Key questions for modelling COVID-19 exit strategies

A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

Fitting Early Phases of the COVID-19 Outbreak: A Comparison of the Performances of Used Models

The COVID-19 outbreak involved a spread of prediction efforts, especially in the early pandemic phase. A better understanding of the epidemiological implications of the different models seems crucial for tailoring prevention policies. This study aims to explore the concordance and discrepancies in outbreak prediction produced by models implemented and used in the first wave of the epidemic. To evaluate the performance of the model, an analysis was carried out on Italian pandemic data from February 24, 2020. The epidemic models were fitted to data collected at 20, 30, 40, 50, 60, 70, 80, 90, and 98 days (the entire time series). At each time step, we made predictions until May 31, 2020. The Mean Absolute Error (MAE) and the Mean Absolute Percentage Error (MAPE) were calculated. The GAM model is the most suitable parameterization for predicting the number of new cases; exponential or Poisson models help predict the cumulative number of cases. When the goal is to predict the epidemic peak, GAM, ARIMA, or Bayesian models are preferable. However, the prediction of the pandemic peak could be made carefully during the early stages of the epidemic because the forecast is affected by high uncertainty and may very likely produce the wrong results.

Simulation Models for Suicide Prevention: A Survey of the State-of-the-Art

Suicide is a leading cause of death and a global public health problem, representing more than one in every 100 deaths in 2019. Modeling and Simulation (M&S) is widely used to address public health problems, and numerous simulation models have investigated the complex, dependent, and dynamic risk factors contributing to suicide. However, no review has been dedicated to these models, which prevents modelers from effectively learning from each other and raises the risk of redundant efforts. To guide the development of future models, in this paper we perform the first scoping review of simulation models for suicide prevention. Examining ten articles, we focus on three practical questions. First, which interventions are supported by previous models? We found that four groups of models collectively support 53 interventions. We examined these interventions through the lens of global recommendations for suicide prevention, highlighting future areas for model development. Second, what are the obstacles preventing model application? We noted the absence of cost effectiveness in all models reviewed, meaning that certain simulated interventions may be infeasible. Moreover, we found that most models do not account for different effects of suicide prevention interventions across demographic groups. Third, how much confidence can we place in the models? We evaluated models according to four best practices for simulation, leading to nuanced findings that, despite their current limitations, the current simulation models are powerful tools for understanding the complexity of suicide and evaluating suicide prevention interventions.

Modeling the impact of combined use of COVID Alert SA app and vaccination to curb COVID-19 infections in South Africa

The unanticipated continued deep-rooted trend of the Severe Acute Respiratory Syndrome Corona-virus-2 the originator pathogen of the COVID-19 persists posing concurrent anxiety globally. More effort is affixed in the scientific arena via continuous investigations in a prolific effort to understand the transmission dynamics and control measures in eradication of the epidemic. Both pharmaceutical and non-pharmaceutical containment measure protocols have been assimilated in this effort. In this study, we develop a modified SEIR deterministic model that factors in alternative-amalgamation of use of COVID Alert SA app and vaccination against the COVID-19 to the Republic of South Africa's general public in an endeavor to discontinue the chain of spread for the pandemic. We analyze the key properties of the model not limited to positivity, boundedness, and stability. We authenticate the model by fitting it to the Republic of South Africa's cumulative COVID-19 cases reported data utilizing the Maximum Likelihood Estimation algorithm implemented in fitR package. Sensitivity analysis and simulations for the model reveal that simultaneously-gradually increased implementation of the COVID Alert SA app use and vaccination against COVID-19 to the public substantially accelerate reduction in the plateau number of COVID-19 infections across all the observed vaccine efficacy scenarios. More fundamentally, it is discovered that implementing at least 12% app use (mainly for the susceptible population not vaccinated) with simultaneous vaccination of over 12% of the susceptible population majorly not using the app using a vaccine of at least 50% efficacy would be sufficient in eradicating the pandemic over relatively shorter time span.

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Data-driven multiscale dynamical framework to control a pandemic evolution with non-pharmaceutical interventions

Before the availability of vaccines, many countries have resorted multiple times to drastic social restrictions to prevent saturation of their health care system, and to regain control over an otherwise exponentially increasing COVID-19 pandemic. With the advent of data-sharing, computational approaches are key to efficiently control a pandemic with non-pharmaceutical interventions (NPIs). Here we develop a data-driven computational framework based on a time discrete and age-stratified compartmental model to control a pandemic evolution inside and outside hospitals in a constantly changing environment with NPIs. Besides the calendrical time, we introduce a second time-scale for the infection history, which allows for non-exponential transition probabilities. We develop inference methods and feedback procedures to successively recalibrate model parameters as new data becomes available. As a showcase, we calibrate the framework to study the pandemic evolution inside and outside hospitals in France until February 2021. We combine national hospitalization statistics from governmental websites with clinical data from a single hospital to calibrate hospitalization parameters. We infer changes in social contact matrices as a function of NPIs from positive testing and new hospitalization data. We use simulations to infer hidden pandemic properties such as the fraction of infected population, the hospitalisation probability, or the infection fatality ratio. We show how reproduction numbers and herd immunity levels depend on the underlying social dynamics.

