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The infectivity profile of an individual with COVID-19 is attributed to the paper Temporal dynamics in viral shedding and transmissibility of COVID-19 by He et al., published in Nature Medicine in April 2020. However, the analysis within this paper contains a mistake such that the published infectivity profile is incorrect and the conclusion that infectiousness begins 2.3 days before symptom onset is no longer supported. In this document we discuss the error and compute the correct infectivity profile. We also establish confidence intervals on this profile, quantify the difference between the published and the corrected profiles, and discuss an issue of normalisation when fitting serial interval data. This infectivity profile plays a central role in policy and decision making, thus it is crucial that this issue is corrected with the utmost urgency to prevent the propagation of this error into further studies and policies. We hope that this preprint will reach all researchers and policy makers who are using the incorrect infectivity profile to inform their work., Comment: 5 pages, 2 figures

The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic, societal or scientific relevance. A particular challenge is the identification of patterns across time, including those that might only become apparent when the temporal dimension is taken into account. Here, we present a novel method that aims to achieve this by detecting dynamic clusters, i.e. structural elements that can be present over prolonged durations. It is based on an adaptive identification of majority overlaps between groups at different time points and accommodates the transient decompositions in otherwise persistent dynamic clusters. Our method enables the detection of persistent structural elements with internal dynamics and can be applied to any classifiable data, ranging from social contact networks to arbitrary sets of time stamped feature vectors. It represents a unique tool to study systems with non-trivial temporal dynamics and has a broad applicability to scientific, societal and economic data.

Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously migrating between these two compartments. Here we construct an individual-based mathematical model of this process, which is parametrised using existing empirical findings from mice. This approach allows us to quantify the amount of migration between the bone marrow niches and the peripheral blood. We use this model to investigate clonal hematopoiesis, which is a significant risk factor for hematologic cancers. We also analyse the engraftment of donor stem cells into non-conditioned and conditioned hosts, quantifying the impact of different treatment scenarios. The simplicity of the model permits a thorough mathematical analysis, providing deeper insights into the dynamics of both the model and of the real-world system. We predict the time taken for mutant clones to expand within a host, as well as chimerism levels that can be expected following transplantation therapy, and the probability that a preconditioned host is reconstituted by donor cells., Comment: 46 pages, 11 figures (inclusive of SI)

Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and time to resistance. Specifically we address scenarios with sufficiently efficient therapies that suppress growth of all preexisting genetic variants in the compartment with highest drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance we analyze a multitype stochastic branching process describing growth of cancer cells in two compartments with different drug concentration and limited migration between compartments. We show that resistance is more likely to arise first in the low drug compartment and from there populate the high drug compartment. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end., Comment: Collaborations on further followup work are extremely welcome. Please see contact details at http://www.tb.ethz.ch/people/person-detail.html?persid=189998

Plant diseases often cause serious yield losses in agriculture. A pathogen's reproductive fitness can be quantified by the basic reproductive number, R0. Since pathogen transmission between host plants depends on the spatial separation between them, R0 is strongly influenced by the spatial scales of pathogen dispersal and the spatial scales of the host population. The basic reproductive number was found to increase with the field size at small field sizes and to saturate to a constant value at large field sizes. It reaches a maximum in quadratic fields and decreases as the field becomes elongated. This pattern appears to be quite general: it holds for dispersal kernels that decrease exponentially or faster as well as for "fat-tailed" dispersal kernels that decrease slower than exponential (i.e. power-law kernels). We used this approach to estimate R0 in wheat stripe rust (an important pathogen caused by Puccinia striiformis), since disease gradients for this pathogen were thoroughly measured over large distances [Sackett and Mundt, Phytopathology, 95, 983 (2005)]. For the two largest datasets, we estimated R0 in the limit of large fields to be of the order of 50. These estimates are consistent with independent field observations [Cowger et al. (2005), Phytopathology, 95, 97282; Farber et al. (2013), Phytopathology, 103, 41]. We present a proof of principle of a novel approach to estimate the basic reproductive number, R0, of plant pathogens using wheat stripe rust as a case study. We found that the spatial extent over which R0 changes strongly is quite fine-scaled (about 30 m of the linear extension of the field). Our results indicate that in order to optimize the spatial scale of deployment of fungicides or host resistances, the adjustments should be made at a fine spatial scale., Comment: 29 pages, 6 figures

A looming challenge for agriculture is sustainable intensification of food production to feed the growing human population. Current chemical and genetic technologies used to manage plant diseases are highly vulnerable to pathogen evolution and are not sustainable. Pathogen evolution is facilitated by the genetic uniformity underlying modern agroecosystems, suggesting that one path to sustainable disease control lies through increasing genetic diversity at the field scale by using genetically diverse host mixtures. We investigate how host mixtures can improve disease control using a population dynamics model. We find that when a population of crop plants is exposed to host-specialized pathogen species or strains, the overall disease severity is smaller in the mixture of two host varieties than in each of the corresponding pure stands. The disease severity can be minimized over a range of mixing ratios. These findings may help in designing host mixtures that efficiently control diseases of crops. We then generalize the model to describe host mixtures with many components. We find that when pathogens exhibit host specialization, the overall disease severity decreases with the number of components in the mixture. As the degree of specialization increases, the decrease in disease severity becomes larger. Using these model outcomes, we propose ways to optimize the use of host mixtures to decrease disease in agroecosystems.

Fungicide mixtures produced by the agrochemical industry often contain low-risk fungicides, to which fungal pathogens are fully sensitive, together with high-risk fungicides known to be prone to fungicide resistance. Can these mixtures provide adequate disease control while minimizing the risk for the development of resistance? We present a population dynamics model to address this question. We found that the fitness cost of resistance is a crucial parameter to determine the outcome of competition between the sensitive and resistant pathogen strains and to assess the usefulness of a mixture. If fitness costs are absent, then the use of the high-risk fungicide in a mixture selects for resistance and the fungicide eventually becomes nonfunctional. If there is a cost of resistance, then an optimal ratio of fungicides in the mixture can be found, at which selection for resistance is expected to vanish and the level of disease control can be optimized., Comment: 51 pages, 6 figures, accepted for publication in Phytopathology