Vaccine hesitancy promotes emergence of new SARS-CoV-2 variants.

The successive emergence of SARS-CoV-2 mutations has led to an unprecedented increase in COVID-19 incidence worldwide. Currently, vaccination is considered to be the best available solution to control the ongoing COVID-19 pandemic. However, public opposition to vaccination persists in many countries, which can lead to increased COVID-19 caseloads and hence greater opportunities for vaccine-evasive mutant strains to arise. To determine the extent that public opinion regarding vaccination can induce or hamper the emergence of new variants, we develop a model that couples a compartmental disease transmission framework featuring two strains of SARS-CoV-2 with game theoretical dynamics on whether or not to vaccinate. We combine semi-stochastic and deterministic simulations to explore the effect of mutation probability, perceived cost of receiving vaccines, and perceived risks of infection on the emergence and spread of mutant SARS-CoV-2 strains. We find that decreasing the perceived costs of being vaccinated and increasing the perceived risks of infection (that is, decreasing vaccine hesitation) will decrease the possibility of vaccine-resistant mutant strains becoming established by about fourfold for intermediate mutation rates. Conversely, we find increasing vaccine hesitation to cause both higher probability of mutant strains emerging and more wild-type cases after the mutant strain has appeared. We also find that once a new variant has emerged, perceived risk of being infected by the original variant plays a much larger role than perceptions of the new variant in determining future outbreak characteristics. Furthermore, we find that rapid vaccination under non-pharmaceutical interventions is a highly effective strategy for preventing new variant emergence, due to interaction effects between non-pharmaceutical interventions and public support for vaccination. Our findings indicate that policies that combine combating vaccine-related misinformation with non-pharmaceutical interventions (such as reducing social contact) will be the most effective for avoiding the establishment of harmful new variants.

Explainability of the COVID-19 epidemiological model with nonnegative tensor factorization.

The world is witnessing the devastating effects of the COVID-19 pandemic. Each country responded to contain the spread of the virus in the early stages through diverse response measures. Interpreting these responses and their patterns globally is essential to inform future responses to COVID-19 variants and future pandemics. A stochastic epidemiological model (SEM) is a well-established mathematical tool that helps to analyse the spread of infectious diseases through communities and the effects of various response measures. However, interpreting the outcome of these models is complex and often requires manual effort. In this paper, we propose a novel method to provide the explainability of an epidemiological model. We represent the output of SEM as a tensor model. We then apply nonnegative tensor factorization (NTF) to identify patterns of global response behaviours of countries and cluster the countries based on these patterns. We interpret the patterns and clusters to understand the global response behaviour of countries in the early stages of the pandemic. Our experimental results demonstrate the advantage of clustering using NTF and provide useful insights into the characteristics of country clusters.

Reducing societal impacts of SARS-CoV-2 interventions through subnational implementation.

To curb the initial spread of SARS-CoV-2, many countries relied on nation-wide implementation of non-pharmaceutical intervention measures, resulting in substantial socio-economic impacts. Potentially, subnational implementations might have had less of a societal impact, but comparable epidemiological impact. Here, using the first COVID-19 wave in the Netherlands as a case in point, we address this issue by developing a high-resolution analysis framework that uses a demographically stratified population and a spatially explicit, dynamic, individual contact-pattern based epidemiology, calibrated to hospital admissions data and mobility trends extracted from mobile phone signals and Google. We demonstrate how a subnational approach could achieve similar level of epidemiological control in terms of hospital admissions, while some parts of the country could stay open for a longer period. Our framework is exportable to other countries and settings, and may be used to develop policies on subnational approach as a better strategic choice for controlling future epidemics.

A comparison of COVID-19 outbreaks across US Combined Statistical Areas using new methods for estimating R0 and social distancing behaviour.