Adapting a Physical Earthquake-Aftershock Model to Simulate the Spread of COVID-19

There exists a need for a simple, deterministic, scalable, and accurate model that captures the dominant physics of pandemic propagation. We propose such a model by adapting a physical earthquake/aftershock model to COVID-19. The aftershock model revealed the physical basis for the statistical Epidemic Type Aftershock Sequence (ETAS) model as a highly non-linear diffusion process, thus permitting a grafting of the underlying physical equations into a formulation for calculating infection pressure propagation in a pandemic-type model. Our model shows that the COVID-19 pandemic propagates through an analogous porous media with hydraulic properties approximating beach sand and water. Model results show good correlations with reported cumulative infections for all cases studied. In alphabetical order, these include Austria, Belgium, Brazil, France, Germany, Italy, New Zealand, Melbourne (AU), Spain, Sweden, Switzerland, the UK, and the USA. Importantly, the model is predominantly controlled by one parameter (α), which modulates the societal recovery from the spread of the virus. The obtained recovery times for the different pandemic waves vary considerably from country to country and are reflected in the temporal evolution of registered infections. These results provide an intuition-based approach to designing and implementing mitigation measures, with predictive capabilities for various mitigation scenarios.

Beyond compliance: Good citizenship during the COVID-19 pandemic

In the UK, discussion of good citizenship during the COVID-19 pandemic largely focused on compliance and non-compliance with government rules. In this paper, we offer an alternative point of focus. Pandemic governance proceeded not only through rules/morality, but also through freedom/ethics. Good citizenship, therefore, involved practical reasoning in response to situations. We demonstrate this using diaries and other forms of writing collected by Mass Observation during the first six months of the pandemic. Responses to government rules and guidance varied by situation. Many people found governance through freedom/ethics confusing and burdensome. Faced with ethical dilemmas, they managed risks and responsibilities by deliberating, weighing justifications, and sometimes falling back on rules of thumb or heuristics. Discussion of good citizenship during future emergencies would benefit from a greater focus on situations, dilemmas, and justifications.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The challenges of data in future pandemics

The use of data has been essential throughout the unfolding COVID-19 pandemic. We have needed it to populate our models, inform our understanding, and shape our responses to the disease. However, data has not always been easy to find and access, it has varied in quality and coverage, been difficult to reuse or repurpose. This paper reviews these and other challenges and recommends steps to develop a data ecosystem better able to deal with future pandemics by better supporting preparedness, prevention, detection and response.

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.

Modeling the COVID-19 pandemic: a primer and overview of mathematical epidemiology

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape. From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Are epidemic growth rates more informative than reproduction numbers?

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

Immunity acquired by a minority active fraction of the population could explain COVID-19 spread in Greater Buenos Aires (June-November 2020)

The coronavirus disease 2019 (COVID-19) pandemic had an uneven development in different countries. In Argentina, the pandemic began in March 2020 and, during the first 3 months, the vast majority of cases were concentrated in a densely populated region that includes the city of Buenos Aires (country capital) and the Greater Buenos Aires (GBA) area that surrounds it. This work focuses on the spread of COVID-19 between June and November 2020 in GBA. Within this period of time there was no vaccine, basically only the early wild strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was present, and the official restriction and distancing measures in this region remained more or less constant. Under these particular conditions, the incidences show a sharp rise from June 2020 and begin to decrease towards the end of August until the end of November 2020. In this work we study, through mathematical modelling and available epidemiological information, the spread of COVID-19 in this region and period of time. We show that a coherent explanation of the evolution of incidences can be obtained assuming that only a minority fraction of the population got involved in the spread process, so that the incidences decreased as this group of people was becoming immune. The observed evolution of the incidences could then be a consequence at the population level of lasting immunity conferred by SARS-CoV-2.

Refining reproduction number estimates to account for unobserved generations of infection in emerging epidemics

Background

Estimating the transmissibility of infectious diseases is key to inform situational awareness and for response planning. Several methods tend to overestimate the basic (R₀) and effective (R_t) reproduction numbers during the initial phases of an epidemic. In this work we explore the impact of incomplete observations and underreporting of the first generations of infections during the initial epidemic phase.

Methods

We propose a debiasing procedure that utilizes a linear exponential growth model to infer unobserved initial generations of infections and apply it to EpiEstim. We assess the performance of our adjustment using simulated data, considering different levels of transmissibility and reporting rates. We also apply the proposed correction to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence data reported in Italy, Sweden, the United Kingdom, and the United States.

