Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks.

The basic reproduction number, , is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not.

Eco-evolutionary dynamics in finite network-structured populations with migration.

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes.

Aortic stenosis post-COVID-19: a mathematical model on waiting lists and mortality.

Objectives: To provide estimates for how different treatment pathways for the management of severe aortic stenosis (AS) may affect National Health Service (NHS) England waiting list duration and associated mortality.

Design: We constructed a mathematical model of the excess waiting list and found the closed-form analytic solution to that model. From published data, we calculated estimates for how the strategies listed under Interventions may affect the time to clear the backlog of patients waiting for treatment and the associated waiting list mortality.

Effectiveness of the BNT162b2 (Pfizer-BioNTech) and the ChAdOx1 nCoV-19 (Oxford-AstraZeneca) vaccines for reducing susceptibility to infection with the Delta variant (B.1.617.2) of SARS-CoV-2.

Background: From January to May 2021 the alpha variant (B.1.1.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics.

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour.

Divide-and-conquer: machine-learning integrates mammalian and viral traits with network features to predict virus-mammal associations.

Our knowledge of viral host ranges remains limited. Completing this picture by identifying unknown hosts of known viruses is an important research aim that can help identify and mitigate zoonotic and animal-disease risks, such as spill-over from animal reservoirs into human populations. To address this knowledge-gap we apply a divide-and-conquer approach which separates viral, mammalian and network features into three unique perspectives, each predicting associations independently to enhance predictive power.

Evolutionary bet-hedging in structured populations.

As ecosystems evolve, species can become extinct due to fluctuations in the environment. This leads to the evolutionary adaption known as bet-hedging, where species hedge against these fluctuations to reduce their likelihood of extinction. Environmental variation can be either within or between generations.

Evolutionary graph theory derived from eco-evolutionary dynamics.

A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes.

Impact of climatic, demographic and disease control factors on the transmission dynamics of COVID-19 in large cities worldwide.

Approximately a year into the COVID-19 pandemic caused by the SARS-CoV-2 virus, many countries have seen additional "waves" of infections, especially in the temperate northern hemisphere. Other vulnerable regions, such as South Africa and several parts of South America have also seen cases rise, further impacting local economies and livelihoods. Despite substantial research efforts to date, it remains unresolved as to whether COVID-19 transmission has the same sensitivity to climate observed for other common respiratory viruses such as seasonal influenza.

Integration of shared-pathogen networks and machine learning reveals the key aspects of zoonoses and predicts mammalian reservoirs.

Diseases that spread to humans from animals, zoonoses, pose major threats to human health. Identifying animal reservoirs of zoonoses and predicting future outbreaks are increasingly important to human health and well-being and economic stability, particularly where research and resources are limited. Here, we integrate complex networks and machine learning approaches to develop a new approach to identifying reservoirs.

Localization of eigenvector centrality in networks with a cut vertex.

We show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set, the most extreme example being networks with a cut vertex. Three distinct types of localization are identified in these structures. One is related to the well-established hub node localization phenomenon and the other two are introduced and characterized here.

Methods for approximating stochastic evolutionary dynamics on graphs.

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the evolutionary process. However, for more complicated heterogeneous structures, computationally intensive methods are required such as individual-based stochastic simulations.

A Combined In Vitro/In Silico Approach to Identifying Off-Target Receptor Toxicity.

Many xenobiotics can bind to off-target receptors and cause toxicity via the dysregulation of downstream transcription factors. Identification of subsequent off-target toxicity in these chemicals has often required extensive chemical testing in animal models. An alternative, integrated in vitro/in silico approach for predicting toxic off-target functional responses is presented to refine in vitro receptor identification and reduce the burden on in vivo testing.

Impact of the infectious period on epidemics.

The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time.

A control analysis perspective on Katz centrality.

Methods for efficiently controlling dynamics propagated on networks are usually based on identifying the most influential nodes. Knowledge of these nodes can be used for the targeted control of dynamics such as epidemics, or for modifying biochemical pathways relating to diseases. Similarly they are valuable for identifying points of failure to increase network resilience in, for example, social support networks and logistics networks.

The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models.

We consider a very general stochastic model for an SIR epidemic on a network which allows an individual's infectious period, and the time it takes to contact each of its neighbours after becoming infected, to be correlated. We write down the message passing system of equations for this model and prove, for the first time, that it has a unique feasible solution. We also generalise an earlier result by proving that this solution provides a rigorous upper bound for the expected epidemic size (cumulative number of infection events) at any fixed time [Formula: see text].

The Differential Warming Response of Britain's Rivers (1982-2011).

River water temperature is a hydrological feature primarily controlled by topographical, meteorological, climatological, and anthropogenic factors. For Britain, the study of freshwater temperatures has focussed mainly on observations made in England and Wales; similar comprehensive data sets for Scotland are currently unavailable. Here we present a model for the whole of mainland Britain over three recent decades (1982-2011) that incorporates geographical extrapolation to Scotland.

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks.

Complete hierarchies of SIR models on arbitrary networks with exact and approximate moment closure.

We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on arbitrary graphs (networks). For Poisson transmission and removal processes, this enables us to obtain a systematic reduction in the number of differential equations needed for an exact 'moment closure' representation of the underlying stochastic model.

Epidemic control analysis: designing targeted intervention strategies against epidemics propagated on contact networks.

In cases where there are limited resources for the eradication of an epidemic, or where we seek to minimise possible adverse impacts of interventions, it is essential to optimise the efficacy of control measures. We introduce a new approach, Epidemic Control Analysis (ECA), to design effective targeted intervention strategies to mitigate and control the propagation of infections across heterogeneous contact networks. We exemplify this methodology in the context of a newly developed individual-level deterministic Susceptible-Infectious-Susceptible (SIS) epidemiological model (we also briefly consider applications to Susceptible-Infectious-Removed (SIR) dynamics).

Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks.

The message passing approach of Karrer and Newman [Phys. Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite trees.

Tight control of hypoxia-inducible factor-α transient dynamics is essential for cell survival in hypoxia.

Intracellular signaling involving hypoxia-inducible factor (HIF) controls the adaptive responses to hypoxia. There is a growing body of evidence demonstrating that intracellular signals encode temporal information. Thus, the dynamics of protein levels, as well as protein quantity and/or localization, impacts on cell fate.

A novel untargeted metabolomics correlation-based network analysis incorporating human metabolic reconstructions.

Background: Metabolomics has become increasingly popular in the study of disease phenotypes and molecular pathophysiology. One branch of metabolomics that encompasses the high-throughput screening of cellular metabolism is metabolic profiling. In the present study, the metabolic profiles of different tumour cells from colorectal carcinoma and breast adenocarcinoma were exposed to hypoxic and normoxic conditions and these have been compared to reveal the potential metabolic effects of hypoxia on the biochemistry of the tumour cells; this may contribute to their survival in oxygen compromised environments.

An exact relationship between invasion probability and endemic prevalence for Markovian SIS dynamics on networks.

Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD).

Deterministic epidemic models on contact networks: correlations and unbiological terms.

The relationship between system-level and subsystem-level master equations is investigated and then utilised for a systematic and potentially automated derivation of the hierarchy of moment equations in a susceptible-infectious-removed (SIR) epidemic model. In the context of epidemics on contact networks we use this to show that the approximate nature of some deterministic models such as mean-field and pair-approximation models can be partly understood by the identification of implicit anomalous terms. These terms describe unbiological processes which can be systematically removed up to and including the nth order by nth order moment closure approximations.