Modelling digital and manual contact tracing for COVID-19 Are low uptakes and missed contacts deal-breakers?

ABSTRACTComprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccines are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-Cov-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies using a generalized multi-site mean-field model, which can naturally assess the impact of both manual and digital approaches. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of several complex pathogens. We use this technique to simulate a new epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

The Fair Proportion is a Shapley Value on phylogenetic networks too

The Fair Proportion of a species in a phylogenetic tree is a very simple measure that has been used to assess its value relative to the overall phylogenetic diversity represented by the tree. It has recently been proved by Fuchs and Jin to be equal to the Shapley Value of the coallitional game that sends each subset of species to its rooted Phylogenetic Diversity in the tree. We prove in this paper that this result extends to the natural translations of the Fair Proportion and the rooted Phylogenetic Diversity to rooted phylogenetic networks. We also generalize to rooted phylogenetic networks the expression for the Shapley Value of the unrooted Phylogenetic Diversity game on a phylogenetic tree established by Haake, Kashiwada and Su.

Evolutionary Isolation and Phylogenetic Diversity Loss Under Random Extinction Events

The extinction of species at the present leads to the loss of ‘phylogenetic diversity’ (PD) from the evolutionary tree in which these species lie. Prior to extinction, the total PD present can be divided up among the species in various ways using measures of evolutionary isolation (such as ‘fair proportion’ and ‘equal splits’). However, the loss of PD when certain combinations of species become extinct can be either larger or smaller than the cumulative loss of the isolation values associated with the extinct species. In this paper, we show that for trees generated under neutral evolutionary models, the loss of PD under a null model of random extinction at the present can be predicted from the loss of the cumulative isolation values, by applying a non-linear transformation that is independent of the tree. Moreover, the error in the prediction provably converges to zero as the size of the tree grows, with simulations showing good agreement even for moderate sized trees (n = 64).

Time-Series Analysis of Suicidal and Undetermined Deaths

The suicide rate and the death rate for undetermined causes were negatively associated over time from 1968 to 1990 in the USA, suggesting that these undetermined deaths may include a fair proportion of suicides. In contrast, there was no association between suicide and undetermined death rates over the states in 1980.

Fungal sporocarp mediated losses of Ca, Fe, K, Mg, Mn, N, P, and Zn from conifer logs in the early stages of decomposition

The export of mass and nutrients associated with the formation of fungal sporocarps during the first 7 years of decomposition of logs of four conifer species (Abiesamabilis Dougl. ex Forbes, Pseudotsugamenziesii (Mirb.) Franco, Thujaplicata D. Don, and Tsugaheterophylla (Raf.) Sarg.) was investigated in western Oregon. Abundance of the most common fungal species, Naematolomacapnoides (Fr.:Fr.) P. Kumm, differed significantly with log species; the fungus was most abundant on Abies and least abundant on Thuja. Fungi increased concentrations of N, K, and P over those found in associated logs by as much as 38, 115, and 136 times, respectively. Thus, a fair proportion of the initial N (0.9–2.9%), K (1.8–4.5%), and P (1.9–6.6%) was transported out of logs via sporocarps at a time when immobilization would have been predicted from critical element ratios (e.g., C/N).

A lost cartulary of St Albans Abbey

It would be a truism among Anglo-Saxonists to say that we depend for our knowledge of a fair proportion of pre-Conquest literary and historical texts on the labours of scholars active in the sixteenth, seventeenth and early eighteenth centuries. Among the many important texts which were casualties, for example, of the Cotton fire on 23 October 1731, and for which we now depend on early modern transcripts and printed editions, one thinks immediately of Asser's Life of King Alfred and of the poem on the battle of Maldon (in Cotton Otho A. xii), of manuscript G of the Anglo-Saxon Chronicle (in Cotton Otho B. xi), and of Ealdorman Æthelweard's Chronicle (in Cotton Otho A. x). Should one choose to venture into the realm of Anglo-Saxon charters, the importance of antiquarian transcripts of manuscripts now lost becomes ever more apparent. The most spectacular addition to the corpus of charters made since the publication of Professor Sawyer's catalogue in 1968 arose from the examination of a sixteenth-century cartulary of Ilford Hospital preserved at Hatfield House, which proved to contain the texts of eleven pre-Conquest charters derived ultimately from the archives of Barking abbey in Essex; of course this manuscript is an ‘original’ cartulary, as opposed to an antiquarian transcript, but it serves here as a salutary reminder of the treasures which may lurk as yet unidentified in libraries and archives throughout the country. Other ‘discoveries’ include a seventeenth-century copy of a charter by which King Edgar granted an estate at Ballidon, in Derbyshire, to his thegn Æthelferth, Sir Henry Spelman's extracts from a lost cartulary of Abbotsbury abbey, and notes made by the jurist John Selden from a charter-roll formerly preserved in the archives of St Paul's Cathedral in London.