The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical ferromagnetic Ising and Potts models. In this paper, we study a natural non-local Markov chain known as the Chayes–Machta (CM) dynamics for the mean-field case of the random-cluster model, where the underlying graph is the complete graph on n vertices. The random-cluster model is parametrised by an edge probability p and a cluster weight q. Our focus is on the critical regime: $p = p_c(q)$ and $q \in (1,2)$, where $p_c(q)$ is the threshold corresponding to the order–disorder phase transition of the model. We show that the mixing time of the CM dynamics is $O({\log}\ n \cdot \log \log n)$ in this parameter regime, which reveals that the dynamics does not undergo an exponential slowdown at criticality, a surprising fact that had been predicted (but not proved) by statistical physicists. This also provides a nearly optimal bound (up to the $\log\log n$ factor) for the mixing time of the mean-field CM dynamics in the only regime of parameters where no non-trivial bound was previously known. Our proof consists of a multi-phased coupling argument that combines several key ingredients, including a new local limit theorem, a precise bound on the maximum of symmetric random walks with varying step sizes and tailored estimates for critical random graphs. In addition, we derive an improved comparison inequality between the mixing time of the CM dynamics and that of the local Glauber dynamics on general graphs; this results in better mixing time bounds for the local dynamics in the mean-field setting.

West Nile neuroinvasive disease (WNND) is a severe neurological illness that can result from West Nile virus (WNV) infection, with long-term disability and death being common outcomes. Although WNV arrived in North America over two decades ago, risk factors for WNND are still being explored. The objective of this study was to identify WNND comorbid risk factors in the Ontario population using a retrospective, population-based cohort design. Incident WNV infections from laboratory records between 1 January 2002 – 31 December 2012 were individually-linked to health administrative databases to ascertain WNND outcomes and comorbid risk factors. WNND incidence was compared among individuals with and without comorbidities using risk ratios (RR) calculated with log binomial regression.

Three hundred and forty-five individuals developed WNND (18.3%) out of 1884 WNV infections. West Nile encephalitis was driving most associations with comorbidities. Immunocompromised (aRR 2.61 [95% CI 1.23–4.53]) and male sex (aRR 1.32 [95% CI 1.00–1.76]) were risk factors for encephalitis, in addition to age, for which each 1-year increase was associated with a 2% (aRR 1.02 [95% CI 1.02–1.03]) relative increase in risk. Our results suggest that individuals living with comorbidities are at higher risk for WNND, in particular encephalitis, following WNV infection.

This paper investigates potential biodiversity valuation tools which actuaries could use in their work. It is an initial research paper into a selection of UK-based biodiversity valuation tools identified by the Department for Environment and Rural Affairs in its publication “Enabling a Natural Capital Approach Guidance”. The “Enabling a Natural Capital Approach Guidance” publication is seen as a comprehensive practical guide to natural capital and therefore is determined a sensible starting point on which to base this research. This research paper is not intended to be an exhaustive exploration of all biodiversity tools available, but rather is intended to identify a selection of tools which may be candidates for further research into their actuarial use case. We conclude that there are tools which merit additional research, and we recommend that these tools be further investigated to understand (i) the specific actuarial use case(s), (ii) whether the tools are applicable to direct infrastructure investments only or a broad range of asset classes, and (iii) whether their scope can be extended beyond the UK.

This paper follows on from the initial position paper on “The Importance of Biodiversity Risks”, prepared by the Biodiversity and Natural Capital Working party, a volunteer group working under the Sustainability Board. This paper explores the link between zoonotic disease and biodiversity loss and aims to raise awareness and discussion within the actuarial community on why this should be an important consideration in risk management. This paper focuses on how zoonotic diseases emerge, how they are linked to biodiversity loss, the potential impacts in the future and progress within the financial sector. This paper forms part of a collection of papers prepared by volunteers under the Sustainability Board that focus on different elements of biodiversity risk considerations.

