Using statistics and mathematical modelling to understand infectious disease outbreaks: COVID-19 as an example

Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks; an application to COVID-19

We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases. We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing. The model is fitted to data reported for the early spread of COVID-19 in South Korea, Brazil, and Venezuela. The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries. Using the fitted values, we estimate the effective reproduction number R e and investigate its responses to varied control scenarios of contact tracing. Alongside the positivity of solutions, and a stability analysis of the disease-free equilibrium are provided.

Precision epidemiology at the nexus of mathematics and nanotechnology: Unraveling the dance of viral dynamics

The intersection of mathematical modeling, nanotechnology, and epidemiology marks a paradigm shift in our battle against infectious diseases, aligning with the focus of the journal on the regulation, expression, function, and evolution of genes in diverse biological contexts. This exploration navigates the intricate dance of viral transmission dynamics, highlighting mathematical models as dual tools of insight and precision instruments, a theme relevant to the diverse sections of Gene. In the context of virology, ethical considerations loom large, necessitating robust frameworks to protect individual rights, an aspect essential in infectious disease research. Global collaboration emerges as a critical pillar in our response to emerging infectious diseases, fortified by the predictive prowess of mathematical models enriched by nanotechnology. The synergy of interdisciplinary collaboration, training the next generation to bridge mathematical rigor, biology, and epidemiology, promises accelerated discoveries and robust models that account for real-world complexities, fostering innovation and exploration in the field. In this intricate review, mathematical modeling in viral transmission dynamics and epidemiology serves as a guiding beacon, illuminating the path toward precision interventions, global preparedness, and the collective endeavor to safeguard human health, resonating with the aim of advancing knowledge in gene regulation and expression.

Respiratory disease contact patterns in the US are stable but heterogeneous

Background

Contact plays a critical role in infectious disease transmission. Characterizing heterogeneity in contact patterns across individuals, time, and space is necessary to inform accurate estimates of transmission risk, particularly to explain superspreading, predict age differences in vulnerability, and inform social distancing policies. Current respiratory disease models often rely on data from the 2008 POLYMOD study conducted in Europe, which is now outdated and potentially unrepresentative of behavior in the US. We seek to understand the variation in contact patterns across spatial scales and demographic and social classifications, whether there is seasonality to contact patterns, and what social behavior looks like at baseline in the absence of an ongoing pandemic.

Methods

We analyze spatiotemporal non-household contact patterns across 11 million survey responses from June 2020 - April 2021 post-stratified on age and gender to correct for sample representation. To characterize spatiotemporal heterogeneity in respiratory contact patterns at the county-week scale, we use generalized additive models. In the absence of pre-pandemic data on contact in the US, we also use a regression approach to produce baseline contact estimates to fill this gap.

Findings

Although contact patterns varied over time during the pandemic, contact is relatively stable after controlling for disease. We find that the mean number of non-household contacts is spatially heterogeneous regardless of disease. There is additional heterogeneity across age, gender, race/ethnicity, and contact setting, with mean contact decreasing with age and lower in women. The contacts of white individuals and contacts at work or social events change the most under increased national incidence.

Interpretation

We develop the first county-level estimates of non-pandemic contact rates for the US that can fill critical gaps in parameterizing disease models. Our results identify that spatiotemporal, demographic, and social heterogeneity in contact patterns is highly structured, informing the risk landscape of respiratory disease transmission in the US.

Understanding the infection severity and epidemiological characteristics of mpox in the UK

In May 2022, individuals infected with the monkeypox virus were detected in the UK without clear travel links to endemic areas. Understanding the clinical characteristics and infection severity of mpox is necessary for effective public health policy. The study period of this paper, from the 1st June 2022 to 30th September 2022, included 3,375 individuals that tested positive for the monkeypox virus. The posterior mean times from infection to hospital admission and length of hospital stay were 14.89 days (95% Credible Intervals (CrI): 13.60, 16.32) and 7.07 days (95% CrI: 6.07, 8.23), respectively. We estimated the modelled Infection Hospitalisation Risk to be 4.13% (95% CrI: 3.04, 5.02), compared to the overall sample Case Hospitalisation Risk (CHR) of 5.10% (95% CrI: 4.38, 5.86). The overall sample CHR was estimated to be 17.86% (95% CrI: 6.06, 33.11) for females and 4.99% (95% CrI: 4.27, 5.75) for males. A notable difference was observed between the CHRs that were estimated for each sex, which may be indicative of increased infection severity in females or a considerably lower infection ascertainment rate. It was estimated that 74.65% (95% CrI: 55.78, 86.85) of infections with the monkeypox virus in the UK were captured over the outbreak.

