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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].
Acknowledgement
The authors wish to express their sincere gratitude to the anonymous referees whose forceful emphasis to base the concepts of the study on biological grounds has improved the manuscript a great deal. The comments of one anonymous referee particularly made us realize that there is no end to improvement.
Funding
The first author (MS) acknowledges the financial support for this work from the University Grants Commission, New Delhi under Major Research Project Grant No. 37-483/2009(SR).