title: A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue.
abstract: In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K (+))-limited environment. Our both continuous and discrete models illustrate 'cancer immunoediting' as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202-206].
authors: a Department of Applied Mathematics , Z.H. College of Engineering and Technology, A.M.U ., Aligarh 202002 , India.
authors: M
authors: M
authors: Saleem
authors: Tanuja
authors: T
authors: Agrawal
authors: Afzal
authors: A
authors: Anees
mesh_terms: D049109:Cell Proliferation; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted
keywords: 92B05; 92C50; 93D20; cancer modelling; ecological stoichiometry; predator–prey interactions; tumour growth