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

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.

STOCHASTIC DIFFERENTIAL GAMES IN DISTRIBUTED SYSTEMS WITH DELAY

We study a differential game of approach in a delay stochastic system. The evolution of the system is described by Ito`s linear stochastic differential equation in Hilbert space. The considered Hilbert spaces are assumed to be real and separable. The Wiener process takes values in a Hilbert space and has a nuclear symmetric positive covariance operator. The pursuer and evader controls are non-anticipating random processes, taking on values, generally, in different Hilbert spaces. The operator multiplying the system state is the generator of an analytic semigroup. Solutions of the equation are represented with the help of a formula of variation of constants by the initial data and the control block. The delay effect is taken into account by summing shift type operators. To study the differential game, the method of resolving functions is extended to case of delay stochastic systems in Hilbert spaces. The technique of set-valued mappings and their selectors is used. We consider the application of obtained results in abstract Hilbert spaces to systems described by stochastic partial differential equations with time delay. By taking into account a random external influence and time delay, we study the heat propagation process with controlled distributed heat source and leak.

Time Varying Parameter Estimation Scheme for a Linear Stochastic Differential Equation

In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining $m_{k}$ as the local admissible sample/data observation size at time $t_{k}$, parameters and state at time $t_{k}$ are estimated using past data on interval $[t_{k-m_{k}+1}, t_{k}]$. We show that the parameter estimates at each time $t_{k}$ converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy commodities and stock price processes.

Random Vibration Model in Linear and Non Linear Structure, Application in Engineering Structure

Response of linear or complex nonlinear structures takes form in a characteristic functions and in the deterministic or stochastic external loads. Non linear model with non linear structure stiffness is a type of Duffing equation. Stochastic external loads system is referred to a random signal white noise with a constant power spectral density (So), while non linear system identification of deterministic system's is based on time history, phase plane and Poincare map. Methods of Galerkin and Runge-Kutta are used to solve the partial non linear governing diferential equations. Mean value , Standard deviation and Probability Density Function (PDF) is stated as statistical responses due to stochastic response of random variables. The analysis of random vibration in the solution of non linear stochastic differential equation is solved