Households represent a key unit of interest in infectious disease epidemiology, in both empirical studies and mathematical modelling. The within-household transmission potential of a disease is often summarised by a secondary attack ratio (SAR). Despite its widespread use, the SAR depends on the household size distribution (HHSD) seen during the study period, making it difficult to generalise to new contexts. Extending estimates of transmission potential to new populations instead requires estimates of person-to-person transmission rates which can be convoluted with data on population structure to parametrise mechanistic transmission models. In this study we present a new Bayesian inference method which uses an MCMC algorithm to infer the transmission intensity by imputing the unreported household structure underlying the epidemic. This method can be run on household epidemiological data reported at varying levels of resolution. For synthetic data from a realistic underlying HHSD, we were able to achieve over 95

Contact (or mixing, or more generally connectivity) matrices are a fundamental component of modelling and inference for infectious disease epidemiology. Their structure and parametrisation directly accounts for the frequency of interactions between different subpopulations of individuals, as well as having the potential to encode dynamic heterogeneity in these interactions across demographic axes, space and time. Considerable research has been devoted to the structure and estimation of (components of) these matrices to help inform outbreak control and forecast disease spread. In this paper, we review the existing literature on the data types used to construct contact matrices and the methods for incorporating uncertainties and heterogeneities into them. We also highlight remaining challenges and future directions in the use of these contact matrices for epidemiological research.

Early in an infectious disease outbreak, key policy questions include whether and how the outbreak can be brought under control. In the epidemiological modelling literature, analyses of outbreak controllability have often focused on metrics such as reproduction numbers (which quantify the number of infections generated by each infected individual). However, whether an outbreak can be controlled is a complex question, depending on both the precise definition of 'under control' used and numerous factors affecting decision-makers' ability to implement transmission-reducing measures. Here, based on discussions at the Isaac Newton Institute's 'Modelling and inference for pandemic preparedness' programme (5-30 August 2024), we describe a wide range of factors affecting outbreak controllability in practice. Programme participants came from institutions in ten countries, enabling discussions to reflect experiences of using models to inform policy in different settings. We divide the factors according to whether they relate predominantly to characteristics of the pathogen, host population or available interventions, and describe policy considerations when assessing whether an outbreak is controllable.