We investigated the initial outbreak rates and subsequent social distancing behaviour over the initial phase of the COVID-19 pandemic across 29 Combined Statistical Areas (CSAs) of the United States. We used the Numerus Model Builder Data and Simulation Analysis (NMB-DASA) web application to fit the exponential phase of a SCLAIV+D (Susceptible, Contact, Latent, Asymptomatic infectious, symptomatic Infectious, Vaccinated, Dead) disease classes model to outbreaks, thereby allowing us to obtain an estimate of the basic reproductive number R0 for each CSA. Values of R0 ranged from 1.9 to 9.4, with a mean and standard deviation of 4.5±1.8. Fixing the parameters from the exponential fit, we again used NMB-DASA to estimate a set of social distancing behaviour parameters to compute an epidemic flattening index cflatten. Finally, we applied hierarchical clustering methods using this index to divide CSA outbreaks into two clusters: those presenting a social distancing response that was either weaker or stronger. We found cflatten to be more influential in the clustering process than R0. Thus, our results suggest that the behavioural response after a short initial exponential growth phase is likely to be more determinative of the rise of an epidemic than R0 itself.

Cost-effectiveness of a whole-area testing pilot of asymptomatic SARS-CoV-2 infections with lateral flow devices: a modelling and economic analysis study.

BACKGROUND: Mass community testing for SARS-CoV-2 by lateral flow devices (LFDs) aims to reduce prevalence in the community. However its effectiveness as a public heath intervention is disputed. METHOD: Data from a mass testing pilot in the Borough of Merthyr Tydfil in late 2020 was used to model cases, hospitalisations, ICU admissions and deaths prevented. Further economic analysis with a healthcare perspective assessed cost-effectiveness in terms of healthcare costs avoided and QALYs gained. RESULTS: An initial conservative estimate of 360 (95% CI: 311-418) cases were prevented by the mass testing, representing a would-be reduction of 11% of all cases diagnosed in Merthyr Tydfil residents during the same period. Modelling healthcare burden estimates that 24 (16-36) hospitalizations, 5 (3-6) ICU admissions and 15 (11-20) deaths were prevented, representing 6.37%, 11.1% and 8.2%, respectively of the actual counts during the same period. A less conservative, best-case scenario predicts 2333 (1764-3115) cases prevented, representing 80% reduction in would-be cases. Cost -effectiveness analysis indicates 108 (80-143) QALYs gained, an incremental cost-effectiveness ratio of £2,143 (£860-£4,175) per QALY gained and net monetary benefit of £6.2 m (£4.5 m-£8.4 m). In the best-case scenario, this increases to £15.9 m (£12.3 m-£20.5 m). CONCLUSIONS: A non-negligible number of cases, hospitalisations and deaths were prevented by the mass testing pilot. Considering QALYs gained and healthcare costs avoided, the pilot was cost-effective. These findings suggest mass testing with LFDs in areas of high prevalence (> 2%) is likely to provide significant public health benefit. It is not yet clear whether similar benefits will be obtained in low prevalence settings or with vaccination rollout.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations.

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model.

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization.

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when R 0 > 1 under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the R 0 and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.

Modelling the effect of non-pharmaceutical interventions on COVID-19 transmission from mobility maps.

The world has faced the COVID-19 pandemic for over two years now, and it is time to revisit the lessons learned from lockdown measures for theoretical and practical epidemiological improvements. The interlink between these measures and the resulting change in mobility (a predictor of the disease transmission contact rate) is uncertain. We thus propose a new method for assessing the efficacy of various non-pharmaceutical interventions (NPI) and examine the aptness of incorporating mobility data for epidemiological modelling. Facebook mobility maps for the United Arab Emirates are used as input datasets from the first infection in the country to mid-Oct 2020. Dataset was limited to the pre-vaccination period as this paper focuses on assessing the different NPIs at an early epidemic stage when no vaccines are available and NPIs are the only way to reduce the reproduction number ( R 0 ). We developed a travel network density parameter ß t to provide an estimate of NPI impact on mobility patterns. Given the infection-fatality ratio and time lag (onset-to-death), a Bayesian probabilistic model is adapted to calculate the change in epidemic development with ß t . Results showed that the change in ß t clearly impacted R 0 . The three lockdowns strongly affected the growth of transmission rate and collectively reduced R 0 by 78% before the restrictions were eased. The model forecasted daily infections and deaths by 2% and 3% fractional errors. It also projected what-if scenarios for different implementation protocols of each NPI. The developed model can be applied to identify the most efficient NPIs for confronting new COVID-19 waves and the spread of variants, as well as for future pandemics.