Approximating reproduction numbers: a general numerical method for age-structured models

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

Time series analysis and short-term forecasting of monkeypox outbreak trends in the 10 major affected countries

BACKGROUND

Considering the rapidly spreading monkeypox outbreak, WHO has declared a global health emergency. Still in the category of being endemic, the monkeypox disease shares numerous clinical characters with smallpox. This study focuses on determining the most effective combination of autoregressive integrated moving average model to encapsulate time dependent flow behaviour of the virus with short run prediction.

METHODS

This study includes the data of confirmed reported cases and cumulative cases from eight most burdened countries across the globe, over the span of May 18, 2022, to December 31, 2022. The data was assembled from the website of Our World in Data and it involves countries such as United States, Brazil, Spain, France, Colombia, Mexico, Peru, United Kingdom, Germany and Canada. The job of modelling and short-term forecasting is facilitated by the employment of autoregressive integrated moving average. The legitimacy of the estimated models is argued by offering numerous model performance indices such as, root mean square error, mean absolute error and mean absolute prediction error.

RESULTS

The best fit models were deduced for each country by using the data of confirmed reported cases of monkeypox infections. Based on diverse set of performance evaluation criteria, the best fit models were then employed to provide forecasting of next twenty days. Our results indicate that the USA is expected to be the hardest-hit country, with an average of 58 cases per day with 95% confidence interval of (00-400). The second most burdened country remained Brazil with expected average cases of 23 (00-130). The outlook is not much better for Spain and France, with average forecasts of 52 (00-241) and 24 (00-121), respectively.

CONCLUSION

This research provides profile of ten most severely hit countries by monkeypox transmission around the world and thus assists in epidemiological management. The prediction trends indicate that the confirmed cases in the USA may exceed than other contemporaries. Based on the findings of this study, it remains plausible to recommend that more robust health surveillance strategy is required to control the transmission flow of the virus especially in USA.

Real-world performance of SARS-Cov-2 serology tests in the United States, 2020

BACKGROUND

Real-world performance of COVID-19 diagnostic tests under Emergency Use Authorization (EUA) must be assessed. We describe overall trends in the performance of serology tests in the context of real-world implementation.

METHODS

Six health systems estimated the odds of seropositivity and positive percent agreement (PPA) of serology test among people with confirmed SARS-CoV-2 infection by molecular test. In each dataset, we present the odds ratio and PPA, overall and by key clinical, demographic, and practice parameters.

RESULTS

A total of 15,615 people were observed to have at least one serology test 14-90 days after a positive molecular test for SARS-CoV-2. We observed higher PPA in Hispanic (PPA range: 79-96%) compared to non-Hispanic (60-89%) patients; in those presenting with at least one COVID-19 related symptom (69-93%) as compared to no such symptoms (63-91%); and in inpatient (70-97%) and emergency department (93-99%) compared to outpatient (63-92%) settings across datasets. PPA was highest in those with diabetes (75-94%) and kidney disease (83-95%); and lowest in those with auto-immune conditions or who are immunocompromised (56-93%). The odds ratios (OR) for seropositivity were higher in Hispanics compared to non-Hispanics (OR range: 2.59-3.86), patients with diabetes (1.49-1.56), and obesity (1.63-2.23); and lower in those with immunocompromised or autoimmune conditions (0.25-0.70), as compared to those without those comorbidities. In a subset of three datasets with robust information on serology test name, seven tests were used, two of which were used in multiple settings and met the EUA requirement of PPA ≥87%. Tests performed similarly across datasets.

CONCLUSION

Although the EUA requirement was not consistently met, more investigation is needed to understand how serology and molecular tests are used, including indication and protocol fidelity. Improved data interoperability of test and clinical/demographic data are needed to enable rapid assessment of the real-world performance of in vitro diagnostic tests.

