Beyond SIRD models: a novel dynamic model for epidemics, relating infected with entries to health care units and application for identification and restraining policy.

Epidemic models of susceptibles, exposed, infected, recovered and deceased (SΕIRD) presume homogeneity, constant rates and fixed, bilinear structure. They produce short-range, single-peak responses, hardly attained under restrictive measures. Tuned via uncertain I,R,D data, they cannot faithfully represent long-range evolution. A robust epidemic model is presented that relates infected with the entry rate to health care units (HCUs) via population averages. Model uncertainty is circumvented by not presuming any specific model structure, or constant rates. The model is tuned via data of low uncertainty, by direct monitoring: (a) of entries to HCUs (accurately known, in contrast to delayed and non-reliable I,R,D data) and (b) of scaled model parameters, representing population averages. The model encompasses random propagation of infections, delayed, randomly distributed entries to HCUs and varying exodus of non-hospitalized, as disease severity subdues. It closely follows multi-pattern growth of epidemics with possible recurrency, viral strains and mutations, varying environmental conditions, immunity levels, control measures and efficacy thereof, including vaccination. The results enable real-time identification of infected and infection rate. They allow design of resilient, cost-effective policy in real time, targeting directly the key variable to be controlled (entries to HCUs) below current HCU capacity. As demonstrated in ex post case studies, the policy can lead to lower overall cost of epidemics, by balancing the trade-off between the social cost of infected and the economic contraction associated with social distancing and mobility restriction measures.

COVID-19 in Scottish care homes: A metapopulation model of spread among residents and staff.

The movement of populations between locations and activities can result in complex transmission dynamics, posing significant challenges in controlling infectious diseases like COVID-19. Notably, networks of care homes create an ecosystem where staff and visitor movement acts as a vector for disease transmission, contributing to the heightened risk for their vulnerable communities. Care homes in the UK were disproportionately affected by the first wave of the COVID-19 pandemic, accounting for almost half of COVID-19 deaths during the period of 6th March - 15th June 2020 and so there is a pressing need to explore modelling approaches suitable for such systems. We develop a generic compartmental Susceptible - Exposed - Infectious - Recovered - Dead (SEIRD) metapopulation model, with care home residents, care home workers, and the general population modelled as subpopulations, interacting on a network describing their mixing habits. We illustrate the model application by analysing the spread of COVID-19 over the first wave of the COVID-19 pandemic in the NHS Lothian health board, Scotland. We explicitly model the outbreak's reproduction rate and care home visitation level over time for each subpopulation and execute a data fit and sensitivity analysis, focusing on parameters responsible for inter-subpopulation mixing: staff-sharing, staff shift patterns and visitation. The results from our sensitivity analysis show that restricting staff sharing between homes and staff interaction with the general public would significantly mitigate the disease burden. Our findings indicate that protecting care home staff from disease, coupled with reductions in staff-sharing across care homes and expedient cancellations of visitations, can significantly reduce the size of outbreaks in care home settings.

Emergence of the reproduction matrix in epidemic forecasting.

During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.

Including transgender populations in mathematical models for HIV treatment and prevention: current barriers and policy implications.