Abstract Background In England, the burden of respiratory infections varies by ethnicity, contributing to health inequalities, but the role of additional demographic factors remains underexplored. We quantified how differences in social mixing and demographic characteristics between ethnic groups cause inequalities in transmission dynamics. Methods We analysed the association between the ethnicity and the number of contacts of 12,484 participants in the 2024–2025 Reconnect social contact survey, using a negative binomial regression model. We simulated respiratory pathogen epidemics using a compartmental model stratified by age, ethnicity, and contact levels, at a national level and in major cities in England. Findings After adjusting for demographic variables, participants of Black and Mixed ethnicities had more contacts than those of White ethnicity (rate ratios (RR): 1.18 [95% Credible Interval (CI): 1.11-1.26], and 1.31 [95% CI: 1.14-1.52]). Participants of Asian ethnicity had fewer contacts (RR: 0.85 [95% CI: 0.79-0.91]). In national-level simulations, individuals of White ethnicity had the lowest attack rates due to demographic differences and mixing patterns. Local demographic structures changed simulated dynamics: attack rates in individuals of Black and Mixed ethnicities were approximately double those of White ethnicity in Birmingham, but less than 60% higher in Liverpool. Interpretation Demographic characteristics and mixing patterns create inequalities in transmission dynamics between ethnicities, while local demographic characteristics and pathogen infectiousness change the expected relative burden. To ensure mitigation strategies are effective and equitable, their evaluation must explicitly account for inequalities arising from local context. Funding Medical Research Council, National Institute for Health and Care Research, Wellcome Trust Research in context Evidence before this study We searched PubMed for population-based studies quantifying differences in respiratory infections between ethnic groups, up to 1 April 2026, with no language restrictions. Keywords included: (respiratory pathogens OR influenza OR COVID-19) AND (ethnic* OR race) AND (inequ*) AND (compartmental model OR incidence rate ratio OR hazard ratio). We excluded studies that focused on non-respiratory pathogens (e.g. looking at consequences of COVID-19 on incidence of other pathogens). A population-based cohort study showed that influenza infection risk was higher in South Asian, Black, and Mixed ethnic groups compared to White ethnicity in England. Another population-based cohort study highlighted that during the first wave of COVID-19 in England, the South Asian, Black, and Mixed ethnic groups were more likely to test positive and to be hospitalised than the White ethnic group. Census data in England showed that the distributions of age, household size, household income and employment status differed between ethnic groups, and the recent Reconnect social contact surveys highlighted the impact of each demographic factor on the participants’ number of contacts. Added value of this study Our study shows that social contact patterns, mixing, and demographic structure all lead to unequal infection risk between ethnic groups in respiratory pathogen epidemics. Using the largest available social contact survey in England, we show that both the average number of contacts and the proportion of high-contact individuals varied by ethnic group, even after adjusting for participants’ demographics. These differences, together with mixing patterns and age structure, led to lower expected incidence among individuals of White ethnicity than in all other ethnic groups in simulated outbreaks. The level of inequality between ethnic groups changed when we used different values of pathogen transmissibility. Finally, as ethnic composition and population structure differ between cities in England, our results show differences in expected inequalities at a local level. Implications of all the available evidence Inequalities in infection risk between ethnic groups are context- and pathogen-dependent. They arise from both local population structure and contact patterns. Detailed information on mixing between groups and population structure is needed to accurately measure group-specific infection risk. These findings indicate that public health interventions based only on national-level estimates conceal regional variation in risk and may ultimately increase inequalities. Public health interventions need to be tailored to local contexts to be equitable and effective. Finally, our findings provide a foundation for understanding the progression from infection-risk inequalities to disparities in disease presentation and clinical outcomes.

The COVID-19 crisis required scientists worldwide to contribute to complex, hectic, and unfamiliar governmental decision-processes. In this Perspective, we reflect on this intense interaction between science and health policy for pandemic response, drawing from the experience of infectious disease modellers across the world. We highlight the diversity of actors and interests in government, aiming to demystify the elusive ‘policy makers’. We present a general taxonomy to help research scientists more effectively support evidence-based policy. We stress the importance of building and maintaining relationships appropriate to the diverse pool of government actors. Not recognising this diversity may lead to miscommunication and reduce the positive impacts of scientific evidence for public policy in crisis and non-crisis situations.

Abstract The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

During the COVID-19 pandemic, the emergence of novel variants of concern (VoCs) prompted different responses from governments across the world aimed at mitigating the impacts of more transmissible or more harmful strains. We model the invasion of a novel VoC into a population with heterogeneous vaccine- and infection-acquired immunity using a multi-type branching process framework with immigration. We define the number of cases needed to be reached to ensure stochastic extinction of this strain is unlikely and, therefore, the strain has become established in the population. To estimate the first-passage time distribution to reach this number of cases we use a mixture of stochastic simulations and analytic results. The first-passage time distribution gives a time window that is useful for policymakers planning interventions aimed at suppressing or delaying the introduction of novel VoC. We apply our method to a model of COVID-19 in the United Kingdom, though our results are applicable to other pathogens and settings.

The genus Neisseria includes two major human pathogens: N. meningitidis causing bacterial meningitis/septicemia and N. gonorrhoeae causing gonorrhoea. Mathematical models have been used to simulate their transmission and control strategies, and the recent observation of a meningococcal B (MenB) vaccine being partially effective against gonorrhoea has led to an increased modeling interest. Here we conducted a systematic review of the literature, focusing on studies that model vaccination strategies with MenB vaccines against Neisseria incidence and antimicrobial resistance. Using journal, preprint, and grey literature repositories, we identified 52 studies that we reviewed for validity, model approaches and assumptions. Most studies showed a good quality of evidence, and the variety of approaches along with their different modeling angles, was assuring especially for gonorrhoea studies. We identified options for future research, including the combination of both meningococcal and gonococcal infections in studies to have better estimates for vaccine benefits, and the spill over of gonorrhoea infections from the heterosexual to the MSM community and vice versa. Cost-effectiveness studies looking at at-risk and the wider populations can then be used to inform vaccine policies on gonorrhoea, as they have for meningococcal disease.

