The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting with an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population. To this end, we introduce a parsimonious model that captures both quarantine of symptomatic infected individuals, as well as population-wide isolation practices in response to containment policies or behavioral changes, and show that the model captures the observed growth behavior accurately. The insights provided here may aid the careful implementation of containment strategies for ongoing secondary outbreaks of COVID-19 or similar future outbreaks of other emergent infectious diseases.

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the “small-world” effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by “flattening” the epidemic curve and delaying the spread to geographically distant regions.

The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, subexponential increase of confirmed cases with time during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak with sufficiently large reproduction rate. Although case counts vary significantly between affected provinces in Mainland China, the scaling law t µ is surprisingly universal, with a range of exponents µ = 2.1 ± 0.3. The universality of this behavior indicates that, in spite of social, regional, demographical, geographical, and socio-economical heterogeneities of affected Chinese provinces, this outbreak is dominated by fundamental mechanisms that are not captured by standard epidemiological models. We show that the observed scaling law is a direct consequence of containment policies that effectively deplete the susceptible population. To this end we introduce a parsimonious model that captures both, quarantine of symptomatic infected individuals as well as population wide isolation in response to mitigation policies or behavioral changes. For a wide range of parameters, the model reproduces the observed scaling law in confirmed cases and explains the observed exponents. Quantitative fits to empirical data permit the identification of peak times in the number of asymptomatic or oligo-symptomatic, unidentified infected individuals, as well as estimates of local variations in the basic reproduction number. The model implies that the observed scaling law in confirmed cases is a direct signature of effective contaiment strategies and/or systematic behavioral changes that affect a substantial fraction of the susceptible population. These insights may aid the implementation of containment strategies in potential export induced COVID-19 secondary outbreaks elsewhere or similar future outbreaks of other emergent infectious diseases.

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T < T_c, we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles.Comment: 23 pages, 4 figures; minor modification

We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This quantity is particularly important for random search processes and target localization in network topologies. Based on the global mean first passage time of target nodes we derive an estimate for the cumulative distribution function of the cover time based on first passage time statistics. We show that our result can be applied to various model networks, including Erdős-Rényi and Barabási-Albert networks, as well as various real-world networks. Our results reveal an intimate link between first passage and cover time statistics in networks in which structurally induced temporal correlations decay quickly and offer a computationally efficient way for estimating cover times in network related applications.