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Closing schools has been a prominent public health control measure for respiratory virus pandemics. However, during the COVID-19 pandemic, they were more contentious, as children were at a lower risk of severe disease while prolonged closures could have affected children's development. Hong Kong experienced a large Omicron epidemic in the spring of 2022, and face-to-face classes were halted and reopened after the peak with daily rapid-antigen test screening. Using counterfactual simulations, we developed a susceptible-exposed-infectious-recovered model calibrated to severe disease data to estimate the impact of the school closures and screening measures. We estimated that the school closures and screening measures prevented an excess of 35.0% (33.2%, 38.8%) more deaths and 17.4% (15.0%, 19.9%) more hospitalizations in a counterfactual scenario without those interventions. In terms of the impact on disease burden, the closure of primary schools outperformed both the closure of secondary schools and rapid antigen testing. Rapid-antigen screening alone was also an effective measure while minimizing the disruption associated with school closures. This demonstrates that implementing school-non-pharmaceutical intervention requires input from community priorities, balancing the population-wide burden of disease (infections, hospitalizations or mortalities) or educational disruptions (missed school days) and economic repercussions (e.g. the cost of daily rapid-antigen screening).

Decisions on public health interventions to control infectious diseases are often informed by computational models. Interpreting the predicted outcomes of a public health decision requires not only high-quality modelling but also an ethical framework for assessing the benefits and harms associated with different options. The design and specification of ethical frameworks matured independently of computational modelling, so many values recognized as important for ethical decision-making are missing from computational models. We demonstrate a proof-of-concept approach to incorporate multiple public health values into the evaluation of a simple computational model for vaccination against a pathogen such as SARS-CoV-2. By examining a bounded space of alternative prioritizations of three values relevant to public health ethics (aggregate clinical burden, equity in clinical burden, equity in adverse effects from vaccination), we identify value trade-offs, where the outcomes of optimal strategies differ depending on the ethical framework. This work demonstrates an approach to incorporating diverse values into decision criteria used to evaluate outcomes of models of infectious disease interventions.

Mathematical models of infectious diseases are frequently used as a tool to support public health policy and decisions around the implementation of interventions such as school closures. However, most publications on policy-relevant modelling lack an ethical framework and do not explicitly consider the ethical implications of the work. This creates a risk that the unintended consequences of interventions are overlooked or that models are used to justify decisions that are inconsistent with public health ethics. In this article, we focus on the case study of school closures as a commonly modelled intervention against pandemic influenza, COVID-19 and other infectious disease threats. We briefly review some of the key concepts in public health ethics and describe approaches to modelling the effects of school closures. We then identify a series of ethical considerations involved in modelling school closures. These include accounting for population heterogeneity and inequalities; including a diversity of viewpoints and expertise in model design; considering the distribution of benefits and harms; and model transparency and contextualization. We conclude with some recommendations to ensure that policy-relevant modelling is consistent with some key ethics values.

The COVID-19 pandemic highlighted significant differences in infectious disease burden among sociodemographic groups in the United States, underscoring the need for modelling approaches that can capture the complex dynamics driving these heterogeneities. Specifically, variation in case incidence, mortality and disease burden has been observed across subpopulations stratified by race, ethnicity, sex, age and geographic region. Accurately incorporating fine-grained sociodemographic attributes into infectious disease models remains challenging due to complex correlations among individual characteristics. Additionally, accurately modelling transmission while accounting for exposure differences among population strata requires a detailed understanding of transmission risk across interaction settings. We address these challenges by incorporating drivers of exposure risk and detailed sociodemographic data into EpiCast-a large-scale agent-based model of respiratory pathogen spread in the United States. Using this model, we demonstrate how differences in the rate of infections between key demographic groups emerge in households, workplaces and schools. Our findings show that embedding fine-grained population heterogeneity into infectious disease models can reveal uneven outcomes in predicted disease burden among racial groups, driven by factors such as household size and workplace exposure risk. This study demonstrates the potential of detailed models of infectious disease spread to inform policy intervention design for future pandemics.

We conducted a methodological study of COVID-19 vaccine allocation modelling papers, specifically looking for publications that considered equity. We found that most models did not take equity into account, with the vast majority of publications presenting aggregated results and no results by any subgroup (e.g. age, race, geography, etc.). We then provide examples of how modelling can be useful to answer equity questions, and highlight some of the findings from the publications that did. Finally, we describe eight considerations that seem important to consider when including equity in future vaccine allocation models.