Infectious disease modelling for SARS-CoV-2 in Africa to guide policy: A systematic review.

Applied epidemiological models have played a critical role in understanding the transmission and control of disease outbreaks. Their utility and accuracy in decision-making on appropriate responses during public health emergencies is however a factor of their calibration to local data, evidence informing model assumptions, speed of obtaining and communicating their results, ease of understanding and willingness by policymakers to use their insights. We conducted a systematic review of infectious disease models focused on SARS-CoV-2 in Africa to determine: a) spatial and temporal patterns of SARS-CoV-2 modelling in Africa, b) use of local data to calibrate the models and local expertise in modelling activities, and c) key modelling questions and policy insights. We searched PubMed, Embase, Web of Science and MedRxiv databases following the PRISMA guidelines to obtain all SARS-CoV-2 dynamic modelling papers for one or multiple African countries. We extracted data on countries studied, authors and their affiliations, modelling questions addressed, type of models used, use of local data to calibrate the models, and model insights for guiding policy decisions. A total of 74 papers met the inclusion criteria, with nearly two-thirds of these coming from 6% (3) of the African countries. Initial papers were published 2 months after the first cases were reported in Africa, with most papers published after the first wave. More than half of all papers (53, 78%) and (48, 65%) had a first and last author affiliated to an African institution respectively, and only 12% (9) used local data for model calibration. A total of 60% (46) of the papers modelled assessment of control interventions. The transmission rate parameter was found to drive the most uncertainty in the sensitivity analysis for majority of the models. The use of dynamic models to draw policy insights was crucial and therefore there is need to increase modelling capacity in the continent.

Assessing fitness-for-purpose and comparing the suitability of COVID-19 multi-country models for local contexts and users: [version 1;peer review: 1 approved, 1 approved with reservations]

Background: Mathematical models have been used throughout the COVID-19 pandemic to inform policymaking decisions. The COVID-19 Multi-Model Comparison Collaboration (CMCC) was established to provide country governments, particularly low- and middle-income countries (LMICs), and other model users with an overview of the aims, capabilities and limits of the main multi-country COVID-19 models to optimise their usefulness in the COVID-19 response. Methods: Seven models were identified that satisfied the inclusion criteria for the model comparison and had creators that were willing to participate in this analysis. A questionnaire, extraction tables and interview structure were developed to be used for each model, these tools had the aim of capturing the model characteristics deemed of greatest importance based on discussions with the Policy Group. The questionnaires were first completed by the CMCC Technical group using publicly available information, before further clarification and verification was obtained during interviews with the model developers. The fitness-for-purpose flow chart for assessing the appropriateness for use of different COVID-19 models was developed jointly by the CMCC Technical Group and Policy Group. Results: A flow chart of key questions to assess the fitness-for-purpose of commonly used COVID-19 epidemiological models was developed, with focus placed on their use in LMICs. Furthermore, each model was summarised with a description of the main characteristics, as well as the level of engagement and expertise required to use or adapt these models to LMIC settings. Conclusions: This work formalises a process for engagement with models, which is often done on an ad-hoc basis, with recommendations for both policymakers and model developers and should improve modelling use in policy decision making.

An assessment of the potential impact of the Omicron variant of SARS-CoV-2 in Aotearoa New Zealand.

