Page 208 - IJOCTA-15-4

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.4, pp.750-778 (2025)
https://doi.org/10.36922/IJOCTA025220106

RESEARCH ARTICLE

Data-driven optimization and parameter estimation for a metric
graph epidemic model with applications to COVID-19 spread in
Poland: A real-world example of optimization for a challenging
Rosenbrock-type objective function

†
†
1*
2
1
Hannah Kravitz , Christina Dur´on , Bryttani Nieves , and Moysey Brio 3 †
1
Fariborz Maseeh Department of Mathematics & Statistics, Portland State University, Portland,
Oregon, United States of America
2
Natural Science Division, Pepperdine University, Malibu, California, United States of America
3
Department of Mathematics, University of Arizona, Tucson, Arizona, United States of America
hkravitz@pdx.edu, christina.duron@pepperdine.edu, bryttani@pdx.edu, brio@arizona.edu
ARTICLE INFO ABSTRACT
Article History: In this paper, we apply data-driven optimization to estimate key parameters
Received: May 29, 2025 in a metric graph-based epidemiological model, with the aim of analyzing the
1st revised: August 13, 2025 effect of road networks on the geographic spread of epidemics. As a case study,
2nd revised: August 28, 2025 we fit our model to data from the COVID-19 pandemic in Poland during 2021.
3rd revised: September 7, 2025 Our dataset integrates county-level daily case reports, national census informa-
Accepted: September 15, 2025 tion, and traffic flow studies. This framework allows us to examine the relative
Published Online: October 14, 2025 contribution of specific travel routes over time and infer unobserved transmis-
sion patterns in the presence of incomplete or unreliable case reporting. The
Keywords:
SIR model optimization problem that arises from the model fitting yields an objective
function resembling the Rosenbrock “banana” or “valley” function, a classi-
Rosenbrock function
cal difficult benchmark for optimization algorithms. To our knowledge, this
Metric graph
represents the first appearance of a Rosenbrock-type function in a real-world
Epidemiology
epidemiological context. We demonstrate that such a structure can emerge
Parameter estimation
naturally from a simple uncoupled SIR model under specific conditions: a low
AMS Classification 2010: initial incidence rate and a prolonged infectious period. This suggests that the
35Q92, 65K05, 90C51, 65Z05, 92B05 Rosenbrock behavior is an intrinsic feature of fitting compartmental models to
approximately Gaussian epidemiological data, providing a realistic yet simple
scenario with which to test optimization algorithms. We explore optimization
strategies suited to the Rosenbrock-type structure and identify a feasible pa-
rameter set for modeling the spread of COVID-19 in Poland. We use this set of
parameters to identify discrepancies between the model and the data, explore
how reducing traffic flow into urban areas can help flatten the infection curve,
and identify some patterns in the distribution of intra- versus inter-city inci-
dence rates. While recognizing the complex interplay of social and behavioral
elements that cannot be fully captured in a high-level geographic model, our
findings highlight the usefulness of metric graph-based models for understand-
ing large-scale disease transmission in structured transportation networks.

1. Introduction the transmission of both waterborne and vector-
borne diseases; cholera can spread through con-
Geographic transport networks play a fundamen- taminated water, 1,2 while mosquitoes (vectors for
tal role in the spread of epidemics. Fluvial sys- diseases like malaria and dengue fever) frequently
3,4
tems, for example, have been shown to facilitate breed near rivers. Highways provide a similar
*Corresponding Author
†These authors contributed equally to this work.
750