We reflect on the sustainability of modelling infectious disease outbreaks from the perspective of modelling as a field of practice. We formed a community of practice among UK infectious disease modellers who had contributed to the UK COVID-19 response. We previously used a participatory workshop approach to highlight issues in the infrastructure and incentives for outbreak modelling, and synthesized our experience into a set of 12 specific recommendations. Here, we track changes in the field of infectious disease modelling 1 year later, collecting the quantitative and qualitative views of change among 14 participants. We found participants continued to highlight a lack of ongoing, sufficient or appropriate action to develop outbreak modelling capacity in the UK, while positively noting collaborations among public health facing institutions. We emphasize the under-prioritization of funding for outbreak modelling outside of emergency response periods, and the continuation of unsustainable working practices. Correcting this is crucial to supporting evidence-based public health policy for outbreak preparedness and response.

Recurrent waves, which are often observed during long pandemics, typically form as a result of several interrelated dynamics, including public health interventions, population mobility and behaviour, varying disease transmissibility due to pathogen mutations, and changes in host immunity due to recency of vaccination or previous infections. Complex nonlinear dependencies among these dynamics, including feedback between disease incidence and the opinion-driven adoption of social distancing (SD) behaviour, remain poorly understood, particularly in scenarios involving heterogeneous population, partial and waning immunity and rapidly changing public opinions. This study addressed this challenge by proposing an opinion dynamics model that accounts for changes in SD behaviour (i.e. whether to adopt SD) by modelling both individual risk perception and peer pressure. The opinion dynamics model was integrated and validated within a large-scale agent-based COVID-19 pandemic simulation that modelled the spread of the Omicron variant of SARS-CoV-2 between December 2021 and June 2022 in Australia. Our study revealed that while holding epidemiological factors constant, the fluctuating adoption of SD, shaped by individual risk aversion and social peer pressure from both household and workplace environments, can reproduce these multi-wave patterns, pointing to the importance of social dynamics in understanding epidemic outcomes.

A broad array of experimental techniques have been used to determine the interactions between genes that regulate key cellular processes such as differentiation, metabolism and the cell cycle. The experimental studies are often complemented by development of models of varying degrees of complexity. We consider the 'inverse problem': to determine the underlying interactions based solely on the observed dynamics. In earlier work, we considered a specific class of ordinary differential equations that are continuous analogues of a Boolean switching network. We developed techniques to analyse and classify the dynamics based on their logical structure. We also developed techniques to solve the inverse problem. In the current work, we extend these earlier methods to analyse a model equation for a genetic network proposed by Cummins and colleagues. For a simple negative feedback system in which there is a cyclic interaction diagram with an odd number of inhibitory links, if the data is sampled at a sufficiently fine time scale with sufficient accuracy that maxima and minima can be determined, the structure can be deduced by considering sequences of maxima and minima. Alternatively, one can use the sequence of logical states found by discretizing the dynamics based on the first derivative of the variables as a function of time. The most useful technique for determining the interactions involves assessing the dependence of the rate of change of each variable as a function of the other variables, taken one at a time.

Protein sequestration motifs appear in many biological regulatory networks and introduce special properties into the network dynamics. Sequestration can be described as a mode of inactivation of a given protein by its binding to a second protein to form a new complex. In this complexed form, the original protein is prevented from performing its specific functions and is thus rendered inactive. We study a mathematical model of the mammalian circadian clock with a protein sequestration motif, which generates one of the negative feedback loops that guarantees periodic behaviour. First, the motif permits a time-scale separation, which can be used to simplify the model. We show that the simplified model admits a periodic orbit over a fairly large region of parameters. Second, we are able to show that the sequestration motif induces a phase response curve with a very specific form, implying that external perturbations can affect the system only in a narrow window of the periodic orbit. Finally, we compare our model with a classic Goodwin oscillator, to illustrate the dynamical and robustness properties induced by the protein sequestration motif.

This tutorial provides stepwise instructions to install over 20 tools, written in multiple languages. Their integration in the CoLoMoTo software suite makes them accessible with a single popular language (Python), thereby enabling reproducible and sophisticated dynamical analyses of logical models of complex cellular networks. The tutorial specifically focuses on the analysis of a previously published model of the regulatory network controlling mammalian cell proliferation. It includes chunks of Python code to reproduce several of the results and figures published in the original article, and further extends these results with the help of selected tools included in the CoLoMoTo suite. The tutorial covers the visualization of the network with the tool GINsim, an attractor analysis with bioLQM, the computation of synchronous attractors with BNS, the extraction of modules from the full model, stochastic simulations of the wild-type model and of selected perturbations with MaBoSS and finally the delineation of compressed probabilistic state transition graphs. The integration of all these analyses in an executable Jupyter Notebook greatly eases their reproducibility, as well as the inclusion of further extensions. The notebook provided along with this tutorial further constitutes a template, which can be enriched with other ColoMoTo tools, to develop comprehensive dynamical analyses of various biological network models.