Mathematical Modeling of Tumor Growth and Evolution Incorporating Therapeutic Drug Resistance

Abstract

Acquired therapeutic drug resistance continually derails long-term cancer management. To address this, we built an ordinary differential equation framework that tracks tumor progression and evolutionary dynamics across six distinct treatment modalities: chemotherapy, radiotherapy, immunotherapy, hormonal therapy, bone marrow transplantation, and personalized regimens. The underlying mathematical structure couples logistic tumor growth with sensitive-to-resistant phenotypic mutation loops. We explicitly embed oral and intravenous pharmacokinetic pathways alongside Hill-driven pharmacodynamic equations, immune cell clearance mechanisms, and linear-quadratic radiotherapy cell-kill dynamics. The core methodology forms a continuous clinical loop: it informs initial therapy selection, monitors real-time patient response, and predicts clinical outcomes to directly guide adaptive schedule adjustments. We quantified this system using critical parameter sets, including growth rates  carrying capacity (K), mutation rate (μ), drug-kill coefficients (), half-maximal concentrations ), immune interaction factors (β, σ, ρ, ω, γ), and fitness costs (c). Three distinct numerical scenarios validate the model: a baseline cure track with zero resistance, a late-emerging resistance track where adaptive scheduling extends remission, and a rapid-onset track necessitating an immediate second-line pivot. Our simulations demonstrate that catching resistance early and deploying adaptive dosing delays disease progression by 40 to 60 days over traditional maximum tolerated dose protocols. Ultimately, model-guided personalization slashed the fractional resistant burden () by up to 65% compared to standard workflows. These data strongly justify integrating predictive differential equation models into real-time clinical decision-support systems.