Evaluating COVID-19 risk under the estimation of population mean using two attributes

The virus of COVID-19 has affected humans physically, mentally, and economically all over the world. Each country's development level, resources, and immunization to have coping capacity against this covid19 differ country-wise. Thus, understanding socioeconomic vulnerability and coping capacity among countries under different health systems can be crucial. Contrasting most articles on COVID-19, this article focuses on evaluating and estimating the COVID-19 risk and lack of coping capacity in 190 countries. This present study suggests an exponential estimator using two auxiliary attributes. Theoretically, the mean square error expressions are derived and compared with some existing estimators. These findings were supported by using the real data of INFORM COVID-19 risk.

Kombe I, Ojal J, Parisi A, Keeling MJ, Nokes DJ, Manson-Sawko R, House T. A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

Public perceptions and interactions with UK COVID-19 Test, Trace and Isolate policies, and implications for pandemic infectious disease modelling

Background The efforts to contain SARS-CoV-2 and reduce the impact of the COVID-19 pandemic have been supported by Test, Trace and Isolate (TTI) systems in many settings, including the United Kingdom. Mathematical models of transmission and TTI interventions, used to inform design and policy choices, make assumptions about the public’s behaviour in the context of a rapidly unfolding and changeable emergency. This study investigates public perceptions and interactions with UK TTI policy in July 2021, assesses them against how TTI processes are conceptualised and represented in models, and then interprets the findings with modellers who have been contributing evidence to TTI policy. Methods 20 members of the public recruited via social media were interviewed for one hour about their perceptions and interactions with the UK TTI system. Thematic analysis identified key themes, which were then presented back to a workshop of pandemic infectious disease modellers who assessed these findings against assumptions made in TTI intervention modelling. Workshop members co-drafted this report. Results Themes included education about SARS-CoV-2, perceived risks, trust, mental health and practical concerns. Findings covered testing practices, including the uses of and trust in different types of testing, and the challenges of testing and isolating faced by different demographic groups. This information was judged as consequential to the modelling process, from guiding the selection of research questions, influencing choice of model structure, informing parameter ranges and validating or challenging assumptions, to highlighting where model assumptions are reasonable or where their poor reflection of practice might lead to uninformative results. Conclusions We conclude that deeper engagement with members of the public should be integrated at regular stages of public health intervention modelling.

Commentary on the use of the reproduction number R during the COVID-19 pandemic

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Measuring the impact of social-distancing, testing, and undetected asymptomatic cases on the diffusion of COVID-19

The key to overcoming COVID-19 lies, arguably, in the diffusion process of confirmed cases. In view of this, this study has two main aims: first, to investigate the unique characteristics of COVID-19—for the existence of asymptomatic cases—and second, to determine the best strategy to suppress the diffusion of COVID-19. To this end, this study proposes a new compartmental model—the SICUR model—which can address undetected asymptomatic cases and considers the three main drivers of the diffusion of COVID-19: the degree of social distancing, the speed of testing, and the detection rate of infected cases. Taking each country’s situation into account, it is suggested that susceptible cases can be classified into two categories based on their sources of occurrence: internal and external factors. The results show that the ratio of undetected asymptomatic cases to infected cases will, ceteris paribus, be 6.9% for South Korea and 22.4% for the United States. This study also quantitatively shows that to impede the diffusion of COVID-19: firstly, strong social distancing is necessary when the detection rate is high, and secondly, fast testing is effective when the detection rate is low.

Response of vaccination on community transmission of COVID-19: a dynamical approach

Due to the severity of COVID-19, vaccination campaigns have been or are underway in most parts of the world. In the current circumstances, it is obligatory to examine the response of vaccination on transmission of the SARS-CoV-2 virus when there are many vaccines available. Considering the importance of vaccination, a dynamic model has been proposed to provide an insight in the same direction. A mathematical model has been developed where six population compartments viz. susceptible, infected, vaccinated, home-isolated, hospitalized and recovered population are considered. Moreover, two novel parameters are included in the model to ascertain the effectiveness and speed of the vaccination campaign. Reproduction number and local stability of both the disease-free and endemic equilibrium points are studied to examine the nature of population dynamics. Graphical results for the community stage of COVID-19 infection are simulated and compared with real data to ascertain the validity of our model. The data is then studied to understand the impact of vaccination. These numerical results evidently demonstrate that home isolation and hospitalization should continue for the infected people until the transmission of the virus from person to person reduces sufficiently after completely vaccinating every nation. This model also recommends that all type of prevention measures should still be taken to avoid any type of critical situation due to infection and also reduce the death rate.

