Analyzing the mathematical model of non-small cell lung cancer stages and their impact on hepatotoxicity during immunotherapy treatment

Bronchial cancer is considered the leading cause of cancer-related mortality worldwide, in comparison to survival rates of other cancer types. Lung cancer treatments aim to eliminate cancer cells, destroy them, or prevent cancer cell division, using approaches such as immunotherapy. Despite the relatively better effectiveness and tolerability of immunotherapy compared to other treatments, severe side effects related to liver dysfunction, known as hepatotoxicity, can occur in patients. In this study, we evaluated the response of patients with non-small cell lung cancer (NSCLC) to this treatment. These responses are modeled by a system of differential equations based on cancer stage changes, which we analyzed both analytically and numerically. The study methodology encompasses model construction, establishing the existence and uniqueness of the solution, identifying equilibrium points, analyzing stability of equilibrium points using Routh-Hurwitz Criteria, and numerical simulations. The conducted dynamic analysis resulted in determining an asymptotically stable equilibrium point without any prerequisite conditions. The results of the analysis are validated using numerical simulations. This study can serve as an early prediction of cancer progression within a hospital population undergoing immunotherapy. Its objective is to monitor the disease’s behavior over time and to visualize the potential impact of this treatment on the incidence of hepatotoxicity in these patients.