New Zealand delayed the introduction of the Omicron variant of SARS-CoV-2 into the community by the continued use of strict border controls through to January 2022. This allowed time for vaccination rates to increase and the roll out of third doses of the vaccine (boosters) to begin. It also meant more data on the characteristics of Omicron became available prior to the first cases of community transmission. Here we present a mathematical model of an Omicron epidemic, incorporating the effects of the booster roll out and waning of vaccine-induced immunity, and based on estimates of vaccine effectiveness and disease severity from international data. The model considers differing levels of immunity against infection, severe illness and death, and ignores waning of infection-induced immunity. This model was used to provide an assessment of the potential impact of an Omicron wave in the New Zealand population, which helped inform government preparedness and response. At the time the modelling was carried out, the date of introduction of Omicron into the New Zealand community was unknown. We therefore simulated outbreaks with different start dates, as well as investigating different levels of booster uptake. We found that an outbreak starting on 1 February or 1 March led to a lower health burden than an outbreak starting on 1 January because of increased booster coverage, particularly in older age groups. We also found that outbreaks starting later in the year led to worse health outcomes than an outbreak starting on 1 March. This is because waning immunity in older groups started to outweigh the increased protection from higher booster coverage in younger groups. For an outbreak starting on 1 February and with high booster uptake, the number of occupied hospital beds in the model peaked between 800 and 3,300 depending on assumed transmission rates. We conclude that combining an accelerated booster programme with public health measures to flatten the curve are key to avoid overwhelming the healthcare system.

Rule-based epidemic models.

Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in chemistry. An important class of system that would be intractable if expressed as reactions or ordinary differential equations can be efficiently simulated when expressed as rules. In this paper we demonstrate the utility of the rule-based approach for epidemiological modelling presenting a suite of seven models illustrating the spread of infectious disease under different scenarios: wearing masks, infection via fomites and prevention by hand-washing, the concept of vector-borne diseases, testing and contact tracing interventions, disease propagation within motif-structured populations with shared environments such as schools, and superspreading events. Rule-based models allow to combine transparent modelling approach with scalability and compositionality and therefore can facilitate the study of aspects of infectious disease propagation in a richer context than would otherwise be feasible.

Model-based assessment of COVID-19 epidemic dynamics by wastewater analysis.

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective approach for epidemic monitoring and the development of an effective warning system. However, its quantitative link to the epidemic status and the stages of outbreak is still elusive. Modelling is thus crucial to address these challenges. In this study, we present a novel mechanistic model-based approach to reconstruct the complete epidemic dynamics from SARS-CoV-2 viral load in wastewater. Our approach integrates noisy wastewater data and daily case numbers into a dynamical epidemiological model. As demonstrated for various regions and sampling protocols, it quantifies the case numbers, provides epidemic indicators and accurately infers future epidemic trends. Following its quantitative analysis, we also provide recommendations for wastewater data standards and for their use as warning indicators against new infection waves. In situations of reduced testing capacity, our modelling approach can enhance the surveillance of wastewater for early epidemic prediction and robust and cost-effective real-time monitoring of local COVID-19 dynamics.

Borough-level COVID-19 forecasting in London using deep learning techniques and a novel MSE-Moran's I loss function.

Following its identification in late 2019, COVID-19 has spread around the globe, and been declared a pandemic. With this in mind, modelling the spread of COVID-19 remains important for responding effectively. To date research has focused primarily on modelling the spread of COVID-19 on national and regional scales with just a few studies doing so on a city and sub-city scale. However, no attempts have yet been made to design and optimize a model explicitly for accurately forecasting the spread of COVID-19 at sub-city scale. This research aimed to address this research gap by developing an experimental LSTM-ANN deep learning model. The model is largely autoregressive in nature as it considers temporally lagged borough-level COVID-19 cases data from the last 9 days, but also considers temporally lagged (i) borough-level NO2 concentration data, (ii) government stringency data, and (iii) climatic data from the last 9 days, as well as non-temporally variable borough-level urban characteristics data when modelling and forecasting the spread of the disease. The model was also encouraged to learn the spatial relationships between boroughs with regards to the spread of COVID-19 by a novel MSE-Moran's I loss function. Overall, the model's performance appears promising and so the model represents a useful tool for assisting the decision making and interventions of governing bodies within cities. A sensitivity analysis also indicated that of the non COVID-19 variables, the government stringency is particularly important in the modelling process, with this being closely followed by the climatic variables, the NO2 concentration data, and finally the urban characteristics data. Additionally, the introduction of the novel MSE-Moran's I loss function appeared to improve the model's forecasting performance, and so this research has implications at the intersection of deep learning and disease modelling. It may also have implications within spatio-temporal forecasting more generally because such a feature may have the potential to improve forecasting in other spatio-temporal applications.