Bayesian Modeling of COVID-19 to Classify the Infection and Death Rates in a Specific Duration: The Case of Algerian Provinces

COVID-19 causes acute respiratory illness in humans. The direct consequence of the spread of the virus is the need to find appropriate and effective solutions to reduce its spread. Similar to other countries, the pandemic has spread in Algeria, with noticeable variation in mortality and infection rates between regions. We aimed to estimate the proportion of people who died or became infected with SARS-CoV-2 in each provinces using a Bayesian approach. The estimation parameters were determined using a binomial distribution along with an a priori distribution, and the results had a high degree of accuracy. The Bayesian model was applied during the third wave (1 January-15 August 2021), in all Algerian's provinces. For spatial analysis of duration, geographical maps were used. Our findings show that Tissemsilt, Ain Defla, Illizi, El Taref, and Ghardaia (Mean = 0.001) are the least affected provinces in terms of COVID-19 mortality. The results also indicate that Tizi Ouzou (Mean = 0.0694), Boumerdes (Mean = 0.0520), Annaba (Mean = 0.0483), Tipaza (Mean = 0.0524), and Tebessa (Mean = 0.0264) are more susceptible to infection, as they were ranked in terms of the level of corona infections among the 48 provinces of the country. Their susceptibility seems mainly due to the population density in these provinces. Additionally, it was observed that northeast Algeria, where the population is concentrated, has the highest infection rate. Factors affecting mortality due to COVID-19 do not necessarily depend on the spread of the pandemic. The proposed Bayesian model resulted in being useful for monitoring the pandemic to estimate and compare the risks between provinces. This statistical inference can provide a reasonable basis for describing future pandemics in other world geographical areas.

Convex-Concave fitting to successively updated data and its application to covid-19 analysis

Let n measurements of a process be provided sequentially, where the process follows a sigmoid shape, but the data have lost sigmoidicity due to measuring errors. If we smooth the data by making least the sum of squares of errors subject to one sign change in the second divided differences, then we obtain a sigmoid approximation. It is known that the optimal fit of this calculation is composed of two separate sections, one best convex and one best concave. We propose a method that starts at the beginning of the data and proceeds systematically to construct the two sections of the fit for the current data, step by step as n is increased. Although the minimization calculation at each step may have many local minima, it can be solved in about O ( n 2 ) operations, because of properties of the join between the convex and the concave section. We apply this method to data of daily Covid-19 cases and deaths of Greece, the United States of America and the United Kingdom. These data provide substantial differences in the final approximations. Thus, we evaluate the performance of the method in terms of its capabilities as both constructing a sigmoid-type approximant to the data and a trend detector. Our results clarify the optimization calculation both in a systematic manner and to a good extent. At the same time, they reveal some features of the method to be considered in scenaria that may involve predictions, and as a tool to support policy-making. The results also expose some limitations of the method that may be useful to future research on convex-concave data fitting.

Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of information using data and models to help inform policy. In this paper, we identify and discuss four broad challenges in the estimation paradigm relating to infectious disease modelling, namely the Uncertainty Quantification framework, data challenges in estimation, model-based inference and prediction, and expert judgement. We also postulate priorities in estimation methodology to facilitate preparation for future pandemics.

Microfluidic Point-of-Care (POC) Devices in Early Diagnosis: A Review of Opportunities and Challenges

The early diagnosis of infectious diseases is critical because it can greatly increase recovery rates and prevent the spread of diseases such as COVID-19; however, in many areas with insufficient medical facilities, the timely detection of diseases is challenging. Conventional medical testing methods require specialized laboratory equipment and well-trained operators, limiting the applicability of these tests. Microfluidic point-of-care (POC) equipment can rapidly detect diseases at low cost. This technology could be used to detect diseases in underdeveloped areas to reduce the effects of disease and improve quality of life in these areas. This review details microfluidic POC equipment and its applications. First, the concept of microfluidic POC devices is discussed. We then describe applications of microfluidic POC devices for infectious diseases, cardiovascular diseases, tumors (cancer), and chronic diseases, and discuss the future incorporation of microfluidic POC devices into applications such as wearable devices and telemedicine. Finally, the review concludes by analyzing the present state of the microfluidic field, and suggestions are made. This review is intended to call attention to the status of disease treatment in underdeveloped areas and to encourage the researchers of microfluidics to develop standards for these devices.

