A collection of ideas that need could be implemented.
If rates have an explicit temporal dependency, the exact method for stochastic simulations solves an integral numerically.
We should introduce a method in
EpiModel.get_time_leap_and_proposed_compartment_changes
that approximates rates as either
- constant. Just sample a time leap from an exponential distribution based on the current rates. Re-evaluate rates at the new time and choose event from those.
- linear. Sample a time leap from an exponential distribution, evaluate rates at the new time. Assume linear interpolation and solve this integral for a new time leap. Re-evaluate rates at the new time and choose event from those.
Based on our implementation in the metapop-prototype (github.com/benmaier/metapop), it should be fairly simple to set up more efficient reaction-diffusion systems for MatrixEpiModel.
- using
lmfit, we could implement a concise fitting tool to fit models to data - or pymc3: https://docs.pymc.io/notebooks/ODE_API_introduction.html#Non-linear-Differential-Equations
- https://docs.pymc.io/notebooks/ODE_with_manual_gradients.html