Results

In all simulation scenarios, our adjustment outperforms the original EpiEstim method. The proposed correction reduces the systematic bias, and the quantification of uncertainty is more precise, as better coverage of the true R₀ values is achieved with tighter credible intervals. When applied to real-world data, the proposed adjustment produces basic reproduction number estimates that closely match the estimates obtained in other studies while making use of a minimal amount of data.

Conclusions

The proposed adjustment refines the reproduction number estimates obtained with the current EpiEstim implementation by producing improved, more precise estimates earlier than with the original method. This has relevant public health implications.

Inference of the SARS-CoV-2 generation time using UK household data

The distribution of the generation time (the interval between individuals becoming infected and transmitting the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to data from the early months of the COVID-19 pandemic (December 2019-March 2020) compared to existing models (Hart et al., 2021). However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March to November 2020 in the UK, we provide updated estimates of the generation time. We considered both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% credible interval 3.3–5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0–8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (5.9 days, 5.2–7.0 days) and a similar standard deviation (4.8 days, 4.0–6.3 days). As well as estimating the generation time using data from the entire study period, we also considered whether the generation time varied temporally. Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, further data collection and analysis is necessary to continue to monitor ongoing transmission and inform future public health policy decisions.

The Hybrid Incidence Susceptible-Transmissible-Removed Model for Pandemics : Scaling Time to Predict an Epidemic's Population Density Dependent Temporal Propagation

The susceptible-transmissible-removed (STR) model is a deterministic compartment model, based on the susceptible-infected-removed (SIR) prototype. The STR replaces 2 SIR assumptions. SIR assumes that the emigration rate (due to death or recovery) is directly proportional to the infected compartment’s size. The STR replaces this assumption with the biologically appropriate assumption that the emigration rate is the same as the immigration rate one infected period ago. This results in a unique delay differential equation epidemic model with the delay equal to the infected period. Hamer’s mass action law for epidemiology is modified to resemble its chemistry precursor—the law of mass action. Constructing the model for an isolated population that exists on a surface bounded by the extent of the population’s movements permits compartment density to replace compartment size. The STR reduces to a SIR model in a timescale that negates the delay—the transmissible timescale. This establishes that the SIR model applies to an isolated population in the disease’s transmissible timescale. Cyclical social interactions will define a rhythmic timescale. It is demonstrated that the geometric mean maps transmissible timescale properties to their rhythmic timescale equivalents. This mapping defines the hybrid incidence (HI). The model validation demonstrates that the HI-STR can be constructed directly from the disease’s transmission dynamics. The basic reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0) is an epidemic impact property. The HI-STR model predicts that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0 \propto \root \mathfrak{B} \of {\rho_n}$$\end{document}R0∝ρnB where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is the population density, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{B}}$$\end{document}B is the ratio of time increments in the transmissible- and rhythmic timescales. The model is validated by experimentally verifying the relationship. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{R}}_0$$\end{document}R0’s dependence on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho_n$$\end{document}ρn is demonstrated for droplet-spread SARS in Asian cities, aerosol-spread measles in Europe and non-airborne Ebola in Africa.

The dynamical formation of ephemeral groups on networks and their effects on epidemics spreading

In network models of propagation processes, the individual, microscopic level perspective is the norm, with aggregations studied as possible outcomes. On the contrary, we adopted a mesoscale perspective with groups as the core element and in this sense we present a novel agent-group dynamic model of propagation in networks. In particular, we focus on ephemeral groups that dynamically form, create new links, and dissolve. The experiments simulated 160 model configurations and produced results describing cases of consecutive and non-consecutive dynamic grouping, bounded or unbounded in the number of repetitions. Results revealed the existence of complex dynamics and multiple behaviors. An efficiency metric is introduced to compare the different cases. A Null Model analysis disclosed a pattern in the difference between the group and random models, varying with the size of groups. Our findings indicate that a mesoscopic construct like the ephemeral group, based on assumptions about social behavior and absent any microscopic level change, could produce and describe complex propagation dynamics. A conclusion is that agent-group dynamic models may represent a powerful approach for modelers and a promising new direction for future research in models of coevolution between propagation and behavior in society.

Optimal strategies to protect a sub-population at risk due to an established epidemic

Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a ‘high-value’ sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding ‘buffer region’ can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.

The impact of multiple non-pharmaceutical interventions on controlling COVID-19 outbreak without lockdown in Hong Kong: A modelling study

Background

The 'third wave' of COVID-19 in Hong Kong, China was suppressed by non-pharmaceutical interventions (NPIs). Although social distancing regulations were quickly strengthened, the outbreak continued to grow, causing increasing delays in tracing and testing. Further regulations were introduced, plus 'targeted testing' services for at-risk groups. Estimating the impact of individual NPIs could provide lessons about how outbreaks can be controlled without radical lockdown. However, the changing delays in confirmation time challenge current modelling methods. We used a novel approach aimed at disentangling and quantifying the effects of individual interventions.

