Matt Keeling

Much of the literature and intuition associated with mathematical epidemiology is driven by deterministic models, which are a reasonable assumption when the population size is large. Stochastic models, especially individual based models, are however considered vital when dealing with small population sizes, especially at times of invasion or extinction. The overwhelming majority of these models (both deterministic and stochastic) assume that the underlying parameters are fixed (or follow a regular seasonal pattern). Here, we consider an analytic framework for dealing with randomly varying parameters through the use of stochastic differential equations - thereby capturing the action of external noisy processes such as weather. In particular, we focus on when the transmission rate, β, varies as the solution to a Cox-Ingersoll-Ross Model, such that β is gamma distributed with autocorrelation. We consider the impact of this parameter variation on a stochastic version of the Susceptible-Infected-Recovered model, and for this 'double-stochastic' model show through simulation and analytical results that exogenous noise increases the impact of stochasticity, potentially leading to more early extinctions, wider variations in the number of cases at equilibrium, but that early growth rate can be faster or slower depending on the precise parameters.

Symptom propagation occurs when the symptoms of secondary cases are related to those of the primary case as a result of epidemiological mechanisms. Determining whether - and to what extent - symptom propagation occurs requires data-driven methods. Here we quantify the strength of symptom propagation as the increase in risk of a secondary case developing severe symptoms if the primary case has severe symptoms. We first used synthetic results to determine the data requirements to robustly estimate the strength of symptom propagation and to investigate the effect of severity-dependent reporting bias. Categorising symptom severity into two group (mild or severe; asymptomatic or symptomatic), our estimation requires only four summary statistics - the number of primary-secondary case pairs of each combination of symptom presentations. Our analysis showed that a relatively small number (100) of synthetic primary-secondary case pairs was sufficient to obtain a reasonable estimate of the strength of symptom propagation and 1,000 pairs meant errors were consistently small across replicates. Our estimates were robust to severity-dependent reporting bias. We also explored how symptom propagation can be separated from other individual-level factors affecting severity, using age dependence as an example. Although synthetic data generated from an age-structured model led to overestimations of the strength of symptom propagation, allowing disease severity to be age-dependent restored the accuracy of parameter estimation. Finally, we applied our methodology to estimate the strength of symptom propagation from three publicly available data collected during the COVID-19 pandemic with data on presence or absence of symptoms: England households, Israel households, and Norway contact tracing. Our age-free methodology indicated a 12-17% increase in the risk of being symptomatic if infected by someone symptomatic. Our positive estimates for the strength of symptom propagation persisted when applying our age-dependent methodology to the two household data sets with age-structured information (England and Israel). These findings demonstrate evidence for symptom propagation of SARS-CoV-2 and provide consistent estimates for its strength. Our synthetic data analysis supports the conclusion that these correlations are not a result of reporting bias or age-dependent effects. This work provides a practical tool for estimating the strength of symptom propagation that has minimal data requirements, enabling application across a wide range of pathogens and epidemiological settings.

Capturing the structured mixing within a population is key to the reliable projection of infectious disease dynamics and hence informed control. Both heterogeneity in the number of epidemiologically-relevant contacts and age-structured mixing have been repeatedly demonstrated as fundamental, yet are rarely combined. Networks provide a powerful and intuitive method to realise these two elements of population structure, and simulate infection dynamics. While there are a few key examples of contact networks being measured explicitly, this is not scalable to larger populations, where representative networks must be constructed from more ubiquitous individual-level data. Here, using data from social contact surveys, we develop a generalisable and robust algorithm utilizing machine learning to generate a surrogate population-scale network that preserves both age-structured mixing and heterogeneity of contacts. For different datasets and network construction assumptions we simulate the spread of infection, considering how the epidemic size varies over basic reproduction number ( R ₀ ) scenarios - mirroring the process of determining public health impact from early epidemic growth. Our approach shows that both age structure and degree heterogeneity substantially reduce the epidemic size (for a given R ₀ ) compared to simpler models. We also demonstrate that these simulations more accurately re-capture the heterogeneity in secondary cases that has been observed, when transmission is scaled by contact duration to dampen the effect of highly connected nodes (“super-spreaders”). By using survey data collected during 2020-2022, these network models also inform about the impacts of control and targeting of public health interventions: quantifying the non-linear reduction in transmission opportunities that occurred during lockdowns, and the ages and contact types most responsible for onward transmission. Our robust methodology therefore allows for the inclusion of the full wealth of data commonly collected by surveys but frequently overlooked to be incorporated into more realistic transmission models of infectious diseases.

Infection with pnuemococcus bacteria is generally mild but can be more severe in the young and elderly, causing invasive pneumococcal disease (IPD) and community-acquired pneumonia (CAP). Although paediatric pneumococcal conjugate vaccine (PCV) programmes and elderly pneumococcal polysaccharide vaccine (PPV) programmes have reduced cases, we estimate that pneumococcal infection still leads to direct health care costs of around £68M and approximately 16 thousand QALY losses in England per year. The public health situation is complicated by the large number of interacting serotypes, such that while serotype-specific vaccines reduced the target serotypes others arose to replace them. Here we develop a novel (relatively) low-dimensional model to capture the interaction of 26 common pneumococcal serotypes. The model is matched to English IPD data from 2000-2023 and to five carriage studies (conducted in 2001/02, 2008, 2012, 2015 and 2018). When combined with a health economic approach, this model allows us to calculate the willingness to pay for paediatric vaccination with PCV7 (introduced in England in 2006), PCV13 (introduced in England in 2010) and the future vaccination of both the young and elderly with PCV20, which offers protection against 20 serotypes. Due to rapid serotype replacement, we find that the introduction of PCV7 vaccination in 2006 was not cost effective - a result that could not have been anticipated at the time, but is supported by simple statistical fits to the IPD data. In contrast, switching to PCV13 in 2010 and switching to PCV20 in 2026 are both associated with a high willingness to pay for a single dose. Given pneumococcal disease has shifted over time to become predominantly in the older adult population, we find that switching from PPV23 to PCV20 vaccination in those aged 65 and introducing an additional PCV20 vaccine at age 75 are both cost effective for a sufficiently low vaccine price. The inference that underpins our model is unfortunately limited by the available data and the high-dimensional nature of multiple interacting serotypes. Future sampling of carriage from older adults would greatly improve our confidence, as would national estimates of CAP.

