A Study on lung cancer using nabla discrete fractional-order model

David Amilo, Bilgen Kaymakamzade, Evren Hınçal

This study proposes a nabla discrete fractional-order system of differential equations to model lung cancer and its interactions with lung epithelial cells, mutated cells, oncogenes, tumor suppressor genes, immune cells, cytokines, growth factors, angiogenic factors, and extracellular matrix. The proposed model can help predict cancer growth, metastasis, and response to treatment. Analytical results show the system is stable with a unique solution, and the model predicts that the immune system responds to cancer cells but eventually becomes overpowered. The numerical analysis employed the forward and backward Euler method and demonstrated that changes in parameter values have significant effects on the steady-state solution. The findings show that the growth of lung epithelial cells or their interaction with immune cells can cause an increase in the number of lung cancer cells. Conversely, an increase in cell death or a reduction in the interaction between lung epithelial cells and immune cells can decrease the number of lung cancer cells. The study highlights the usefulness of the nabla discrete fractional model in studying lung cancer dynamics.