NOTES: unusual hour, etc (remove this line if not necessary).
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Requisite to identifiability from a finite amount of noisy data is that model parameters are first structurally identifiable: a mathematical question that establishes whether multiple parameter values may give rise to indistinguishable model outputs. Approaches to assess structural identifiability of deterministic ordinary differential equation models are well-established, however tools for the assessment of the increasingly relevant stochastic and spatial models remain in their infancy.
I provide in this talk an introduction to structural identifiability, before presenting new frameworks for the assessment of stochastic and partial differential equations. Importantly, I discuss the relevance of our methodology to model selection, and more the practical and aptly named practical identifiability of parameters in the context of experimental data. Finally, I conclude with a brief discussion of future research directions and remaining open questions.
Every population consists of individuals that vary in many traits, and each trait may or may not be associated with fitness. Variation in fitness traits lends population studies prone to selective depletion biases. When an ageing cohort exhibits declining mortality, it could be individuals becoming healthier or selective depletion of the frail. In an epidemic, when growth in cumulative infections decelerates, it could be individuals cautiously changing behaviour or selective depletion of the most susceptible. In microbial populations, when an isogenic population is stressed by antimicrobial treatment and some cells survive, this could be due to individual cells switching between normal and persister phenotypes or antibiotic selectively killing cells that divide faster. In each case, the first explanation invokes individuals changing (1), while the second posits selection on pre-existing variation changing (2). While explanations of type (1) are intuitive and widely adopted, those of type (2) are more neutral and rarely considered due to cognitive biases and challenges in estimating all variation that matters. While both are plausibly operating in most real systems, neglect of (2) leads to over-attribution of results to (1), wrong predictions, bad policy decisions and poor reproducibility, negatively impacting science, economics and ethics.
To overcome this selective depletion bias, we propose a pragmatic approach to study design and analysis whereby we infer distributions of characteristics that respond to selection and reframe theories accordingly. The approach is based on remodelling selection (mathematically by introducing key parametric distributions into population dynamic models, and empirically by measuring quantities of interest along selection gradients) and statistical inference (by fitting mathematical models to data). The procedure is being tested in systems where trait distributions can be inferred from population trends as well as reconstructed directly from individual measurements. Results of this ongoing research will be presented, and the wider applicability discussed.
Antimicrobial resistance (AMR) is a global threat, and combating its spread is of paramount importance. AMR often results from cooperative behaviour involving shared drug protection [1]. Microbial communities typically evolve in volatile, spatially structured environments. Migration, fluctuations, and environmental variability therefore strongly influence AMR. While AMR is enhanced by cell migration under static conditions, this picture changes fundamentally in time-fluctuating, spatially structured environments [2].
In this seminar, we consider a two-dimensional metapopulation consisting of demes (subpopulations) in which drug-resistant and drug-sensitive cells evolve in a time-varying environment containing a toxin against which protection can be shared. Cells migrate between demes, thereby coupling them. When environmental changes and variations in deme composition occur on comparable timescales, strong population bottlenecks lead to fluctuation-driven extinction events, which are countered by migration. By assessing the combined influence of migration and environmental variability on AMR, we identify near-optimal conditions for fluctuation-driven resistance eradication and show that slow migration can accelerate and enhance AMR clearance.
The first part of this work was carried out with Lluís Hernández-Navarro, Matthew Asker, and Alastair Rucklidge; the second part was done with Lluís Hernández-Navarro, Kenneth Distefano and Uwe Täuber. This research was funded by the EPSRC and NSF. Project website: https://eedfp.com/
References:
[1] L. Hernández-Navarro, M. Asker, A. M. Rucklidge, and M. Mobilia, J. R. Soc. Interface 20, 20230393 (2023): https://royalsocietypublishing.org/doi/10.1098/rsif.2023.0393
[2] L. Hernández-Navarro, K. Distefano, U. C. Täuber, and M. Mobilia, bioRxiv (2024), 2024.12.30.630406 (for PLOS Computational Biology): https://doi.org/10.1101/2024.12.30.630406
In this talk we revisit the Wells-Riley model which has been widely used to estimate airborne infection risk in indoor settings. We consider a probabilistic framework which allows one to quantify infection risk as a probability distribution in the scenario that variation is observed in the model parameters (e.g. due to heterogeneity, or uncertainty in measurements). By using fitted Gamma distributions, we show how the classical Wells-Riley approach can lead to systematic inaccuracies. Population-related uncertainties (e.g. quanta emission rate, pulmonary rate, exposure time) can cause infection risk overestimation, whilst environmental uncertainties (e.g. ventilation rate) can lead to infection risk underestimation. Furthermore, we investigate the effects of simultaneously random parameters and the cases where one tends to dominate the stochasticity of the final distribution over the other. Considering entire risk distributions allows for more accurate risk assessments and can help prevent extreme infection events caused by significantly low ventilation or unusually high quanta emission.
Infectious diseases are often modelled via stochastic individual-level state-transition processes. As the transmission process is typically only partially and noisily observed, inference for these models generally follows a Bayesian data augmentation approach. However, standard data augmentation Markov chain Monte Carlo (MCMC) methods for individual-level epidemic models are often inefficient in terms of their mixing or challenging to implement. In this talk, I will introduce a novel data-augmentation MCMC method for discrete-time individual-level epidemic models, called the Rippler algorithm. I will explain how the Rippler algorithm works and how its performance compares to the standard and the state-of-the-art inference methods for individual-level models. I will also present results of application of the algorithm to data on AMR E. coli from Malawi.
