Simulation of Linear and Nonlinear Models

The two-compartment model and the model of the enzymatic reaction (cf. Sections 9.1.2 and 8.5.1, respectively) will be presented as typical cases for linear and nonlinear models, respectively. For these simulations, the model parameters were set as follows  

Initial conditions for the compartmental model and the enzymatic reaction were set to n0 = [10 5], and s0 = 10, eo = 5, and c0 = 0, respectively. These values are very low regarding the experimental reality, but they were deliberately chosen as such to facilitate the computation of the exact solution. 

Two-Compartment Model First, we develop full probabilistic transfer modeling. Consider the number of particles in the first and second compartments being rq and 712, respectively, at time t + At, where At is some small time interval. There are a number of mutually exclusive ways in which this event could have come about, starting from time t. Specifically, they are  

Because this set of mutually exclusive pathways to the desired event at t + At is exhaustive, the probability of size ni,n2 at t + At may be written as the sum of the individual probabilities of these pathways. Symbolically, using the assumptions for possible changes, one has for suitably small At, 

Second, considering now the exchange processes between compartment and environment as the set of first-order reactions, 

---