Optimal Design of Experimental Epidemics

We consider the optimal design of experimental epidemics modelled as density dependent Markov processes. We focus on finding (i) the optimal times at which to collect data about the state of the system for a small number of discrete observations, (ii) the optimal numbers of susceptible and infective individuals to begin an experiment with, and (iii) the optimal number of replicate epidemics to use. We answer these questions by looking at three commonly used compartmental models in experimental epidemiology: the SI (Susceptible to Infected), SIS (Susceptible to Infected to Susceptible) and partially observed SIR (Susceptible to Infected to Recovered) epidemics. In particular, to demonstrate the wide range of density dependent models to which our methodology can be applied, we use a time-homogeneous SIS epidemic, a time-inhomogeneous SI epidemic with exponentially decreasing transmission rates and an partially observed SIR epidemic where the infectious period for an individual has a gamma distribution. Whilst compartmental models are ∗Principal corresponding author ∗∗Corresponding author Email addresses: [email protected] (D.E. Pagendam), [email protected] (P.K. Pollett) Preprint submitted to Journal of Statistical Planning and Inference April 18, 2012 widely applied in natural systems, we focus on the use of the models in the context of controlled experimental epidemics or transmission experiments, whose purpose is to inform the practitioner about disease transmission and recovery rates. We adopt the popular D-optimality criterion as providing an appropriate objective function for designing our experiments, since this leads to point estimates with maximum precision. As D-optimal designs for non-linear models are only locally optimal, we also consider the robustness of the designs relative to the misspecification of the model parameters.