Cost-effectiveness analyses (CEA) typically involve comparing the effectiveness and costs of one or more interventions compared to the standard of care, in order to determine which intervention should be optimally implemented to maximise population health within the constraints of the healthcare budget. Traditionally, cost-effectiveness evaluations are expressed using incremental cost-effectiveness ratios (ICERs), which are compared with a fixed willingness-to-pay (WTP) threshold. Due to the inherent uncertainty in intervention costs and the overall burden of disease, particularly with regard to diseases in populations that are difficult to study, it becomes important to consider uncertainty quantification while estimating ICERs. To tackle the challenges of uncertainty quantification in CEA, we propose an alternative paradigm utilizing the Linear Wasserstein framework combined with Linear Discriminant Analysis (LDA) using a demonstrative example of lymphatic filariasis (LF). This approach uses geometric embeddings of the overall costs for treatment and surveillance, disability-adjusted life-years (DALYs) averted for morbidity by quantifying the burden of disease due to the years lived with disability, and probabilities of local elimination over a time-horizon of 20 years to evaluate the cost-effectiveness of lowering the stopping thresholds for post-surveillance determination of LF elimination as a public health problem. Our findings suggest that reducing the stopping threshold from <1 % to <0.5 % microfilaria (mf) prevalence for adults aged 20 years and above, under various treatment coverages and baseline prevalences, is cost-effective. When validated on 20 % of test data, for 65 % treatment coverage, a government expenditure of WTP ranging from $500 to $3000 per 1 % increase in local elimination probability justifies the switch to the lower threshold as cost-effective. Stochastic model simulations often lead to parameter and structural uncertainty in CEA. Uncertainty may impact the decisions taken, and this study underscores the necessity of better uncertainty quantification techniques within CEA for making informed decisions.

The reproduction number, the mean number of secondary cases infected by each primary case, gives an indication of the effort required to control the disease. Beyond the well-known basic reproduction number, there are two natural extensions, namely the control and effective reproduction numbers. As behaviour, population immunity and viral characteristics can change with time, these reproduction numbers can vary over time. Real-world data can be complex, so in this work we consider a generalized additive model to smooth surveillance data through the explicit incorporation of day-of-the-week effects, to provide a simple measure of the time-varying growth rate associated with the data. Converting the resulting spline into an estimator for both the control and effective reproduction numbers requires assumptions on a model structure, which we here assume to be a compartmental model. The reproduction numbers calculated are based on both simulated and real-world data, and are compared with estimates from an already existing tool. The derived method for estimating the time-varying reproduction number is effective, efficient and comparable with other methods. It provides a useful alternative approach, which can be included as part of a toolbox of models, that is particularly apt at smoothing out day-of-the-week effects in surveillance.

Since its emergence in late 2019, SARS-CoV-2 has diversified into a large number of lineages and caused multiple waves of infection globally. Novel lineages have the potential to spread rapidly and internationally if they have higher intrinsic transmissibility and/or can evade host immune responses, as has been seen with the Alpha, Delta, and Omicron variants of concern. They can also cause increased mortality and morbidity if they have increased virulence, as was seen for Alpha and Delta. Phylogenetic methods provide the “gold standard” for representing the global diversity of SARS-CoV-2 and to identify newly emerging lineages. However, these methods are computationally expensive, struggle when datasets get too large, and require manual curation to designate new lineages. These challenges provide a motivation to develop complementary methods that can incorporate all of the genetic data available without down-sampling to extract meaningful information rapidly and with minimal curation. In this paper, we demonstrate the utility of using algorithmic approaches based on word-statistics to represent whole sequences, bringing speed, scalability, and interpretability to the construction of genetic topologies. While not serving as a substitute for current phylogenetic analyses, the proposed methods can be used as a complementary, and fully automatable, approach to identify and confirm new emerging variants.

Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health interventions. The time taken for an outbreak to become large is inherently stochastic, and therefore uncertain, but after a sufficient number of infections has been reached the subsequent dynamics can be modelled accurately using ordinary differential equations. Here, we present analytical and numerical methods for approximating the time at which a stochastic model of a disease outbreak reaches a large number of cases and for quantifying the uncertainty arising from demographic stochasticity around that time. We then project this uncertainty forwards in time using an ordinary differential equation model in order to obtain a distribution for the peak timing of the epidemic that agrees closely with large simulations but that, for error tolerances relevant to most realistic applications, requires a fraction of the computational cost of full Monte Carlo approaches.

Mathematical modelling has played an important role in offering informed advice during the COVID-19 pandemic. In England, a cross government and academia collaboration generated medium-term projections (MTPs) of possible epidemic trajectories over the future 4–6 weeks from a collection of epidemiological models. In this article, we outline this collaborative modelling approach and evaluate the accuracy of the combined and individual model projections against the data over the period November 2021–December 2022 when various Omicron subvariants were spreading across England. Using a number of statistical methods, we quantify the predictive performance of the model projections for both the combined and individual MTPs, by evaluating the point and probabilistic accuracy. Our results illustrate that the combined MTPs, produced from an ensemble of heterogeneous epidemiological models, were a closer fit to the data than the individual models during the periods of epidemic growth or decline, with the 90% confidence intervals widest around the epidemic peaks. We also show that the combined MTPs increase the robustness and reduce the biases associated with a single model projection. Learning from our experience of ensemble modelling during the COVID-19 epidemic, our findings highlight the importance of developing cross-institutional multi-model infectious disease hubs for future outbreak control.

We propose a method to estimate the household secondary attack rate (hSAR) of COVID-19 in the United Kingdom based on activity on the social media platform X, formerly known as Twitter. Conventional methods of hSAR estimation are resource intensive, requiring regular contact tracing of COVID-19 cases. Our proposed framework provides a complementary method that does not rely on conventional contact tracing or laboratory involvement, including the collection, processing, and analysis of biological samples. We use a text classifier to identify reports of people tweeting about themselves and/or members of their household having COVID-19 infections. A probabilistic analysis is then performed to estimate the hSAR based on the number of self or household, and self and household tweets of COVID-19 infection. The analysis includes adjustments for a reluctance of Twitter users to tweet about household members, and the possibility that the secondary infection was not acquired within the household. Experimental results for the UK, both monthly and weekly, are reported for the period from January 2020 to February 2022. Our results agree with previously reported hSAR estimates, varying with the primary variants of concern, e.g. delta and omicron. The serial interval (SI) is based on the time between the two tweets that indicate a primary and secondary infection. Experimental results, though larger than the consensus, are qualitatively similar. The estimation of hSAR and SI using social media data constitutes a new tool that may help in characterizing, forecasting and managing outbreaks and pandemics in a faster, affordable, and more efficient manner.

OBJECTIVE:We aimed to use mathematical models of SARS-COV-2 to assess the potential efficacy of non-pharmaceutical interventions on transmission in the parcel delivery and logistics sector. METHODS:We devloped a network-based model of workplace contacts based on data and consultations from companies in the parcel delivery and logistics sectors. We used these in stochastic simulations of disease transmission to predict the probability of workplace outbreaks in this settings. Individuals in the model have different viral load trajectories based on SARS-CoV-2 in-host dynamics, which couple to their infectiousness and test positive probability over time, in order to determine the impact of testing and isolation measures. RESULTS:The baseline model (without any interventions) showed different workplace infection rates for staff in different job roles. Based on our assumptions of contact patterns in the parcel delivery work setting we found that when a delivery driver was the index case, on average they infect only 0.14 other employees, while for warehouse and office workers this went up to 0.65 and 2.24 respectively. In the LIDD setting this was predicted to be 1.40, 0.98, and 1.34 respectively. Nonetheless, the vast majority of simulations resulted in 0 secondary cases among customers (even without contact-free delivery). Our results showed that a combination of social distancing, office staff working from home, and fixed driver pairings (all interventions carried out by the companies we consulted) reduce the risk of workplace outbreaks by 3-4 times. CONCLUSION:This work suggests that, without interventions, significant transmission could have occured in these workplaces, but that these posed minimal risk to customers. We found that identifying and isolating regular close-contacts of infectious individuals (i.e. house-share, carpools, or delivery pairs) is an efficient measure for stopping workplace outbreaks. Regular testing can make these isolation measures even more effective but also increases the number of staff isolating at one time. It is therefore more efficient to use these isolation measures in addition to social distancing and contact reduction interventions, rather than instead of, as these reduce both transmission and the number of people needing to isolate at one time.

