Emergence of the reproduction matrix in epidemic forecasting.

During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.

Projection of healthcare demand in Germany and Switzerland urged by Omicron wave (January-March 2022).

In January 2022, after the implementation of broad vaccination programs, the Omicron wave was propagating across Europe. There was an urgent need to understand how population immunity affects the dynamics of the COVID-19 pandemic when the loss of vaccine protection was concurrent with the emergence of a new variant of concern. In particular, assessing the risk of saturation of the healthcare systems was crucial to manage the pandemic and allow a transition towards the endemic course of SARS-CoV-2 by implementing more refined mitigation strategies that shield the most vulnerable groups and protect the healthcare systems. We investigated the epidemic dynamics by means of compartmental models that describe the age-stratified social-mixing and consider vaccination status, type, and waning of the efficacy. In response to the acute situation, our model aimed at (i) providing insight into the plausible scenarios that were likely to occur in Switzerland and Germany in the midst of the Omicron wave, (ii) informing public health authorities, and (iii) helping take informed decisions to minimize negative consequences of the pandemic. Despite the unprecedented numbers of new positive cases, our results suggested that, in all plausible scenarios, the wave was unlikely to create an overwhelming healthcare demand; due to the lower hospitalization rate and the effectiveness of the vaccines in preventing a severe course of the disease. This prediction came true and the healthcare systems in Switzerland and Germany were not pushed to the limit, despite the unprecedentedly large number of infections. By retrospective comparison of the model predictions with the official reported data of the epidemic dynamic, we demonstrate the ability of the model to capture the main features of the epidemic dynamic and the corresponding healthcare demand. In a broader context, our framework can be applied also to endemic scenarios, offering quantitative support for refined public health interventions in response to recurring waves of COVID-19 or other infectious diseases.