Despite decades of application of epidemiological models to respiratory viruses such as influenza and coronavirus, there is no standard model for capturing the life history of disease or immunological response, nor a standard approach to inference. I introduce two deterministic epidemic models applied to SARS-CoV-2 (UK) and pH1N1 2009 (UK and Australia). First, I introduce a discrete-time, deterministic model structured by age of infection, and explore how this model structure influences the performance and uncertainty quantification of both maximum likelihood and Bayesian inference methods in the context of SARS-CoV-2. I then present a two-subtype SIRS-like model and examine the conclusions that can be drawn from sparse immunological, microbiological, and serological data regarding the short- and medium-term impact of pH1N1 2009 vaccination. Finally, I review some remaining questions in seasonal influenza modelling, and discuss future work to calibrate mechanistic models that integrate climate variability, host immune dynamics, and behavioural responses.
Co-infection of a single host by different pathogens is ubiquitous in nature. We consider a population of hosts (e.g., small or large vertebrates) and a population of ticks, both of them susceptible to infection with two different strains of a given virus. We note that for the purposes of our models, we have Crimean-Congo hemorrhagic fever virus (a segmented Bunyavirus) in mind, as the application system. First, we focus on the dynamics of a single infection, proposing a deterministic model to understand the role of co-feeding in the transmission of the virus. We then compute the basic reproduction number by making use of the next generation matrix approach. When considering co-infection by two distinct strains (one resident and one invasive), we make use of differential equations to model the dynamics of susceptible, infected and co-infected species, and we compute the invasion reproduction number of the invasive strain. I discuss some problems with the calculation, and the solution proposed by Samuel Alizon and Marc Lipsitch. The second story involves HIV-1 co-infection. In this instance, we are interested in quantifying the potential for a viral recombinant to get established in a population in which two viral HIV-1 subtypes co-circulate. We make use of epidemiological data in Brazil and China, and together with a mathematical model of co-infection describe and quantify infection dynamics. A feature of the model is an essential asymmetric co-infection step. This allows to include in the model both population and within-host parameters that characterize infection dynamics, since recombination takes place in an individual host, and transmission of the recombinant is a population-level rate. We describe how the ability of the viral recombinant to get stablished depends on both types of parameters. We conclude with a perspective on how to improve the current model and the data sets required for its calibration.
Speaker: Prof Carmen Molina-Paris
Affiliation:
(1) Los Alamos National Laboratory, Los Alamos, New Mexico, USA
(2) School of Mathematics, University of Leeds, Leeds, UK
Global changes are affecting the distribution and demographics of several haematophagus arthropods that are relevant reservoirs and transmitters of infectious diseases to animals and humans. Several vector-borne diseases are emerging and re-emerging in several areas of the world, causing unprecedented outbreaks and concern to ecosystem, animal and public health authorities and people. Understanding the ecology of vectors and pathogens through ecological and epidemiological studies requires the application of mathematical and statistical tools to properly understand the complex interaction network of interactions between environment, animals, pathogens and humans. The examples of West Nile fever virus and Crimean-Congo haemorrhagic fever illustrate recent approaches to understand the ecology of two emerging diseases in Europe.
Speakers: Dr José Francisco Ruiz Fons (1) & Dr Zati Vatansever (2)
(1) Spanish Game & Wildlife Research Institute (IREC); Spanish Scientific Research Council (CSIC) & University of Castilla-La Mancha, Ciudad Real, Spain
(2) Kafkas University, Turkey
Many biological and social systems can be modelled as dynamical processes on networks. An important example are epidemics, where vertices in the network represent people, edges indicate social contacts and the dynamic describes how people’s health (susceptible to infection, infected, recovered etc.) changes in time in response to the health of the people they come into contact with. Biological models based on chemical reaction networks can also be described as dynamics on networks when there is network structure that governs which units can interact, and consequently the law of mass action no longer holds. These examples, and others, can be described exactly as Markov chains, but typically there are too many states for this to be of practical use. Thus it is standard to derive "mean-field" approximations, although this is often done using probabilistic intuition. In this talk I will describe a robust method to approximate a class of dynamical processes on networks based on an explicit average of their exact Markov chain description. While this provides a systematic method to derive mean-field approximations, it remains an open challenge to quantify the error introduced.
Malaria transmission and persistence depend critically on the interaction between parasite dynamics, human immunity, and epidemiological feedbacks. I will review recent work with collaborators developing and analysing structured PDE models spanning both population and within-host scales. At the population level, we couple vector–host epidemiology with the acquisition and loss of anti-disease immunity. Bifurcation analysis reveals the changing structure of endemic equilibria as transmission intensity rises, and our exploration of vaccination strategies, motivated by the RTS,S vaccine, highlights how seasonal transmission profiles may impact interventions. We also investigate multiple potential causes of backward bifurcation in this model. At the within-host level, we examine how parasites allocate resources between proliferation and transmission stages under immune pressure. Using an age‑of‑infection–structured model, we characterize immune-driven clearance thresholds and analyse parasite investment strategies, contrasting constant versus time-varying allocation rules. Our results indicate that adaptive immunity can impose a survival-reproduction tradeoff that explains why malaria parasites cannot evolve ever faster within-host multiplication. Together, these studies illustrate how immunity and feedbacks across scales shape malaria outcomes and inform intervention strategies.
