Perfect counterfactuals for epidemic simulations

Simulation studies are often used to predict the expected impact of control measures in infectious disease outbreaks. Typically, two independent sets of simulations are conducted, one with the intervention, and one without, and epidemic sizes (or some related metric) are compared to estimate the effect of the intervention. Since it is possible that controlled epidemics are larger than uncontrolled ones if there is substantial stochastic variation between epidemics, uncertainty intervals from this approach can include a negative effect even for an effective intervention. To more precisely estimate the number of cases an intervention will prevent within a single epidemic, here we develop a 'single-world' approach to matching simulations of controlled epidemics to their exact uncontrolled counterfactual. Our method borrows concepts from percolation approaches, prunes out possible epidemic histories and creates potential epidemic graphs (i.e. a mathematical representation of all consistent epidemics) that can be 'realized' to create perfectly matched controlled and uncontrolled epidemics. We present an implementation of this method for a common class of compartmental models (e.g. SIR models), and its application in a simple SIR model. Results illustrate how, at the cost of some computation time, this method substantially narrows confidence intervals and avoids nonsensical inferences. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.