Vaccination against COVID-19 with the recently approved mRNA vaccines BNT162b2 (BioNTech/Pfizer) and mRNA-1273 (Moderna) is currently underway in a large number of countries. However, high incidence rates and rapidly spreading SARS-CoV-2 variants are
concerning. In combination with acute supply deficits in Europe in early 2021, the question arises of whether stretching the vaccine, for instance by delaying the second dose, can make a significant contribution to preventing deaths, despite associated risks such as lower vaccine efficacy, the potential emergence of escape mutants, enhancement, waning immunity, reduced social acceptance of off-label vaccination, and liability shifts. A quantitative epidemiological assessment of risks and benefits of non-standard vaccination protocols remains elusive. To clarify the situation and to provide a quantitative epidemiological foundation we develop a stochastic epidemiological model that integrates specific vaccine rollout protocols into a risk-group structured infectious disease dynamical model. Using the situation and conditions in Germany as a reference system, we show that delaying the second vaccine dose is expected to prevent deaths in the four to five digit range, should the incidence resurge. We show that this considerable public health benefit relies on the fact that both mRNA vaccines provide substantial protection against severe COVID-19 and death beginning 12 to 14 days after the first dose. The benefits of protocol change are attenuated should vaccine compliance decrease substantially. To quantify the impact of protocol change on vaccination adherence we performed a large-scale online survey. We find that, in Germany, changing vaccination protocols may lead to small reductions in vaccination intention. In sum, we therefore expect the benefits of a strategy change to remain substantial and stable.
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path len
gths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not complex. In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe non-vanishing clustering or community structure.
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 ErdH{o}s-Renyi and Barabasi-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.
