A mathematical model of lung cancer incorporating drug resistance, macrophage polarization, and immune escape

Source abstract

Abstract Lung cancer remains a leading cause of cancer-related mortality globally, presenting a major clinical challenge across both smoking and non-smoking populations. Deciphering the complex architecture of the tumor microenvironment, specifically the dynamic cross-talk between drug-resistant malignant sub-populations, effector cells, and infiltrating macrophages, is crucial for designing optimal therapeutic regimens that mitigate treatment failure. In this study, we formulate a data-driven, non-linear system of ordinary differential equations (ODEs) to rigorously quantify cellular evolutionary dynamics, M1/M2 macrophage polarization, and immune escape mechanisms during lung cancer progression. The mathematical validation of the model confirms its epidemiological and biological well-posedness, establishing that state solutions remain strictly non-negative and bounded within a defined invariant region. Using the next generation matrix operator, we analytically derive the basic reproduction number ($R_0$), a pivotal threshold governing cellular proliferation and tumor persistence. Local and global sensitivity analyzes were performed to identify the neoplastic proliferation rate, macrophage phenotypic transition rates, and therapeutic efficacy parameters as the primary drivers governing $R_0$, providing quantitative guidance for adaptive drug dosing strategies. The selection and comparison of models are a critical component of this study. To identify the most parsimonious and accurate model, we evaluated candidate models using both the Akaike Information Criterion, small sample AIC, and the Bayesian Information Criterion. MSC 2020: 92C50; 34D20; 34D23; 49J15; 92B05; 92C60.