Framework for enhancing the estimation of model parameters for data with a high level of uncertainty

Reliable data are essential to obtain adequate simulations for forecasting the dynamics of epidemics. In this context, several political, economic, and social factors may cause inconsistencies in the reported data, which reflect the capacity for realistic simulations and predictions. In the case of COVID-19, for example, such uncertainties are mainly motivated by large-scale underreporting of cases due to reduced testing capacity in some locations. In order to mitigate the effects of noise in the data used to estimate parameters of models, we propose strategies capable of improving the ability to predict the spread of the diseases. Using a compartmental model in a COVID-19 study case, we show that the regularization of data by means of Gaussian process regression can reduce the variability of successive forecasts, improving predictive ability. We also present the advantages of adopting parameters of compartmental models that vary over time, in detriment to the usual approach with constant values.

Priority and age specific vaccination algorithm for the pandemic diseases: a comprehensive parametric prediction model

BACKGROUND

There have been several destructive pandemic diseases in the human history. Since these pandemic diseases spread through human-to-human infection, a number of non-pharmacological policies has been enforced until an effective vaccine has been developed. In addition, even though a vaccine has been developed, due to the challenges in the production and distribution of the vaccine, the authorities have to optimize the vaccination policies based on the priorities. Considering all these facts, a comprehensive but simple parametric model enriched with the pharmacological and non-pharmacological policies has been proposed in this study to analyse and predict the future pandemic casualties.

METHOD

This paper develops a priority and age specific vaccination policy and modifies the non-pharmacological policies including the curfews, lockdowns, and restrictions. These policies are incorporated with the susceptible, suspicious, infected, hospitalized, intensive care, intubated, recovered, and death sub-models. The resulting model is parameterizable by the available data where a recursive least squares algorithm with the inequality constraints optimizes the unknown parameters. The inequality constraints ensure that the structural requirements are satisfied and the parameter weights are distributed proportionally.

RESULTS

The results exhibit a distinctive third peak in the casualties occurring in 40 days and confirm that the intensive care, intubated, and death casualties converge to zero faster than the susceptible, suspicious, and infected casualties with the priority and age specific vaccination policy. The model also estimates that removing the curfews on the weekends and holidays cause more casualties than lifting the restrictions on the people with the chronic diseases and age over 65.

CONCLUSION

Sophisticated parametric models equipped with the pharmacological and non-pharmacological policies can predict the future pandemic casualties for various cases.

Estimating a time-to-event distribution from right-truncated data in an epidemic: A review of methods

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020.

Baseline Accuracies of Forecasting COVID-19 Cases in Russian Regions on a Year in Retrospect Using Basic Statistical and Machine Learning Methods

The large amount of data accumulated so far on the dynamics of the COVID-19 outbreak has allowed assessing the accuracy of forecasting methods in retrospect. This work compares several basic time series analysis methods, including machine learning methods, for forecasting the number of confirmed cases for some days ahead. Year-long data for all regions of Russia has been used from the Yandex DataLens platform. As a result, accuracy estimates for these basic methods have been obtained for Russian regions and Russia as a whole, in dependence on the forecasting horizon. The best basic models for forecasting for 14 days are exponential smoothing and ARIMA, with an error of 11-19% by the MAPE metric for the latest part of the course of the epidemic. The accuracies obtained can be considered as baselines for more complex prospective models.

Predicting Hospital Resource Use During COVID-19 Surges: A Simple but Flexible Discretely Integrated Condition Event Simulation of Individual Patient-Hospital Trajectories

OBJECTIVES

To assist with planning hospital resources, including critical care (CC) beds, for managing patients with COVID-19.