INTRODUCTION: Mathematical models of HIV have been uniquely important in directing and evaluating HIV policy. Transgender and nonbinary people are disproportionately impacted by HIV; however, few mathematical models of HIV transmission have been published that are inclusive of transgender and nonbinary populations. This commentary discusses current structural challenges to developing robust and accurate trans-inclusive models and identifies opportunities for future research and policy, with a focus on examples from the United States. DISCUSSION: As of April 2024, only seven published mathematical models of HIV transmission include transgender people. Existing models have several notable limitations and biases that limit their utility for informing public health intervention. Notably, no models include transgender men or nonbinary individuals, despite these populations being disproportionately impacted by HIV relative to cisgender populations. In addition, existing mathematical models of HIV transmission do not accurately represent the sexual network of transgender people. Data availability and quality remain a significant barrier to the development of accurate trans-inclusive mathematical models of HIV. Using a community-engaged approach, we developed a modelling framework that addresses the limitations of existing model and to highlight how data availability and quality limit the utility of mathematical models for transgender populations. CONCLUSIONS: Modelling is an important tool for HIV prevention planning and a key step towards informing public health interventions, programming and policies for transgender populations. Our modelling framework underscores the importance of accurate trans-inclusive data collection methodologies, since the relevance of these analyses for informing public health decision-making is strongly dependent on the validity of the model parameterization and calibration targets. Adopting gender-inclusive and gender-specific approaches starting from the development and data collection stages of research can provide insights into how interventions, programming and policies can distinguish unique health needs across all gender groups. Moreover, in light of the data structure limitations, designing longitudinal surveillance data systems and probability samples will be critical to fill key research gaps, highlight progress and provide additional rigour to the current evidence. Investments and initiatives like Ending the HIV Epidemic in the United States can be further expanded and are highly needed to prioritize and value transgender populations across funding structures, goals and outcome measures.

SIR or MADAM? The impact of privilege on careers in epidemic modelling.

As we emerge from what may be the largest global public health crises of our lives, our community of epidemic modellers is naturally reflecting. What role can modelling play in supporting decision making during epidemics? How could we more effectively interact with policy makers? How should we design future disease surveillance systems? All crucial questions. But who is going to be addressing them in 10 years' time? With high burnout and poor attrition rates in academia, both magnified in our field by our unprecedented efforts during the pandemic, and with low wages coinciding with inflation at its highest for decades, how do we retain talent? This is a multifaceted challenge, that I argue is underpinned by privilege. In this perspective, I introduce the notion of privilege and highlight how various aspects of privilege (namely gender, ethnicity, sexual orientation, language and caring responsibilities) may affect the ability of individuals to access to and progress within academic modelling careers. I propose actions that members of the epidemic modelling research community may take to mitigate these issues and ensure we have a more diverse and equitable workforce going forward.

The COVID-19 vaccination campaign in Switzerland and its impact on disease spread.

We analyse infectious disease case surveillance data to estimate COVID-19 spread and gain an understanding of the impact of introducing vaccines to counter the disease in Switzerland. The data used in this work is extensive and detailed and includes information on weekly number of cases and vaccination rates by age and region. Our approach takes into account waning immunity. The statistical analysis allows us to determine the effects of choosing alternative vaccination strategies. Our results indicate greater uptake of vaccine would have led to fewer cases with a particularly large effect on undervaccinated regions. An alternative distribution scheme not targeting specific age groups also leads to fewer cases overall but could lead to more cases among the elderly (a potentially vulnerable population) during the early stage of prophylaxis rollout.

Congruity of genomic and epidemiological data in modelling of local cholera outbreaks.

Cholera continues to be a global health threat. Understanding how cholera spreads between locations is fundamental to the rational, evidence-based design of intervention and control efforts. Traditionally, cholera transmission models have used cholera case-count data. More recently, whole-genome sequence data have qualitatively described cholera transmission. Integrating these data streams may provide much more accurate models of cholera spread; however, no systematic analyses have been performed so far to compare traditional case-count models to the phylodynamic models from genomic data for cholera transmission. Here, we use high-fidelity case-count and whole-genome sequencing data from the 1991 to 1998 cholera epidemic in Argentina to directly compare the epidemiological model parameters estimated from these two data sources. We find that phylodynamic methods applied to cholera genomics data provide comparable estimates that are in line with established methods. Our methodology represents a critical step in building a framework for integrating case-count and genomic data sources for cholera epidemiology and other bacterial pathogens.

On the impact of mass screening for SARS-CoV-2 through self-testing in Greece.