Methods

We incorporated the causes of delays in tracing and testing (i.e. load-efficiency relationship) and the consequences from such delays (i.e. the proportion of un-traced cases and the proportion of traced-cases with confirmation delay) into a deterministic transmission model, which was fitted to the daily number of cases with and without an epi‑link (an indication of being contact-traced). The effect of each NPI was then calculated.

Findings

The model estimated that after earlier relaxation of regulations, Re rose from 0.7 to 3.2. Restoration of social distancing to the previous state only reduced Re to 1.3, because of increased delay in confirmation caused by load on the contact-tracing system. However, Re decreased by 20.3% after the introduction of targeted testing and by 17.5% after extension of face-mask rules, reducing Re to 0.9 and suppressing the outbreak. The output of the model without incorporation of delay failed to capture important features of transmission and Re.

Interpretation

Changing delay in confirmation has a significant impact on disease transmission and estimation of transmissibility. This leads to a clear recommendation that delay should be monitored and mitigated during outbreaks, and that delay dynamics should be incorporated into models to assess the effects of NPIs.

Funding

City University of Hong Kong and Health and Medical Research Fund.

How can risk of COVID-19 transmission be minimised in domiciliary care for older people: development, parameterisation and initial results of a simple mathematical model

This paper proposes and analyses a stochastic model for the spread of an infectious disease transmitted between clients and care workers in the UK domiciliary (home) care setting. Interactions between clients and care workers are modelled using specially generated networks, with network parameters reflecting realistic patterns of care needs and visit allocation. These networks are then used to simulate a susceptible-exposed-infected-recovered/dead (SEIR/D)-type epidemic dynamics with different numbers of infectious and recovery stages. The results indicate that with the same overall capacity provided by care workers, the minimum peak proportion of infection and the smallest overall size of infection are achieved for the highest proportion of overlap between visit allocation, i.e. when care workers have the highest chances of being allocated a visit to the same client they have visited before. An intuitive explanation of this is that while providing the required care coverage, maximising overlap in visit allocation reduces the possibility of an infectious care worker inadvertently spreading the infection to other clients. The model is generic and can be adapted to any directly transmitted infectious disease, such as, more recently, corona virus disease 2019, provided accurate estimates of disease parameters can be obtained from real data.

Competing Health Risks Associated with the COVID-19 Pandemic and Early Response: A Scoping Review

BACKGROUND

COVID-19 has rapidly emerged as a global public health threat with infections recorded in nearly every country. Responses to COVID-19 have varied in intensity and breadth, but generally have included domestic and international travel limitations, closure of non-essential businesses, and repurposing of health services. While these interventions have focused on testing, treatment, and mitigation of COVID-19, there have been reports of interruptions to diagnostic, prevention, and treatment services for other public health threats.

OBJECTIVES

We conducted a scoping review to characterize the early impact of COVID-19 on HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition.

METHODS

A scoping literature review was completed using searches of PubMed and preprint servers (medRxiv/bioRxiv) from January 1st to October 31st, 2020, using Medical Subject Headings (MeSH) terms related to SARS-CoV-2 or COVID-19 and HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition. Empiric studies reporting original data collection or mathematical models were included, and available data synthesized by region. Studies were excluded if they were not written in English.

RESULTS

A total of 1604 published papers and 205 preprints met inclusion criteria, including 8.2% (132/1604) of published studies and 10.2% (21/205) of preprints: 7.3% (68/931) on HIV, 7.1% (24/339) on tuberculosis, 11.6% (26/224) on malaria, 7.8% (13/166) on sexual and reproductive health, and 9.8% (13/132) on malnutrition. Thematic results were similar across competing health risks, with substantial indirect effects of the COVID-19 pandemic and response on diagnostic, prevention, and treatment services for HIV, tuberculosis, malaria, sexual and reproductive health, and malnutrition.

DISCUSSION

COVID-19 emerged in the context of existing public health threats that result in millions of deaths every year. Thus, effectively responding to COVID-19 while minimizing the negative impacts of COVID-19 necessitates innovation and integration of existing programs that are often siloed across health systems. Inequities have been a consistent driver of existing health threats; COVID-19 has worsened disparities, reinforcing the need for programs that address structural risks. The data reviewed here suggest that effective strengthening of health systems should include investment and planning focused on ensuring the continuity of care for both rapidly emergent and existing public health threats.

