The workshop will focus on emerging challenges in mathematical epidemiology. While many of those challenges have been brought about by the ongoing COVID-19 pandemic, the aim and the scope of the workshop go beyond the pandemic. It is hoped to serve as an opportunity to re-evaluate the state of the art and the fundamentals of the discipline.
School of Mathematical Sciences
The University of Nottingham
School of Mathematical Sciences
The University of Nottingham
School of Mathematical Sciences
The University of Nottingham
Title: Frailty Variation in Population Dynamics
Abstract: Selection acting on unmeasured individual variation is a common source of bias in the analysis of populations. It has been shown to affect measured rates of mortality, the survival of endangered species, the scope of neutral theories of biodiversity and molecular evolution, measured risks of diseases whether non-communicable or infectious, the efficacy of interventions such as vaccines or symbionts, and it may be an underappreciated cause for widely debated reproducibility issues in science. Forms of variation that respond to selection and impact population dynamics, termed frailty variation in demography, remain elusive in many disciplines. I will present some examples, including how this appears to affect the estimation of efficacy of vaccine.
Title: Trackable species dynamics in reaction network models
Abstract: In a stochastic reaction network setting we define a subset of species as ’trackable’ if we can consistently follow the fate of its individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single molecule of trackable species in a simple and computationally efficient way. We give examples on how this approach may be used to obtain various characteristics of single-molecule dynamics. In particular, we apply the idea to obtain the distribution of the number of infections in a single individual in the course of an epidemic and the activity time of a single enzyme molecule. Joint work with Daniele Cappelletti.
Title: Likelihood approximations for stochastic epidemic models
Abstract: Individual-level stochastic models for infectious diseases invariably describe how the disease is transmitted from one individual to another. Conversely, in real life we rarely observe transmission, but instead we observe symptoms of disease. In many settings this complicates statistical inference because the likelihood of the observed data is intractable. Although methods such as data-augmented MCMC can deal with this, they can struggle in large-population settings. We describe a way to approximate the likelihood using interactions between pairs of individuals in the population.
Title: Data-rich but time-poor: the challenges of modelling in a global pandemic
Abstract: A personal view on the practicalities of providing scientific advice in a fast-paced emergency and the challenges of influencing government policy. I will illustrate these challenges with examples of developing scientific understanding of lateral flow testing in schools.
Title: On parameter identifiability in network-based epidemic models
Abstract: Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g., explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this we define strong and weak identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is they are weakly identifiable. This means that there exists multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data.
Title: Bayesian Non-Parametric Inference for Stochastic Epidemic Models
Abstract: The vast majority of epidemic models in the literature are parametric, meaning that they contain inherent assumptions about how transmission occurs in a population. However, such assumptions can be lacking in appropriate biological or epidemiological justification and in consequence lead to erroneous scientific conclusions and misleading predictions. In this talk I will give an overview of some recent developments in Bayesian non-parametric inference for stochastic epidemic models and discuss future challenges in this area.
Title: Hierarchical Bayesian model for the chemical reaction with time delay and its application to epidemics
Abstract: Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. This approach can be computationally challenging in simple systems, leading to significant uncertainties and identifiability problems in parameter estimation. Indeed, complex dynamics of chemical reactions may have hidden or indirectly measured compartments. This makes it challenging to construct a model of the whole process. Model simplification, including time delay, is essential for identifying model estimation. We will require alternative approaches to efficiently uncover the interactions in complex biochemical networks with time delay. We propose a Bayesian inference framework to replace uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to construct the likelihoods of the model parameters. We utilized MCMC methods to estimate reaction rate constants efficiently and delay distribution parameters from simpler states. We illustrate the proposed approach’s advantages and pitfalls using a birth-death model with both synthetic and experimental data and show that we can robustly infer model parameters using relatively small measurements. We also applied the proposed method to complex epidemic models when all compartments of the epidemic model are not observed.
Title: Estimating transmission and prevalence in populations under repeated testing
Abstract: Repeated testing is a powerful tool for tracking and managing disease outbreaks and has seen widespread use throughout the SARS-CoV-2 pandemic. However, under such testing regimes, naïve estimates of disease prevalence (and thus also estimates of quantities derived from prevalence estimates) are biased. We develop a method called interval dynamic survival analysis (IDSA) that adapts the strategy of dynamic survival analysis to the repeated testing scenario where data consist of the test times and test results of all individuals in the population, allowing us to estimate transmission and prevalence while accounting for the effects of the testing regime. The basic approach of IDSA is to treat individuals' test results as censorings of their infectious periods. We additionally model test sensitivity that may depend on age of infection. We implement an MCMC estimation scheme and fit our model to synthetic data and to real data collected from repeated testing of undergraduates at The Ohio State University. This is joint work with Patrick Schnell, Wasiur KhudaBukhsh, Mikkel Quam, Joseph Tien, and Grzegorz Rempała.
Title: ncorporating behaviour into epidemiological models - challenges and questions
Abstract: My personal view on the challenges and questions for epidemiological-behavioural modelling that have arisen in the midst of the COVID-19 pandemic. I will also discuss the themes that arose from a set of Isaac Newton Institute Newton Gateway workshops on "Modelling Behaviour to Inform Policy for Pandemics", hosted in November 2021 and February 2022.
Title: Enhancing global preparedness during an ongoing pandemic from imperfect data
Abstract: We show that, in the early stages of an emerging variant, integrating data from national genomic surveillance and global human mobility with large-scale epidemic modeling allows to quantify its pandemic potential, providing quantifiable indicators for pro-active policy interventions. We validate our framework on worldwide spreading variants and gain insights about the pandemic potential of BA.5 and BA.2.75 sub-lineages. Country-level epidemic intelligence is not enough to contrast the pandemic of respiratory pathogens such as SARS-CoV-2 and a scalable integrated approach, i.e. pandemic intelligence, is required to enhance global preparedness.
Title: Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models
Abstract: We consider how modelling choices for the distributions representing host infectiousness and the infection-to-death time-scale, within deterministic population-level epidemic models, impact inferred epidemic characteristics. We introduce an SIR-type model with the infected population structured by `infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly misspecify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK SARS-CoV-2 data in the period 15 Feb--14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty.
Title: Motif-based Mean-field Approximations and Mean-field Games for Epidemiology
Abstract: It is well-known that mean-field equations facilitate otherwise computationally-expensive stochastic analysis of microscopic agent-based models for epidemic spread by considering the evolution of fractions of agents in certain states. However, existing mean-field approximations remain oblivious of higher-order interactions that are common in practice. In this talk, we begin by considering a novel higher-order mean-field approximation, capable of handling clustered sparse graphs and going beyond pairwise interactions via the use of motifs. In the second half of the talk we consider epidemics control problems on dense graphs in discrete-time, where (e.g. human) agents are self-interested and may take egoistic decisions. We will consider mean-field games for analyzing rational equilibrium behavior of agents during pandemics. Here, we will focus on discrete-time models and present a learning-based solution.
Title: The impact of household structure on herd immunity
Abstract: This work concerns vaccination, in particular the use of disease-induced herd immunity; the spread of infection can be considered as a targeted vaccine, with an aim to prevent a major outbreak. The required proportion to be targeted in order to do so is referred to as the disease-induced herd immunity level. Often heterogeneity in the population can lower the disease-induced herd immunity level. We consider disease-induced herd immunity in the households model and compare it to the classical herd immunity level in which individuals are vaccinated uniformly at random among the population.