I will describe how to write down the equations for the state of a system when the system is characterized by conservation of the constituent parts, covering both discrete and continuous states. Examples include infectious disease models (individuals moving between susceptible, infectious and possibly other states - discrete), enzyme activation (phosphorylation/dephosphorylation of proteins - discrete), molecular diffusion (redistribution of molecules through space - continuous), models for the length, position, angle, and growth/shrinkage state of cytoskeletal polymers (hybrid discrete/continuous), population models with age distribution (continuous), within/between host infectious disease models (with a continuous stage-of-infection state).
I will introduce stochastic models for some of the phenomena mentioned above, show how to simulate them (e.g. using Gillespie’s algorithm) and how to derive ODEs for the expected behaviour of the stochastic systems (Kolmogorov Forward Equations)