Parameter estimation of the stochastic model for oral cancer in response to thymoquinone (TQ) as anticancer therapeutics

Abstract

Oral Cancer is considered as one of the common problems of global public health and despite the progress in advanced research, the mortality rate has not been improved significantly in the last few decades. A natural product such as Thymoquinone, black seeds (TQ), is an active component of Nigella sativa or black cumin elicits cytotoxic effects on various oral cancer cell lines. A wide range of studies have been concluded that the TQ has two different anti-neoplastic actions that might trigger apoptosis, have the capacity to induce cell death in oral cancer cells. In the presence of TQ, oral cancer has been proved experimentally shows the decelerating trend of the growth. This article models the decelerating of the oral cancer growth by using a linear stochastic differential equation (SDEs). The Markov Chain Monte Carlo (MCMC) method used to estimate model parameters for 100, 500,1000 and 2000 simulations. The best set of kinetic parameters are identified. It can be seen that for 1000 simulations of the sample paths, the model fitted well the data, hence indicating a good fit. However, if the number of simulation is incerasing up to 2000, the parameter obtained shows instablity of the solution. This is due to the high numbers of noise generated, may influenced the stability of the solution.