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H. Kravitz et al. / IJOCTA, Vol.15, No.4, pp.750-778 (2025)
low inter-city incidence. Contributing features in as Tikhonov regularization may prove useful for
the model likely include a low value of α, low pop- stabilizing parameter inference and avoiding over-
ulation on the incident edges (see Figure 10), and fitting in high-dimensional settings. Further-
two out of its five adjacent vertices being unpop- more, we plan to investigate uncertainty quan-
ulated. tification approaches to better characterize con-
Vertex v 10 (Bielsko-Bia la) is balanced - the fidence in parameter estimates and model pre-
intra- and inter-city incidences have similar mag- dictions, which will enhance the robustness and
nitudes compared to the other vertices, and both interpretability of the framework. Finally, we
are high. In general, the intra-city incidence con- plan to undertake a more granular location-based
tributes significantly more than the inter-city in- sensitivity analysis, which may yield deeper in-
cidence to the normalized infection inflow. sight into the interplay between network topology,
parameter heterogeneity, and the most effective
4. Conclusion means to slow the spread of an epidemic. 110

In this paper, we applied a data-driven optimiza-
tion methodology to estimate key parameters in
a metric graph-based epidemiological model, us- Acknowledgments
ing data from an early 2021 wave of COVID-19 in HK, CD, and MB thank the American Institute
Poland as a case study. We found that this prob- of Mathematics for the time and space to work on
lem is a difficult optimization problem, as indi- this project as part of their SQuaRE program.
cated by the presence of a Rosenbrock-type func-
tion. We were able to make the Rosenbrock be-
havior appear for a simple, uncoupled SIR model, Funding
thus showing that the Rosenbrock behavior is an
This research was partially supported by BN’s
intrinsic feature of fitting certain SIR models to
work funded through the NSF grant #136228.
approximately Gaussian data and not a result of
the complex network structure. This discovery
provides a real-world test case with which to test Conflict of interest
optimization algorithms rather than using the ar-
tificially constructed classic Rosenbrock function. The authors declare they have no competing in-
Having found a plausible set of parameters terests.
for COVID-19 in Poland, we presented two appli-
cations: reducing traffic inflow into the cities to
flatten the infection curve and the identification Author contributions
of some particular patterns in the distribution of Conceptualization: All authors
intra- versus inter-city incidence rates.
Formal analysis: All authors
Methodology: All authors
4.1. Future work
Software: Hannah Kravitz, Bryttani Nieves
There are a number of potential directions in Visualization: Hannah Kravitz, Christina Dur´on
which this work could be extended. First, we Writing–original draft: Hannah Kravitz
aim to couple the metric graph framework to a Writing–review & editing: All authors
surrounding two-dimensional spatial domain 30 to
better capture the effect of a transportation net-
work on rural spread. Second, we intend to incor- Availability of data
porate transport terms along the edges to more
The raw case data is freely available from the
accurately model directed traffic flow, comple-
Polish Ministry of Health (MOH)’s website
menting the existing diffusion-based framework.
(https://www.gov.pl/web/koronawirus/wykaz-
We also plan to introduce source/sink terms at
zarazen-koronawirusem-sars-cov-2). The model
international border crossings in order to study
results supporting this article will be made avail-
the effect of cross-border movement on epidemic
able by the authors on request.
dynamics and containment strategies. Allow-
ing susceptible mobility or incorporating infection
during travel are further natural extensions that
would better capture more realistic mixing across
AI tools statement
cities.
As the model is extended and calibrated in The authors have utilized ChatGPT for minor
finer spatial detail, regularization techniques such grammatical and formatting assistance.
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