Background: Screening programs that pre-emptively and routinely test population groups for disease at a massive scale were first implemented during the COVID-19 pandemic in a handful of countries. One of these countries was Greece, which implemented a mass self-testing program during 2021. In contrast to most other non-pharmaceutical interventions (NPIs), mass self-testing programs are particularly attractive for their relatively small financial and social burden, and it is therefore important to understand their effectiveness to inform policy makers and public health officials responding to future pandemics. This study aimed to estimate the number of deaths and hospitalizations averted by the program implemented in Greece and evaluate the impact of several operational decisions. Methods: Granular data from the mass self-testing program deployed by the Greek government between April and December 2021 were obtained. The data were used to fit a novel compartmental model that was developed to describe the dynamics of the COVID-19 pandemic in Greece in the presence of self-testing. The fitted model provided estimates on the effectiveness of the program in averting deaths and hospitalizations. Sensitivity analyses were used to evaluate the impact of operational decisions, including the scale of the program, targeting of sub-populations, and sensitivity (i.e., true positive rate) of tests. Results: Conservative estimates show that the program reduced the reproduction number by 4%, hospitalizations by 25%, and deaths by 20%, translating into approximately 20,000 averted hospitalizations and 2,000 averted deaths in Greece between April and December 2021. Conclusion: Mass self-testing programs are efficient NPIs with minimal social and financial burden; therefore, they are invaluable tools to be considered in pandemic preparedness and response.

Exploring a targeted approach for public health capacity restrictions during COVID-19 using a new computational model.

This work introduces the Queen's University Agent-Based Outbreak Outcome Model (QUABOOM). This tool is an agent-based Monte Carlo simulation for modelling epidemics and informing public health policy. We illustrate the use of the model by examining capacity restrictions during a lockdown. We find that public health measures should focus on the few locations where many people interact, such as grocery stores, rather than the many locations where few people interact, such as small businesses. We also discuss a case where the results of the simulation can be scaled to larger population sizes, thereby improving computational efficiency.

Honoring the life and legacy of Fred Brauer.

The work of Fred Brauer (1932-2021) broke new ground in several areas of mathematical population biology, especially mathematical epidemiology and population management. This special issue reflects his legacy: the lines of inquiry he opened, the impact of his research and his books, and his mentoring of generations of young researchers. This dedication highlights milestones in his career and connects his work to the contributions in this issue.

The interplay of social constraints and individual variation in risk tolerance in the emergence of superspreaders.

Individual host behaviours can drastically impact the spread of infection through a population. Differences in the value individuals place on both socializing with others and avoiding infection have been shown to yield emergent homophily in social networks and thereby shape epidemic outcomes. We build on this understanding to explore how individuals who do not conform to their social surroundings contribute to the propagation of infection during outbreaks. We show how non-conforming individuals, even if they do not directly expose a disproportionate number of other individuals themselves, can become functional superspreaders through an emergent social structure that positions them as the functional links by which infection jumps between otherwise separate communities. Our results can help estimate the potential success of real-world interventions that may be compromised by a small number of non-conformists if their impact is not anticipated, and plan for how best to mitigate their effects on intervention success.

Estimating the impact of a police education program on hepatitis C virus transmission and disease burden among people who inject drugs in Tijuana, Mexico: A dynamic modeling analysis.

BACKGROUND AND AIMS: Criminalization of drug use and punitive policing are key structural drivers of hepatitis C virus (HCV) risk among people who inject drugs (PWID). A police education program (Proyecto Escudo) delivering training on occupational safety together with drug law content was implemented between 2015 and 2016 in Tijuana, Mexico, to underpin drug law reform implementation. We used data from a longitudinal cohort of PWID in Tijuana to inform epidemic modeling and assess the long-term impact of Escudo on HCV transmission and burden among PWID in Tijuana. METHODS: We developed a dynamic, compartmental model of HCV transmission and incarceration among PWID and tracked liver disease progression among current and former PWID. The model was calibrated to data from Tijuana, Mexico, with 90% HCV seroprevalence. We used segmented regression analysis to estimate impact of Escudo on recent incarceration among an observational cohort of PWID. By simulating the observed incarceration trends, we estimated the potential impact of the implemented (2-year reduction in incarceration) and an extended (10-year reduction in incarceration) police education program over a 50-year follow-up (2016-2066) on HCV outcomes (incidence, cirrhosis, HCV-related deaths and disability adjusted life-years averted) compared with no intervention. RESULTS: Over the 2-year follow-up, Proyecto Escudo reduced HCV incidence among PWID from 21.5 per 100 person years (/100py) (95% uncertainty interval [UI] = 15.3-29.7/100py) in 2016 to 21.1/100py (UI = 15.0-29.1/100py) in 2018. If continued for 10 years, Escudo could reduce HCV incidence to 20.0/100py (14.0-27.8/100py) by 2026 and avert 186 (32-389) new infections, 76 (UI = 12-160) cases of cirrhosis and 32 (5-73) deaths per 10 000 PWID compared with no intervention over a 50-year time horizon. CONCLUSIONS: In Tijuana, Mexico, implementation of a police education program delivering training on occupational safety and drug law content appears to have reduced hepatitis C virus incidence among people who inject drugs.

