https://doi.org/10.1140/epjp/s13360-025-06789-w
Regular Article
Epidemic models with controlling actions: a Gibbs free energy approach
1
Department of Physics, Santa Catarina State University, 89219-710, Joinville, SC, Brazil
2
Institute of Exact Sciences, Federal University of Alfenas, 37133-840, Alfenas, MG, Brazil
3
Institute of Physics and Chemistry, Federal University of Itajubá, 37500-903, Itajubá, MG, Brazil
4
Department of Physics, Federal University of Triângulo Mineiro, 38025-180, Uberaba, MG, Brazil
Received:
20
June
2025
Accepted:
22
August
2025
Published online:
5
September
2025
As is well known, our understanding of epidemic dynamics relies heavily on compartmental mathematical models, such as the SIR and SEIR frameworks, which categorize individuals according to their disease status. A central concept emerging from these models is the reproductive number (the average number of individuals that a single infected person transmits the disease to during their infectious period). In this work, we explore the relationship between the reproductive number and the Gibbs free energy, drawing an analogy between epidemic spread and spontaneous or catalyzed chemical reactions, as both processes are governed by analogous mathematical structures. Building on this connection, we examine the relation 
, which links the effective reproductive number 
to the Gibbs free energy change 
. This formulation suggests a novel investigative approach: interpreting epidemic progression as a form of phase transition in the thermodynamic sense, thereby opening new perspectives for understanding critical transitions in infectious disease dynamics.
This research was supported by various grants related to epidemic modeling and control.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
