Optimal Control of the Solow Model with an Epidemic Factor Calibrated to Real Data

Sergey Yakunin, Olga Krivorotko

Keywords: Solow growth model, optimal control, epidemic factor, parameter identification, calibration

TL;DR: We develop an economic–epidemiological Solow–ODE optimal-control model for epidemic-era economic dynamics and calibrate it to COVID-19–era annual income and morbidity data via a stabilized inverse-parameter-estimation procedure.

Abstract:

This work develops and identifies an economic--epidemiological model aimed at analyzing economic dynamics during an epidemic,
using COVID-19 as the motivating application. The framework combines (i) an epidemiological block formulated as a system of
ordinary differential equations and (ii) an economic block based on the Solow growth model with control variables that capture
the intensity of anti-epidemic measures and the allocation of resources between consumption, capital accumulation, and
intervention efforts.

At the first stage, we formulate a deterministic optimal control problem and implement a numerical procedure for generating
trajectories on synthetic data under several control regimes. This enables verification of the model dynamics and supports an
interpretation of the resulting control actions.

At the second stage, we solve an inverse problem to adapt the model to real annual income data while accounting for morbidity.
We define an optimization problem for a cost functional, determine the identifiable parameters, and implement a parameter
estimation procedure. To ensure stable calibration under sparse observations, we resolve the scale ambiguity between the
technology multiplier and the initial state by fixing the scale using the first observation. We additionally impose admissible
parameter constraints and evaluate performance on training and validation samples.

This work was supported by the grant of the state program of the "Sirius'' Federal Territory
Scientific and technological development of the "Sirius'' Federal Territory''
(Agreement No.~26-03 dated 07.07.2025).

Submission Number: 82