  Many epidemic models are naturally defined as individual-based models: where
we track the state of each individual within a susceptible population.
Inference for individual-based models is challenging due to the
high-dimensional state-space of such models, which increases exponentially with
population size. We consider sequential Monte Carlo algorithms for inference
for individual-based epidemic models where we make direct observations of the
state of a sample of individuals. Standard implementations, such as the
bootstrap filter or the auxiliary particle filter are inefficient due to
mismatch between the proposal distribution of the state and future
observations. We develop new efficient proposal distributions that take account
of future observations, leveraging the properties that (i) we can analytically
calculate the optimal proposal distribution for a single individual given
future observations and the future infection rate of that individual; and (ii)
the dynamics of individuals are independent if we condition on their infection
rates. Thus we construct estimates of the future infection rate for each
individual, and then use an independent proposal for the state of each
individual given this estimate. Empirical results show order of magnitude
improvement in efficiency of the sequential Monte Carlo sampler for both SIS
and SEIR models.