The SARS-CoV-2 pandemic caused devastating health, social and economic harms. Globally, during the first year of this pandemic, controls were primarily focused on containing the outbreak and minimizing infection, disease and health consequences. However, during the second year (2021) with vaccines being deployed, there was a recognition that mitigation measures needed to consider both infection control and socio-economic priorities, inevitably causing a tension between how these conflicting elements are balanced. In England, this was epitomized by the Roadmap out of Lockdown, which through four planned steps reduced controls from the January 2021 lockdown to no restrictions on social interactions. Here, we adopt a health-economic framework to consider a range of alternative approaches to the relaxation of controls, allowing us to quantitatively assess health losses (measured in quality adjusted life years, QALYs) and economic consequences (measured in terms of gross domestic product, GDP) in a unified framework. Using the UK Treasury framework of valuing one QALY at £70 000, we find that the implemented Roadmap performs extremely well, only being consistently outperformed by a similar strategy that starts all steps one week earlier. This work highlights the power of a holistic framework combining epidemiology and economics and suggests its utility in future outbreaks.

Several African countries experienced a surge in acute hemorrhagic conjunctivitis (AHC) cases in 2024. Investigations in Kenya, Mayotte and Tanzania identified coxsackievirus A24 variant (CV-A24v) as the causative agent. To date, limited genomic data exist to elucidate the sources, epidemiology, and evolution of CV-A24v in Africa. We generated 245 CV-A24v genomes from samples collected between January and September 2024 in coastal Kenya. Phylogenetic analysis showed that these viruses belonged to genotype IV, with two major clusters identified that differed by 52 nucleotides and five amino acids, with recombination detected in the 3D ^pol gene. The sequences clustered closely with contemporaneous Mayotte and Malawi sequences but were distinct from Asian sequences from 2023. Molecular clock dating revealed that the Kenyan sequences had a Most Recent Common Ancestor (MRCA) between June and October 2023. Our study provides the first detailed genomic analysis of CV-A24v from Africa to inform its future control strategies.

The SARS-CoV-2 pandemic caused devastating health, social and economic harms. Globally, during the first year of this pandemic, controls were primarily focused on containing the outbreak and minimising infection, disease and health consequences. However, during the second year (2021) with vaccines being deployed, there was a recognition that mitigation measures needed to consider both infection control and socio-economic priorities, inevitably causing a tension between how these conflicting elements are balanced. In England, this was epitomised by the Roadmap out of Lockdown, which through 4 planned steps reduced controls from the January 2021 lockdown to no restrictions on social interactions. Here, we adopt a health-economic framework to consider a range of alternative approaches to the relaxation of controls, allowing us to quantitatively assess health losses (measured in Quality Adjusted Life Years, QALYs) and economic consequences (measured in terms of Gross Domestic Product, GDP) in a unified framework. Using the UK Treasury framework of valuing one QALY at £70,000, we find that the implemented Roadmap performs extremely well, only being consistently outperformed by a similar strategy that starts all steps one week earlier. This work highlights the power of a holistic framework combining epidemiology and economics, and suggests its utility in future outbreaks.

Background: Psychosocial factors are important for the uptake of livestock disease control measures by farmers and can differ by region, which would have implications for disease control nationally. Methods: We investigated altruism, trust, psychological proximity and the COM‐B behaviour change framework in a survey of 475 British cattle farmers in 2020. Using regression models, we studied associations between the country farmers lived in and psychosocial and behaviour change factors. Results: There were many between‐country differences in farmers' psychosocial and COM‐B profiles. Accounting for multiple tests, Scottish cattle farmers reported higher trust in governmental judgements for disease control and greater social opportunity to control disease than English cattle farmers. Limitations: There were relatively low numbers of respondents from Scotland and Wales. As such, the results should be interpreted with caution. Northern Irish farmers could not be included in the analyses as there were too few responses. Conclusion: Cattle farmers differed in their psychosocial profiles by country. Our sample of Scottish farmers reported higher trust in, and felt better supported by, government in the context of disease control than the English farmers, which could be due to different disease control approaches between devolved governments. Understanding between‐country differences in farmer psychosocial attributes has implications for animal health governance and approaches to disease control.

In locations that do not currently experience vector-borne disease (VBD) outbreaks but may be at risk under climate change, modeling future climate suitability for transmission is important for outbreak preparedness. Uncertainty in the future climate arises from three sources—differences in emissions scenarios, structural uncertainty across climate models, and internal climate variability (ICV)—but ICV is rarely considered in climate-VBD studies. Here, we demonstrate that ICV is a key source of uncertainty in climate suitability for VBD transmission, even decades into the future. Because of ICV, suitable climate conditions for transmission may arise in many locations sooner than expected under climate change alone.