Deciphering early-warning signals of SARS-CoV-2 elimination and resurgence from limited data at multiple scales

Inferring the transmission potential of an infectious disease during low-incidence periods following epidemic waves is crucial for preparedness. In such periods, scarce data may hinder existing inference methods, blurring early-warning signals essential for discriminating between the likelihoods of resurgence versus elimination. Advanced insight into whether elevating caseloads (requiring swift community-wide interventions) or local elimination (allowing controls to be relaxed or refocussed on case-importation) might occur can separate decisive from ineffective policy. By generalizing and fusing recent approaches, we propose a novel early-warning framework that maximizes the information extracted from low-incidence data to robustly infer the chances of sustained local transmission or elimination in real time, at any scale of investigation (assuming sufficiently good surveillance). Applying this framework, we decipher hidden disease-transmission signals in prolonged low-incidence COVID-19 data from New Zealand, Hong Kong and Victoria, Australia. We uncover how timely interventions associate with averting resurgent waves, support official elimination declarations and evidence the effectiveness of the rapid, adaptive COVID-19 responses employed in these regions.

COVID-19 related interdisciplinary methods: Preventing errors and detecting research opportunities

More than 130,000 peer-reviewed studies have been published within one year after COVID-19 emerged in many countries. This large and rapidly growing field may overwhelm the synthesizing abilities of both researchers and policy-makers. To provide a sinopsis, prevent errors, and detect cognitive gaps that may require interdisciplinary research methods, the literature on COVID-19 is summarized, twice. The overall purpose of this study is to generate a dialogue meant to explain the genesis of and/or find remedies for omissions and contradictions. The first review starts in Biology and ends in Policy. Policy is chosen as a destination because it is the setting where cognitive integration must occur. The second review follows the opposite path: it begins with stated policies on COVID-19 and then their assumptions and disciplinary relationships are identified. The purpose of this interdisciplinary method on methods is to yield a relational and explanatory view of the field -one strategy likely to be incomplete but usable when large bodies of literature need to be rapidly summarized. These reviews identify nine inter-related problems, research needs, or omissions, namely: (1) nation-wide, geo-referenced, epidemiological data collection systems (open to and monitored by the public); (2) metrics meant to detect non-symptomatic cases -e.g., test positivity-; (3) cost-benefit oriented methods, which should demonstrate they detect silent viral spreaders even with limited testing; (4) new personalized tests that inform on biological functions and disease correlates, such as cell-mediated immunity, co-morbidities, and immuno-suppression; (5) factors that influence vaccine effectiveness; (6) economic predictions that consider the long-term consequences likely to follow epidemics that growth exponentially; (7) the errors induced by self-limiting and/or implausible paradigms, such as binary and reductionist approaches; (8) new governance models that emphasize problem-solving skills, social participation, and the use of scientific knowledge; and (9) new educational programs that utilize visual aids and audience-specific communication strategies. The analysis indicates that, to optimally address these problems, disciplinary and social integration is needed. By asking what is/are the potential cause(s) and consequence(s) of each issue, this methodology generates visualizations that reveal possible relationships as well as omissions and contradictions. While inherently limited in scope and likely to become obsolete, these shortcomings are avoided when this 'method on methods' is frequently practiced. Open-ended, inter-/trans-disciplinary perspectives and broad social participation may help researchers and citizens to construct, de-construct, and re-construct COVID-19 related research.

Determining travel fluxes in epidemic areas

Infectious diseases attack humans from time to time and threaten the lives and survival of people all around the world. An important strategy to prevent the spatial spread of infectious diseases is to restrict population travel. With the reduction of the epidemic situation, when and where travel restrictions can be lifted, and how to organize orderly movement patterns become critical and fall within the scope of this study. We define a novel diffusion distance derived from the estimated mobility network, based on which we provide a general model to describe the spatiotemporal spread of infectious diseases with a random diffusion process and a deterministic drift process of the population. We consequently develop a multi-source data fusion method to determine the population flow in epidemic areas. In this method, we first select available subregions in epidemic areas, and then provide solutions to initiate new travel flux among these subregions. To verify our model and method, we analyze the multi-source data from mainland China and obtain a new travel flux triggering scheme in the selected 29 cities with the most active population movements in mainland China. The testable predictions in these selected cities show that reopening the borders in accordance with our proposed travel flux will not cause a second outbreak of COVID-19 in these cities. The finding provides a methodology of re-triggering travel flux during the weakening spread stage of the epidemic.