Uncertainty and error in SARS-CoV-2 epidemiological parameters inferred from population-level epidemic models.

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. 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 mis-specify 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 data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

An endemic-epidemic beta model for time series of infectious disease proportions.

Time series of proportions of infected patients or positive specimens are frequently encountered in disease control and prevention. Since proportions are bounded and often asymmetrically distributed, conventional Gaussian time series models only apply to suitably transformed proportions. Here we borrow both from beta regression and from the well-established HHH model for infectious disease counts to propose an endemic-epidemic beta model for proportion time series. It accommodates the asymmetric shape and heteroskedasticity of proportion distributions and is consistent for complementary proportions. Coefficients can be interpreted in terms of odds ratios. A multivariate formulation with spatial power-law weights enables the joint estimation of model parameters from multiple regions. In our application to a flu activity index in the USA, we find that the endemic-epidemic beta model provides a better fit than a seasonal ARIMA model for the logit-transformed proportions. Furthermore, a multivariate approach can improve regional forecasts and reduce model complexity in comparison to univariate beta models stratified by region.

A mixed methods analysis of participation in a social contact survey.

BACKGROUND: Social contact survey data forms a core component of modern epidemic models: however, there has been little assessment of the potential biases in such data. METHODS: We conducted focus groups with university students who had (n = 13) and had never (n = 14) completed a social contact survey during the COVID-19 pandemic. Qualitative findings were explored quantitatively by analysing participation data. RESULTS: The opportunity to contribute to COVID-19 research, to be heard and feel useful were frequently reported motivators for participating in the contact survey. Reductions in survey engagement following lifting of COVID-19 restrictions may have occurred because the research was perceived to be less critical and/or because the participants were busier and had more contacts. Having a high number of contacts to report, uncertainty around how to report each contact, and concerns around confidentiality were identified as factors leading to inaccurate reporting. Focus groups participants thought that financial incentives or provision of study results would encourage participation. CONCLUSIONS: Incentives could improve engagement with social contact surveys. Qualitative research can inform the format, timing, and wording of surveys to optimise completion and accuracy.

Data-driven clustering of infectious disease incidence into age groups.

Understanding the patterns of infectious diseases spread in the population is an important element of mitigation and vaccination programs. A major and common characteristic of most infectious diseases is age-related heterogeneity in the transmission, which potentially can affect the dynamics of an epidemic as manifested by the pattern of disease incidence in different age groups. Currently there are no statistical criteria of how to partition the disease incidence data into clusters. We develop the first data-driven methodology for deciding on the best partition of incidence data into age-groups, in a well defined statistical sense. The method employs a top-down hierarchical partitioning algorithm, with a stopping criteria based on multiple hypotheses significance testing controlling the family wise error rate. The type one error and statistical power of the method are tested using simulations. The method is then applied to Covid-19 incidence data in Israel, in order to extract the significant age-group clusters in each wave of the epidemic.

Modelling the contribution of incarceration and public health oriented drug law reform to HCV transmission and elimination among PWID in Tijuana, Mexico.

