  Agent-based models of disease transmission involve stochastic rules that
specify how a number of individuals would infect one another, recover or be
removed from the population. Common yet stringent assumptions stipulate
interchangeability of agents and that all pairwise contact are equally likely.
Under these assumptions, the population can be summarized by counting the
number of susceptible and infected individuals, which greatly facilitates
statistical inference. We consider the task of inference without such
simplifying assumptions, in which case, the population cannot be summarized by
low-dimensional counts. We design improved particle filters, where each
particle corresponds to a specific configuration of the population of agents,
that take either the next or all future observations into account when
proposing population configurations. Using simulated data sets, we illustrate
that orders of magnitude improvements are possible over bootstrap particle
filters. We also provide theoretical support for the approximations employed to
make the algorithms practical.