Human infectious diseases spread from their origins to other places with population movements. In order to curb the spatial spread of infectious diseases, many countries and regions may introduce some travel restrictions when the epidemic is severe, and reopen the borders as the epidemic eases. This process involves some important issues such as the start and end time of travel restrictions, the geographical scope of the implementation of the exit strategy, and the allowable passenger flow on traffic lines. Here, we integrate multi-source data with a mathematical model, and consequently develop a new method to determine the travel flux in epidemic areas. As an application, we use this method to calculate when and where the travel restrictions targeting COVID-19 in China in early 2020 could be lifted, and how to optimize passenger flow along the traffic lines among the reopened cities. The testable predictions indicate that the population flow in accordance with our proposed movement pattern will not cause a resurgent outbreak of COVID-19 in the cities studied.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed.

Methods

Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel.

Results

We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility.

Conclusions

Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain.

Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.

Challenges on the interaction of models and policy for pandemic control

The COVID-19 pandemic has seen infectious disease modelling at the forefront of government decision-making. Models have been widely used throughout the pandemic to estimate pathogen spread and explore the potential impact of different intervention strategies. Infectious disease modellers and policymakers have worked effectively together, but there are many avenues for progress on this interface. In this paper, we identify and discuss seven broad challenges on the interaction of models and policy for pandemic control. We then conclude with suggestions and recommendations for the future.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

Heterogeneity in susceptibility dictates the order of epidemic models

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but typically do not incorporate population-level heterogeneity in infection susceptibility. Here we combine a generalized analytical framework of contagion with computational models of epidemic dynamics to show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. We find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions are often sculpted towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak. In summary, our study suggests the need to examine the shape of susceptibility in natural populations as part of efforts to improve prediction models and to prioritize interventions that leverage heterogeneity to mitigate against spread.

Understanding small Chinese cities as COVID-19 hotspots with an urban epidemic hazard index

Multiple small- to middle-scale cities, mostly located in northern China, became epidemic hotspots during the second wave of the spread of COVID-19 in early 2021. Despite qualitative discussions of potential social-economic causes, it remains unclear how this unordinary pattern could be substantiated with quantitative explanations. Through the development of an urban epidemic hazard index (EpiRank) for Chinese prefectural districts, we came up with a mathematical explanation for this phenomenon. The index is constructed via epidemic simulations on a multi-layer transportation network interconnecting local SEIR transmission dynamics, which characterizes intra- and inter-city population flow with a granular mathematical description. Essentially, we argue that these highlighted small towns possess greater epidemic hazards due to the combined effect of large local population and small inter-city transportation. The ratio of total population to population outflow could serve as an alternative city-specific indicator of such hazards, but its effectiveness is not as good as EpiRank, where contributions from other cities in determining a specific city's epidemic hazard are captured via the network approach. Population alone and city GDP are not valid signals for this indication. The proposed index is applicable to different epidemic settings and can be useful for the risk assessment and response planning of urban epidemic hazards in China. The model framework is modularized and the analysis can be extended to other nations.

If you build it, will they come? Social, economic, and psychological determinants of COVID-19 testing decisions

BACKGROUND

The efficacy of testing and tracing programs to reduce COVID-19 transmission hinges not only on widespread access to testing, but also on the public's willingness to participate in them. To the extent that testing intentions are patterned by social determinants of health, this constitutes an understudied mechanism of disparities in COVID-19 morbidity and mortality.

DESIGN

Using data from a representative household probability sample, the Person to Person Health Interview Study (n = 935), sociodemographic, economic, and psychological determinants of testing considerations were evaluated across six domains: treatment affordability, ability to work if positive, hospital effectiveness, symptom severity, proximity to infected, and risk of transmitting to others.

RESULTS

Findings demonstrated significant differences in testing motivations across race/ethnicity, education level, socioeconomic status, and worry about self and loved ones. Notably, Black (p<0.01) and Latino (p<0.05) respondents and those experiencing financial strain (p<0.001) were disproportionately likely to indicate that resource factors would influence their decision to get tested. Desire to reduce transmission and concern about proximity to the infected were reported among those who expressed COVID-19 worries (p<0.001).

CONCLUSION

Public health efforts to combat the COVID-19 pandemic must address social, economic, and psychological factors that enable and constrain individual behavior. Increasing access to preventative interventions and technologies, including vaccines, is unlikely to markedly reduce morbidity and mortality without effective messaging and economic support to improve uptake in vulnerable populations.

Controlling the pandemic during the SARS-CoV-2 vaccination rollout

There is a consensus that mass vaccination against SARS-CoV-2 will ultimately end the COVID-19 pandemic. However, it is not clear when and which control measures can be relaxed during the rollout of vaccination programmes. We investigate relaxation scenarios using an age-structured transmission model that has been fitted to age-specific seroprevalence data, hospital admissions, and projected vaccination coverage for Portugal. Our analyses suggest that the pressing need to restart socioeconomic activities could lead to new pandemic waves, and that substantial control efforts prove necessary throughout 2021. Using knowledge on control measures introduced in 2020, we anticipate that relaxing measures completely or to the extent as in autumn 2020 could launch a wave starting in April 2021. Additional waves could be prevented altogether if measures are relaxed as in summer 2020 or in a step-wise manner throughout 2021. We discuss at which point the control of COVID-19 would be achieved for each scenario.

