Understanding how the population of infected individuals (which may be humans, animals or plants) fluctuates in size over the course of an epidemic is an important problem in epidemiology and ecology. The effective reproduction number, R, provides an intuitive and useful way of describing these fluctuations by characterising the growth rate of the infected population. An R > 1 signifies a burgeoning epidemic whereas R < 1 indicates a declining one. Public health agencies often use R to inform or corroborate vaccination and quarantine policies. However, popular approaches to inferring R from epidemic data make heuristic choices, which may lead to visually reasonable estimates that are deceptive or unreliable. By adapting mathematical tools from information theory, we develop a general and principled scheme for estimating R in a data-justified way. Our method exposes the pitfalls of heuristic estimates and provides an easily computable correction that also maximises our ability to predict upcoming population fluctuations. Our work is widely applicable to similar inference problems found in evolution and genetics, demonstrably useful for reliably analysing emerging epidemics in real time and highlights how abstract mathematical concepts can inspire novel and practical biological solutions, showcasing the importance of multidisciplinary research.
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