Wastewater-based reproduction rates for epidemic curve reconstruction.

We introduce a hierarchical Bayesian framework for reconstructing epidemic curves using under-reported case counts and wastewater data. Our approach models wastewater signals as differentiable Gaussian processes, enabling inference on their relative growth rates, which are used to define a wastewater-based reproduction rate. These estimates are incorporated into a binomially thinned Poisson autoregressive model for case counts using a modular inference strategy. We apply this framework to reconstruct the Covid-19 epidemic curve in Toronto, validating our model through out-of-sample forecasts and comparisons with independent serosurvey-based cumulative incidence estimates. We also apply the framework to New Zealand's Covid-19 data to reconstruct its epidemic curve and demonstrate improvements over an existing joint model for wastewater and case data. A key advantage of our framework, highlighted in this comparison, is that it does not rely on pre-specified constant parameters, allowing the model to better adapt to evolving pandemic conditions.