning strategies.

Keywords:
Mathematical epidemiologyOptimisation of systems of ODEsParameter identificationQuasi-Newton methodsSIRD model

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Area of Science:

  • Epidemiology
  • Computational Mathematics
  • Mathematical Modeling

Background:

  • Accurate disease spread modeling relies on precise parameter estimation.
  • Traditional parameter tuning methods may not guarantee optimal fits.
  • Ordinary differential equations (ODEs) are commonly used to describe disease dynamics.

Purpose of the Study:

  • To develop and evaluate a numerical framework for identifying optimal parameters in epidemiological models.
  • To analyze the behavior of optimization algorithms applied to disease propagation models.
  • To provide a reliable method for parameter calibration in compartmental models.

Main Methods:

  • Utilized an optimize-then-discretise approach for parameter identification.
  • Derived first-order optimality conditions to ensure goodness of fit.
  • Implemented and compared numerical methods including projected gradient descent, FISTA, nmAPG, and limited-memory BFGS.

Main Results:

  • Demonstrated the existence of optimal parameters for the considered SIRD model.
  • Evaluated the relative performance of different numerical optimization strategies.
  • Provided insights into the effectiveness of the proposed methods for parameter tuning.

Conclusions:

  • The proposed numerical framework offers effective strategies for optimizing disease spread models.
  • This approach facilitates the calibration of complex compartmental epidemiological models.
  • The study contributes to improving the accuracy and reliability of disease propagation predictions.