An analysis of school absences in England during the COVID-19 pandemic

BACKGROUND

The introduction of SARS-CoV-2, the virus that causes COVID-19 infection, in the UK in early 2020, resulted in the introduction of several control policies to reduce disease spread. As part of these restrictions, schools were closed to all pupils in March (except for vulnerable and key worker children), before re-opening to certain year groups in June. Finally, all school children returned to the classroom in September.

METHODS

Here, we analyse data on school absences in late 2020 as a result of COVID-19 infection and how that varied through time as other measures in the community were introduced. We utilise data from the Department for Education Educational Settings database and examine how pupil and teacher absences change in both primary and secondary schools.

RESULTS

Our results show that absences as a result of COVID-19 infection rose steadily following the re-opening of schools in September. Cases in teachers declined during the November lockdown, particularly in regions previously in tier 3, the highest level of control at the time. Cases in secondary school pupils increased for the first 2 weeks of the November lockdown, before decreasing. Since the introduction of the tier system, the number of absences with confirmed infection in primary schools was observed to be (markedly) lower than that in secondary schools. In December, we observed a large rise in the number of absences per school in secondary school settings in the South East and London, but such rises were not observed in other regions or in primary school settings. We conjecture that the increased transmissibility of the new variant in these regions may have contributed to this rise in secondary school cases. Finally, we observe a positive correlation between cases in the community and cases in schools in most regions, with weak evidence suggesting that cases in schools lag behind cases in the surrounding community.

CONCLUSIONS

We conclude that there is no significant evidence to suggest that schools are playing a substantial role in driving spread in the community and that careful monitoring may be required as schools re-open to determine the effect associated with open schools upon community incidence.

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.

Three pre-vaccine responses to Covid-like epidemics

This paper contains a theoretical study of epidemic control. It is inspired by current events but not intended to be an accurate depiction of the SARS-CoV-2 pandemic. We consider the emergence of a highly transmissible pathogen, focusing on metropolitan areas. To ensure some degree of realism, we present a conceptual model of the outbreak and early attempts to stave off the onslaught, including the use of lockdowns. Model outputs show strong qualitative—in some respects even quantitative—resemblance to the events of Spring 2020 in many cities worldwide. We then use this model to project forward in time to examine different paths in epidemic control after the initial surge is tamed and before the arrival of vaccines. Three very different control strategies are analyzed, leading to vastly different outcomes in terms of economic recovery and total infected population (or progress toward herd immunity). Our model, which is a version of the SEIQR model, is a time-dependent dynamical system with feedback-control. One of the main conclusions of this analysis is that the course of the epidemic is not entirely dictated by the virus: how the population responds to it can play an equally important role in determining the eventual outcome.

Interventions targeting non-symptomatic cases can be important to prevent local outbreaks: SARS-CoV-2 as a case study

During infectious disease epidemics, an important question is whether cases travelling to new locations will trigger local outbreaks. The risk of this occurring depends on the transmissibility of the pathogen, the susceptibility of the host population and, crucially, the effectiveness of surveillance in detecting cases and preventing onward spread. For many pathogens, transmission from pre-symptomatic and/or asymptomatic (together referred to as non-symptomatic) infectious hosts can occur, making effective surveillance challenging. Here, by using SARS-CoV-2 as a case study, we show how the risk of local outbreaks can be assessed when non-symptomatic transmission can occur. We construct a branching process model that includes non-symptomatic transmission and explore the effects of interventions targeting non-symptomatic or symptomatic hosts when surveillance resources are limited. We consider whether the greatest reductions in local outbreak risks are achieved by increasing surveillance and control targeting non-symptomatic or symptomatic cases, or a combination of both. We find that seeking to increase surveillance of symptomatic hosts alone is typically not the optimal strategy for reducing outbreak risks. Adopting a strategy that combines an enhancement of surveillance of symptomatic cases with efforts to find and isolate non-symptomatic infected hosts leads to the largest reduction in the probability that imported cases will initiate a local outbreak.

Trend Analysis and Forecasting the Spread of COVID-19 Pandemic in Ethiopia Using Box-Jenkins Modeling Procedure

INTRODUCTION

COVID-19, which causes severe acute respiratory syndrome, is spreading rapidly across the world, and the severity of this pandemic is rising in Ethiopia. The main objective of the study was to analyze the trend and forecast the spread of COVID-19 and to develop an appropriate statistical forecast model.

