  In this work we construct a joint Gaussian likelihood for approximate
inference on Markov population models. We demonstrate that Markov population
models can be approximated by a system of linear stochastic differential
equations with time-varying coefficients. We show that the system of stochastic
differential equations converges to a set of ordinary differential equations.
We derive our proposed joint Gaussian deterministic limiting approximation
(JGDLA) model from the limiting system of ordinary differential equations. The
results is a method for inference on Markov population models that relies
solely on the solution to a system deterministic equations. We show that our
method requires no stochastic infill and exhibits improved predictive power in
comparison to the Euler-Maruyama scheme on simulated
susceptible-infected-recovered data sets. We use the JGDLA to fit a stochastic
susceptible-exposed-infected-recovered system to the Princess Diamond COVID-19
cruise ship data set.

Methodology