Intensive care unit occupancy predictions in the COVID-19 pandemic based on age-structured modelling and differential flatness.

The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.

Exploring the role of mass immunisation in influenza pandemic preparedness: A modelling study for the UK context.

The nature and timing of the next influenza pandemic is unknown. This makes it difficult for policy makers to assess whether spending money now to prepare for mass immunisation in the event of a pandemic is worthwhile. We used simple epidemiological modelling and health economic analysis to identify the range of pandemic and policy scenarios under which plans to immunise the general UK population would have net benefit if a stockpiled vaccine or, alternatively, a responsively purchased vaccine were used. Each scenario we studied comprised a combination of pandemic, vaccine and immunisation programme characteristics in presence or absence of access to effective antivirals, with the chance of there being a pandemic each year fixed. Monetarised health benefits and cost savings from any influenza cases averted were set against the option, purchase, storage, distribution, administration, and disposal costs relevant for each scenario to give a discounted net present value over 10 years for planning to immunise, accounting for the possibility that there may be no pandemic over the period considered. To support understanding and exploration of model output, an interactive visualisation tool was devised and made available online. We evaluated over 29 million combinations of pandemic and policy characteristics. Preparedness plans incorporating mass immunisation show positive net present value for a wide range of scenarios, predominantly in the absence of effective antivirals. Plans based on the responsive purchase of vaccine have wider benefit than plans reliant on the purchase and maintenance of a stockpile if immunisation can start without extensive delays. This finding is not dependent on responsively purchased vaccine being more effective than stockpiled vaccine, but rather is driven by avoiding the costs of storing and replenishing a stockpile.

Descriptive understanding and prediction in COVID-19 modelling.

COVID-19 has substantially affected our lives during 2020. Since its beginning, several epidemiological models have been developed to investigate the specific dynamics of the disease. Early COVID-19 epidemiological models were purely statistical, based on a curve-fitting approach, and did not include causal knowledge about the disease. Yet, these models had predictive capacity; thus they were used to ground important political decisions, in virtue of the understanding of the dynamics of the pandemic that they offered. This raises a philosophical question about how purely statistical models can yield understanding, and if so, what the relationship between prediction and understanding in these models is. Drawing on the model that was developed by the Institute of Health Metrics and Evaluation, we argue that early epidemiological models yielded a modality of understanding that we call descriptive understanding, which contrasts with the so-called explanatory understanding which is assumed to be the main form of scientific understanding. We spell out the exact details of how descriptive understanding works, and efficiently yields understanding of the phenomena. Finally, we vindicate the necessity of studying other modalities of understanding that go beyond the conventionally assumed explanatory understanding.

Estimation of exogenous drivers to predict COVID-19 pandemic using a method from nonlinear control theory.

The currently ongoing COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. Epidemiological models play a crucial role, thereby assisting policymakers to predict the future course of infections and hospitalizations. One difficulty with current models is the existence of exogenous and unmeasurable variables and their significant effect on the infection dynamics. In this paper, we show how a method from nonlinear control theory can complement common compartmental epidemiological models. As a result, one can estimate and predict these exogenous variables requiring the reported infection cases as the only data source. The method allows to investigate how the estimates of exogenous variables are influenced by non-pharmaceutical interventions and how imminent epidemic waves could already be predicted at an early stage. In this way, the concept can serve as an "epidemometer" and guide the optimal timing of interventions. Analyses of the COVID-19 epidemic in various countries demonstrate the feasibility and potential of the proposed approach. The generic character of the method allows for straightforward extension to different epidemiological models.