BACKGROUND: Incarceration is associated with increased risk of hepatitis C virus (HCV) among people who inject drugs (PWID). Mexico's previous attempt in implementing a public health-oriented drug law reform resulted in minimal impact on incarceration among PWID. However, implementation of reforms alongside Mexico's HCV elimination program has the potential to reshape the HCV epidemic among PWID in the next decade. We use data from a cohort of PWID in Tijuana, Mexico, to inform epidemic modeling to assess the contribution of incarceration and fully implemented drug reform on HCV transmission and elimination among PWID. METHODS: We developed a dynamic, deterministic model of incarceration, HCV transmission and disease progression among PWID. The model was calibrated to data from Tijuana, Mexico, with 90% HCV seroprevalence among 10,000 PWID. We estimated the 10-year population attributable fraction (PAF) of incarceration to HCV incidence among PWID and simulated, from 2022, the potential impact of the following scenarios: 1) decriminalization (80% reduction in incarceration rates); 2) fully implemented drug law reform (decriminalization and diversion to opiate agonist therapy [OAT]); 3) fully implemented drug law reform with HCV treatment (direct-acting antivirals [DAA]). We also assessed the number DAA needed to reach the 80% incidence reduction target by 2030 under these scenarios. RESULTS: Projections suggest a PAF of incarceration to HCV incidence of 5.4% (95% uncertainty interval [UI]:0.6-11.9%) among PWID in Tijuana between 2022-2032. Fully implemented drug reforms could reduce HCV incidence rate by 10.6% (95%UI:3.1-19.2%) across 10 years and reduce the number of DAA required to achieve Mexico's HCV incidence reduction goal by 14.3% (95%UI:5.3-17.1%). CONCLUSIONS: Among PWID in Tijuana, Mexico, incarceration remains an important contributor to HCV transmission. Full implementation of public health-oriented drug law reform could play an important role in reducing HCV incidence and improve the feasibility of reaching the HCV incidence elimination target by 2030.

A mathematical model for simulating the spread of a disease through a country divided into geographical regions with different population densities.

The SIR (susceptible-infectious-recovered) model is a well known method for predicting the number of people (or animals) in a population who become infected by and then recover from a disease. Modifications can include categories such people who have been exposed to the disease but are not yet infectious or those who die from the disease. However, the model has nearly always been applied to the entire population of a country or state but there is considerable observational evidence that diseases can spread at different rates in densely populated urban regions and sparsely populated rural areas. This work presents a new approach that applies a SIR type model to a country or state that has been divided into a number of geographical regions, and uses different infection rates in each region which depend on the population density in that region. Further, the model contains a simple matrix based method for simulating the movement of people between different regions. The model is applied to the spread of disease in the United Kingdom and the state of Rio Grande do Sul in Brazil.

Are epidemic growth rates more informative than reproduction numbers?

statistics, often derived from simplified models of epidemic spread, inform public health policy in real time. The instantaneous reproduction number, R t , is predominant among these statistics, measuring the average ability of an infection to multiply. However, R t encodes no temporal information and is sensitive to modelling assumptions. Consequently, some have proposed the epidemic growth rate, r t , that is, the rate of change of the log-transformed case incidence, as a more temporally meaningful and model-agnostic policy guide. We examine this assertion, identifying if and when estimates of r t are more informative than those of R t . We assess their relative strengths both for learning about pathogen transmission mechanisms and for guiding public health interventions in real time.

Estimating the effect of non-pharmaceutical interventions on US SARS-CoV-2 infections in the first year of the pandemic.

SARS-CoV-2 emerged in late 2019 as a zoonotic infection of humans, and proceeded to cause a worldwide pandemic of historic magnitude. Here, we use a simple epidemiological model and consider the full range of initial estimates from published studies for infection and recovery rates, seasonality, changes in mobility, the effectiveness of masks and the fraction of people wearing them. Monte Carlo simulations are used to simulate the progression of possible pandemics and we show a match for the real progression of the pandemic during 2020 with an R 2 of 0.91. The results show that the combination of masks and changes in mobility avoided approximately 248.3 million (σ = 31.2 million) infections in the US before vaccinations became available.