In most biological systems, multidimensional stochastic processes that involve some type of interaction plays an important role.
For instance gene expression in both prokaryotes and eukaryotes or protein-protein interaction processes are just a few examples
of inherently interacting multidimensional stochastic processes.
So far most of the methods for solving the resulting stochastic equations rely on computer simulations.
In this work we are developing an analytical method to analyze a general multidimensional Markov process with interaction, continues in time and discrete
in a large sample space. We are using the method of dimensionality reduction in order to advance some analytical insights to the resulting
stochastic equations. We discuss the model in steady state for the particular choice of states and transition rules and find exact solutions.
This approach based on techniques from statistical physics is suitable when we have a multidimensional stochastic process on a large phase space.
The analytical result can be used to help developing appropriate numerical methods.
We are applying this methodology on a biophysical model that describes the impact of antibacterial drugs on bacteria population dynamics
and reproduce direct experimental observations.