METHODS

An individual simulation was implemented in Microsoft Excel using a discretely integrated condition event simulation. Expected daily cases presented to the emergency department were modeled in terms of transitions to and from ward and CC and to discharge or death. The duration of stay in each location was selected from trajectory-specific distributions. Daily ward and CC bed occupancy and the number of discharges according to care needs were forecast for the period of interest. Face validity was ascertained by local experts and, for the case study, by comparing forecasts with actual data.

RESULTS

To illustrate the use of the model, a case study was developed for Guy's and St Thomas' Trust. They provided inputs for January 2020 to early April 2020, and local observed case numbers were fit to provide estimates of emergency department arrivals. A peak demand of 467 ward and 135 CC beds was forecast, with diminishing numbers through July. The model tended to predict higher occupancy in Level 1 than what was eventually observed, but the timing of peaks was quite close, especially for CC, where the model predicted at least 120 beds would be occupied from April 9, 2020, to April 17, 2020, compared with April 7, 2020, to April 19, 2020, in reality. The care needs on discharge varied greatly from day to day.

CONCLUSIONS

The DICE simulation of hospital trajectories of patients with COVID-19 provides forecasts of resources needed with only a few local inputs. This should help planners understand their expected resource needs.

Using a household-structured branching process to analyse contact tracing in the SARS-CoV-2 pandemic

We explore strategies of contact tracing, case isolation and quarantine of exposed contacts to control the SARS-CoV-2 epidemic using a branching process model with household structure. This structure reflects higher transmission risks among household members than among non-household members. We explore strategic implementation choices that make use of household structure, and investigate strategies including two-step tracing, backwards tracing, smartphone tracing and tracing upon symptom report rather than test results. The primary model outcome is the effect of contact tracing, in combination with different levels of physical distancing, on the growth rate of the epidemic. Furthermore, we investigate epidemic extinction times to indicate the time period over which interventions must be sustained. We consider effects of non-uptake of isolation/quarantine, non-adherence, and declining recall of contacts over time. Our results find that, compared to self-isolation of cases without contact tracing, a contact tracing strategy designed to take advantage of household structure allows for some relaxation of physical distancing measures but cannot completely control the epidemic absent of other measures. Even assuming no imported cases and sustainment of moderate physical distancing, testing and tracing efforts, the time to bring the epidemic to extinction could be in the order of months to years. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2-4.3 days) and Italian hospital and intensive care unit admissions every 2-3 days; values that are significantly lower than the 5-7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Outbreaks in care homes may lead to substantial disease burden if not mitigated

The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption.

This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

Non-pharmaceutical interventions during the COVID-19 pandemic: A review

Infectious diseases and human behavior are intertwined. On one side, our movements and interactions are the engines of transmission. On the other, the unfolding of viruses might induce changes to our daily activities. While intuitive, our understanding of such feedback loop is still limited. Before COVID-19 the literature on the subject was mainly theoretical and largely missed validation. The main issue was the lack of empirical data capturing behavioral change induced by diseases. Things have dramatically changed in 2020. Non-pharmaceutical interventions (NPIs) have been the key weapon against the SARS-CoV-2 virus and affected virtually any societal process. Travel bans, events cancellation, social distancing, curfews, and lockdowns have become unfortunately very familiar. The scale of the emergency, the ease of survey as well as crowdsourcing deployment guaranteed by the latest technology, several Data for Good programs developed by tech giants, major mobile phone providers, and other companies have allowed unprecedented access to data describing behavioral changes induced by the pandemic. Here, I review some of the vast literature written on the subject of NPIs during the COVID-19 pandemic. In doing so, I analyze 348 articles written by more than 2518 authors in the first 12 months of the emergency. While the large majority of the sample was obtained by querying PubMed, it includes also a hand-curated list. Considering the focus, and methodology I have classified the sample into seven main categories: epidemic models, surveys, comments/perspectives, papers aiming to quantify the effects of NPIs, reviews, articles using data proxies to measure NPIs, and publicly available datasets describing NPIs. I summarize the methodology, data used, findings of the articles in each category and provide an outlook highlighting future challenges as well as opportunities.

A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control

We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.

