A Mathematical Model of Breast Cancer Growth and Drug Resistance Evolution Under Chemotherapy

Marcello Pompa, Giulia Urso, Simona Panunzi (), Dániel András Drexler, Balázs Gombos and Andrea De Gaetano
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Marcello Pompa: Institute of Systems Analysis and Informatics “A. Ruberti” (IASI), National Research Council of Italy, 00185 Rome, Italy
Giulia Urso: Department of Mathematics, University of Palermo, 90123 Palermo, Italy
Simona Panunzi: Institute of Systems Analysis and Informatics “A. Ruberti” (IASI), National Research Council of Italy, 00185 Rome, Italy
Dániel András Drexler: Physiological Controls Research Center, Obuda University, 1034 Budapest, Hungary
Balázs Gombos: Physiological Controls Research Center, Obuda University, 1034 Budapest, Hungary
Andrea De Gaetano: Institute of Systems Analysis and Informatics “A. Ruberti” (IASI), National Research Council of Italy, 00185 Rome, Italy

Mathematics, 2025, vol. 13, issue 7, 1-14

Abstract: Precision medicine aims to tailor treatments to individual patients based on their unique characteristics and disease pathophysiology. This study presents a novel mathematical model of breast tumor growth, specifically focusing on implanted breast tumors in mice treated with Pegylated Liposomal Doxorubicin (PLD). The model describes drug pharmacokinetics, drug resistance development, and the evolution of tumor mass over time. The introduction of a compartment for drug resistance development represents the novel aspect of this work, providing a straightforward description of this critical process. The model was adapted to observed data on two mice and model parameters were estimated. To assess the qualitative properties of the model solutions and to investigate its potential limitations, a stability analysis was conducted to identify equilibrium points. The analysis revealed that if the tumor cell spontaneous elimination rate exceeds the growth rate, then the tumor is stable, preventing any form of treatment. On the contrary, the pathological case occurs, the equilibrium becomes unstable, and the tumor requires treatment. By accurately modeling drug pharmacokinetics and resistance development, this model can inform clinical decisions by predicting patient-specific responses to PLD treatment, thereby guiding personalized therapeutic strategies. The findings from this study contribute to a deeper understanding of tumor growth dynamics and provide valuable insights for the development of personalized treatment strategies.

Keywords: differential equations; mathematical biology; evolution of the tumor mass; laboratory mice; breast cancer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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