# How to model a continuous-time Markov process?

I'm not sure if I'm using the correct nomenclature, but I wish to model a hypothetical biological system. I have a basic knowledge of discrete-time Markov chains, so let me explain the problem as best I can.

Suppose I have a system with two actors, A and B. Each actor, is capable of performing an action at a specific (continuous) rate. Let's assume the rate at which A and B perform work, each follow a Poisson distribution.

Actor A's work rate has a positive feedback effect on A, and inhibitory effect on B. Similarly, actor B's work rate inhibits A, but has a negative feedback effect on B.

Graphically:

A <--- A --X--> B

B <--X-- B --X--> A

Thanks!

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