In this study, we evaluated the impact of viral variant, in addition to other variables, on within-host viral burden, by analysing cycle threshold (Ct) values derived from nose and throat swabs, collected as part of the UK COVID-19 Infection Survey. Because viral burden distributions determined from community survey data can be biased due to the impact of variant epidemiology on the time-since-infection of samples, we developed a method to explicitly adjust observed Ct value distributions to account for the expected bias. By analysing the adjusted Ct values using partial least squares regression, we found that among unvaccinated individuals with no known prior exposure, viral burden was 44% lower among Alpha variant infections, compared to those with the predecessor strain, B.1.177. Vaccination reduced viral burden by 67%, and among vaccinated individuals, viral burden was 286% higher among Delta variant, compared to Alpha variant, infections. In addition, viral burden increased by 17% for every 10-year age increment of the infected individual. In summary, within-host viral burden increases with age, is reduced by vaccination, and is influenced by the interplay of vaccination status and viral variant.

Background Predicting the likely size of future SARS-CoV-2 waves is necessary for public health planning. In England, voluntary “plan B” mitigation measures were introduced in December 2021 including increased home working and face coverings in shops but stopped short of restrictions on social contacts. The impact of voluntary risk mitigation behaviours on future SARS-CoV-2 burden is unknown. Methods We developed a rapid online survey of risk mitigation behaviours ahead of the winter 2021 festive period and deployed in two longitudinal cohort studies in the UK (Avon Longitudinal Study of Parents and Children (ALSPAC) and TwinsUK/COVID Symptom Study (CSS) Biobank) in December 2021. Using an individual-based, probabilistic model of COVID-19 transmission between social contacts with SARS-CoV-2 Omicron variant parameters and realistic vaccine coverage in England, we predicted the potential impact of the SARS-CoV-2 Omicron wave in England in terms of the effective reproduction number and cumulative infections, hospital admissions and deaths. Using survey results, we estimated in real-time the impact of voluntary risk mitigation behaviours on the Omicron wave in England, if implemented for the entire epidemic wave. Results Over 95% of survey respondents (N ALSPAC = 2686 and N Twins = 6155) reported some risk mitigation behaviours, with vaccination and using home testing kits reported most frequently. Less than half of those respondents reported that their behaviour was due to “plan B”. We estimate that without risk mitigation behaviours, the Omicron variant is consistent with an effective reproduction number between 2.5 and 3.5. Due to the reduced vaccine effectiveness against infection with the Omicron variant, our modelled estimates suggest that between 55% and 60% of the English population could be infected during the current wave, translating into between 12,000 and 46,000 cumulative deaths, depending on assumptions about severity and vaccine effectiveness. The actual number of deaths was 15,208 (26 November 2021–1 March 2022). We estimate that voluntary risk reduction measures could reduce the effective reproduction number to between 1.8 and 2.2 and reduce the cumulative number of deaths by up to 24%. Conclusions Predicting future infection burden is affected by uncertainty in disease severity and vaccine effectiveness estimates. In addition to biological uncertainty, we show that voluntary measures substantially reduce the projected impact of the SARS-CoV-2 Omicron variant but that voluntary measures alone would be unlikely to completely control transmission.