This paper highlights the urgent need for actuaries to take into account the importance, perils and impacts of global biodiversity risks. The Biodiversity and Natural Capital Working Party has been set up to take forward a series of activities including think pieces, webinars and external engagement to ensure our proactive engagement with these risks.

This study aimed to determine the epidemiology and association of antimicrobial resistance (AMR) among Escherichia coli and Salmonella in Thailand. The E. coli (n = 1047) and Salmonella (n = 816) isolates from pigs, pork and humans were screened for 18 replicons including HI1, HI2, I1-γ, X, L/M, N, FIA, FIB, W, Y, P, FIC, A/C, T, FIIAs, F, K and B/O using polymerase chain reaction-based replicon typing. The E. coli (n = 26) and Salmonella (n = 3) isolates carrying IncF family replicons, ESBL and/or mcr genes were determined for FAB formula. IncF represented the major type of plasmids. Sixteen and eleven Inc groups were identified in E. coli (85.3%) and Salmonella (25.7%), respectively. The predominant replicon patterns between E. coli and Salmonella were IncK-F (23.7%) and IncF (46.2%). Significant correlations (P < 0.05) were observed between plasmid-replicon type and resistance phenotype. Plasmid replicon types were significantly different among sources of isolates and sampling periods. The most common FAB types between E. coli and Salmonella were F2:A-:B- (30.8%) and S1:A-:B- (66.7%), respectively. In conclusion, various plasmids present in E. coli and Salmonella. Responsible and prudent use of antimicrobials is suggested to reduce the selective pressures that favour the spread of AMR determinants. Further studies to understand the evolution of R plasmids and their contribution to the dissemination of AMR genes are warranted.

The classical Andrásfai-Erdős-Sós theorem considers the chromatic number of $K_{r + 1}$-free graphs with large minimum degree, and in the case, $r = 2$ says that any n-vertex triangle-free graph with minimum degree greater than $2/5 \cdot n$ is bipartite. This began the study of the chromatic profile of triangle-free graphs: for each k, what minimum degree guarantees that a triangle-free graph is k-colourable? The chromatic profile has been extensively studied and was finally determined by Brandt and Thomassé. Triangle-free graphs are exactly those in which each neighbourhood is one-colourable. As a natural variant, Luczak and Thomassé introduced the notion of a locally bipartite graph in which each neighbourhood is 2-colourable. Here we study the chromatic profile of the family of graphs in which every neighbourhood is b-colourable (locally b-partite graphs) as well as the family where the common neighbourhood of every a-clique is b-colourable. Our results include the chromatic thresholds of these families (extending a result of Allen, Böttcher, Griffiths, Kohayakawa and Morris) as well as showing that every n-vertex locally b-partite graph with minimum degree greater than $(1 - 1/(b + 1/7)) \cdot n$ is $(b + 1)$-colourable. Understanding these locally colourable graphs is crucial for extending the Andrásfai-Erdős-Sós theorem to non-complete graphs, which we develop elsewhere.

The COVID-19 pandemic interrupts the relatively steady trend of improving longevity observed in many countries over the last decades. We claim that this needs to be addressed explicitly in many mortality modelling applications, for example, in the life insurance industry. To support this position, we provide a descriptive analysis of the mortality development of several countries up to and including the year 2020. Furthermore, we perform an empirical and theoretical investigation of the impact a mortality jump has on the parameters, forecasts and implied present values of the popular Lee–Carter mortality model. We find that COVID-19 has resulted in substantial mortality shocks in many countries. We show that such shocks have a large impact on point and interval forecasts of death rates and, consequently, on the valuation of mortality-related insurance products. We obtain similar findings under the Cairns–Blake–Dowd mortality model, which demonstrates that the effects caused by COVID-19 show up in a variety of models. Finally, we provide an overview of approaches to handle extreme mortality events such as the COVID-19 pandemic in mortality modelling.