Model-based assessment of COVID-19 epidemic dynamics by wastewater analysis.

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective approach for epidemic monitoring and the development of an effective warning system. However, its quantitative link to the epidemic status and the stages of outbreak is still elusive. Modelling is thus crucial to address these challenges. In this study, we present a novel mechanistic model-based approach to reconstruct the complete epidemic dynamics from SARS-CoV-2 viral load in wastewater. Our approach integrates noisy wastewater data and daily case numbers into a dynamical epidemiological model. As demonstrated for various regions and sampling protocols, it quantifies the case numbers, provides epidemic indicators and accurately infers future epidemic trends. Following its quantitative analysis, we also provide recommendations for wastewater data standards and for their use as warning indicators against new infection waves. In situations of reduced testing capacity, our modelling approach can enhance the surveillance of wastewater for early epidemic prediction and robust and cost-effective real-time monitoring of local COVID-19 dynamics.

The benefits, costs and feasibility of a low incidence COVID-19 strategy.

In the summer of 2021, European governments removed most NPIs after experiencing prolonged second and third waves of the COVID-19 pandemic. Most countries failed to achieve immunization rates high enough to avoid resurgence of the virus. Public health strategies for autumn and winter 2021 have ranged from countries aiming at low incidence by re-introducing NPIs to accepting high incidence levels. However, such high incidence strategies almost certainly lead to the very consequences that they seek to avoid: restrictions that harm people and economies. At high incidence, the important pandemic containment measure 'test-trace-isolate-support' becomes inefficient. At that point, the spread of SARS-CoV-2 and its numerous harmful consequences can likely only be controlled through restrictions. We argue that all European countries need to pursue a low incidence strategy in a coordinated manner. Such an endeavour can only be successful if it is built on open communication and trust.

Mesoscopic behavior from microscopic Markov dynamics and its application to calcium release channels.

A major challenge in biology is to understand how molecular processes determine phenotypic features. We address this fundamental problem in a class of model systems by developing a general mathematical framework that allows the calculation of mesoscopic properties from the knowledge of microscopic Markovian transition probabilities. We show how exact analytic formulae for the first and second moments of resident time distributions in mesostates can be derived from microscopic resident times and transition probabilities even for systems with a large number of microstates. We apply our formalism to models of the inositol trisphosphate receptor, which plays a key role in generating calcium signals triggering a wide variety of cellular responses. We demonstrate how experimentally accessible quantities, such as opening and closing times and the coefficient of variation of inter-spike intervals, and other, more elaborated, quantities can be analytically calculated from the underlying microscopic Markovian dynamics. A virtue of our approach is that we do not need to follow the detailed time evolution of the whole system, as we derive the relevant properties of its steady state without having to take into account the often extremely complicated transient features. We emphasize that our formulae fully agree with results obtained by stochastic simulations and approaches based on a full determination of the microscopic system's time evolution. We also illustrate how experiments can be devised to discriminate between alternative molecular models of the inositol trisphosphate receptor. The developed approach is applicable to any system described by a Markov process and, owing to the analytic nature of the resulting formulae, provides an easy way to characterize also rare events that are of particular importance to understand the intermittency properties of complex dynamic systems.

Calcium signals driven by single channel noise.

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular Ca2+ oscillations are sequences of random spikes despite the involvement of many molecules in spike generation. This randomness arises from the stochastic state transitions of individual Ca2+ release channels and does not average out due to the existence of steep concentration gradients. The system is hierarchical due to the structural levels channel--channel cluster--cell and a corresponding strength of coupling. Concentration gradients introduce microdomains which couple channels of a cluster strongly. But they couple clusters only weakly; too weak to establish deterministic behavior on cell level. Here, we present a multi-scale modelling concept for stochastic hierarchical systems. It simulates active molecules individually as Markov chains and their coupling by deterministic diffusion. Thus, we are able to follow the consequences of random single molecule state changes up to the signal on cell level. To demonstrate the potential of the method, we simulate a variety of experiments. Comparisons of simulated and experimental data of spontaneous oscillations in astrocytes emphasize the role of spatial concentration gradients in Ca2+ signalling. Analysis of extensive simulations indicates that frequency encoding described by the relation between average and standard deviation of interspike intervals is surprisingly robust. This robustness is a property of the random spiking mechanism and not a result of control.