We consider a two-parameter continuous-time Markovian model for patch occupancy in metapopulation, and address the question of when to observe the population in order to obtain the most accurate and precise estimator of the parameters. Using the likelihood obtained from a diffusion approximation we derive a robust procedure for determining the optimal observation schedule, which is considerably simpler than would otherwise be possible. We investigate the performance of two optimality criteria, ED-optimality and a particular form of maximin-optimality. Both allow one to incorporate prior belief about the parameter values before any data is collected. Kernel density estimates of the maximum likelihood estimator are compared under the various combinations of optimality criteria and prior distributions. Our methods are illustrated with reference to a model for the spread of crown of thorns starfish (Acanthaster planci) among the 55 islands comprising the Ryukyu group in Japan.