An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia

The aim of this research is to construct an SIR model for COVID-19 with fuzzy parameters. The SIR model is constructed by considering the factors of vaccination, treatment, obedience in implementing health protocols, and the corona virus-load. Parameters of the infection rate, recovery rate, and death rate due to COVID-19 are constructed as a fuzzy number, and their membership functions are used in the model as fuzzy parameters. The model analysis uses the generation matrix method to obtain the basic reproduction number and the stability of the model's equilibrium points. Simulation results show that differences in corona virus-loads will also cause differences in the transmission of COVID-19. Likewise, the factors of vaccination and obedience in implementing health protocols have the same effect in slowing or stopping the transmission of COVID-19 in Indonesia.

On contact tracing in COVID-19 (SARS-CoV-2) pandemic using lowest common ancestor in m-ary data aggregation tree in the fog-computing enhanced internet of things

Purpose

The purpose of this study is to exploit the lowest common ancestor technique in an m-ary data aggregation tree in the fog computing-enhanced IoT to assist in contact tracing in COVID-19. One of the promising characteristics of the Internet of Things (IoT) that can be used to save the world from the current crisis of COVID-19 pandemic is data aggregation. As the number of patients infected by the disease is already huge, the data related to the different attributes of patients such as patient thermal image record and the previous health record of the patient is going to be gigantic. The authors used the technique of data aggregation to efficiently aggregate the sensed data from the patients and analyse it. Among the various inferences drawn from the aggregated data, one of the most important is contact tracing. Contact tracing in COVID-19 deals with finding out a person or a group of persons who have infected or were infected by the disease.

Design/methodology/approach

The authors propose to exploit the technique of lowest common ancestor in an m-ary data aggregation tree in the Fog-Computing enhanced IoT to help the health-care experts in contact tracing in a particular region or community. In this research, the authors argue the current scenario of COVID-19 pandemic, finding the person or a group of persons who has/have infected a group of people is of extreme importance. Finding the individuals who have been infected or are infecting others can stop the pandemic from worsening by stopping the community transfer. In a community where the outbreak has spiked, the samples from either all the persons or the patients showing the symptoms are collected and stored in an m-ary tree-based structure sorted over time.

Findings

Contact tracing in COVID-19 deals with finding out a person or a group of persons who have infected or were infected by the disease. The authors exploited the technique of lowest common ancestor in an m-ary data aggregation tree in the fog-computing-enhanced IoT to help the health-care experts in contact tracing in a particular region or community. The simulations were carried randomly on a set of individuals. The proposed algorithm given in Algorithm 1 is executed on the samples collected at level-0 of the simulation model, and to aggregate the data and transmit the data, the authors implement Algorithm 2 at the level-1. It is found from the results that a carrier can be easily identified from the samples collected using the approach designed in the paper.

Practical implications

The work presented in the paper can aid the health-care experts fighting the COVID-19 pandemic by reducing the community transfer with efficient contact tracing mechanism proposed in the paper.

Social implications

Fighting COVID-19 efficiently and saving the humans from the pandemic has huge social implications in the current times of crisis.

Originality/value

To the best of the authors’ knowledge, the lowest common ancestor technique in m-ary data aggregation tree in the fog computing-enhanced IoT to contact trace the individuals who have infected or were infected during the transmission of COVID-19 is first of its kind proposed. Creating a graph or an m-ary tree based on the interactions/connections between the people in a particular community like location, friends and time, the authors can attempt to traverse it to find out who infected any two persons or a group of persons or was infected by exploiting the technique of finding out the lowest common ancestor in a m-ary tree.

Mathematical modelling on diffusion and control of COVID-19

In this paper, we develop a mathematical model for the spread and control of the coronavirus disease. An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd, 2020. Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan, China; it is estimated how spread in Wuhan varied between January and February 2020. It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced. It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020. Based on these estimates, it is calculated the probability that freshly introduced cases might produce outbreaks in other regions. Also, it is calculated approximately the median day by day basic reproduction number in Wuhan, refused from 2·45 (95% CI: 1·16-4·87) one week before travel restrictions were introduced on Jan 23rd, 2020, to 1.05 (0·42-2·40) one week after. Based on our estimates of, presumptuous SARS approximating disparity, it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January, some time ago there are at least four independently set up cases, there is a more than fifty percent chance the infection will found within those inhabitants. COVID-19 spreading probably refused in Wuhan during delayed January 2020, corresponding with the prologue of voyage control channels. As more cases arrive in international locations with similar spread potential to Wuhan, before these organize measures, it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.