METHODOLOGY

Data on the daily spread between 13 March, 2020 and 31 August 2020 were collected for the development of the autoregressive integrated moving average (ARIMA) model. Stationarity testing, parameter testing and model diagnosis were performed. In addition, candidate models were obtained using autocorrelation function (ACF) and partial autocorrelation functions (PACF). Finally, the fitting, selection and prediction accuracy of the ARIMA models was evaluated using the RMSE and MAPE model selection criteria.

RESULTS

A total of 51,910 confirmed COVID-19 cases were reported from 13 March to 31 August 2020. The total recovered and death rates as of 31 August 2020 were 37.2% and 1.57%, respectively, with a high level of increase after the mid of August, 2020. In this study, ARIMA (0, 1, 5) and ARIMA (2, 1, 3) were finally confirmed as the optimal model for confirmed and recovered COVID-19 cases, respectively, based on lowest RMSE, MAPE and BIC values. The ARIMA model was also used to identify the COVID-19 trend and showed an increasing pattern on a daily basis in the number of confirmed and recovered cases. In addition, the 60-day forecast showed a steep upward trend in confirmed cases and recovered cases of COVID-19 in Ethiopia.

CONCLUSION

Forecasts show that confirmed and recovered COVID-19 cases in Ethiopia will increase on a daily basis for the next 60 days. The findings can be used as a decision-making tool to implement health interventions and reduce the spread of COVID-19 infection.

Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020

We estimate the weekly excess all-cause mortality in Norway and Sweden, the years of life lost (YLL) attributed to COVID-19 in Sweden, and the significance of mortality displacement. We computed the expected mortality by taking into account the declining trend and the seasonality in mortality in the two countries over the past 20 years. From the excess mortality in Sweden in 2019/20, we estimated the YLL attributed to COVID-19 using the life expectancy in different age groups. We adjusted this estimate for possible displacement using an auto-regressive model for the year-to-year variations in excess mortality. We found that excess all-cause mortality over the epidemic year, July 2019 to July 2020, was 517 (95%CI = (12, 1074)) in Norway and 4329 [3331, 5325] in Sweden. There were 255 COVID-19 related deaths reported in Norway, and 5741 in Sweden, that year. During the epidemic period of 11 March–11 November, there were 6247 reported COVID-19 deaths and 5517 (4701, 6330) excess deaths in Sweden. We estimated that the number of YLL attributed to COVID-19 in Sweden was 45,850 [13,915, 80,276] without adjusting for mortality displacement and 43,073 (12,160, 85,451) after adjusting for the displacement accounted for by the auto-regressive model. In conclusion, we find good agreement between officially recorded COVID-19 related deaths and all-cause excess deaths in both countries during the first epidemic wave and no significant mortality displacement that can explain those deaths.

Localized end-of-outbreak determination for coronavirus disease 2019 (COVID-19): examples from clusters in Japan

OBJECTIVES

End-of-outbreak declarations are an important component of outbreak response because they indicate that public health and social interventions may be relaxed or lapsed. Our study aimed to assess end-of-outbreak probabilities for clusters of coronavirus disease 2019 (COVID-19) cases detected during the first wave of the COVID-19 pandemic in Japan.

METHODS

A statistical model for end-of-outbreak determination, which accounted for reporting delays for new cases, was computed. Four clusters, representing different social contexts and time points during the first wave of the epidemic, were selected and their end-of-outbreak probabilities were evaluated.

RESULTS

The speed of end-of-outbreak determination was most closely tied to outbreak size. Notably, accounting underascertainment of cases led to later end-of-outbreak determinations. In addition, end-of-outbreak determination was closely related to estimates of case dispersionk and the effective reproduction number Re. Increasing local transmission (Re>1) leads to greater uncertainty in the probability estimates.

CONCLUSIONS

When public health measures are effective, lowerRe (less transmission on average) and larger k (lower risk of superspreading) will be in effect, and end-of-outbreak determinations can be declared with greater confidence. The application of end-of-outbreak probabilities can help distinguish between local extinction and low levels of transmission, and communicating these end-of-outbreak probabilities can help inform public health decision making with regard to the appropriate use of resources.

Impact of Personal Protection Habits on the Spread of Pandemics: Insights from an Agent-Based Model

BACKGROUND

After several waves of spread of the COVID-19 pandemic, countries around the world are struggling to regain their economies by slowly lifting mobility restrictions and social distance measures applied during the crisis. Meanwhile, recent studies provide compelling evidence on how contact distancing, the use of face masks, and handwashing habits can reduce the risk of SARS-CoV-2 transmission. In this context, we investigated the effect that these personal protection habits can have in preventing new waves of contagion.

METHODS

We extended an agent-based COVID-19 epidemic model in a simulated community to incorporate the mechanisms of these aforementioned personal care habits and measure their incidence in person-to-person transmission. A full factorial experiment design was performed to illustrate the extent to which the interplay between these personal habits is effective in mitigating the spread of disease. A global sensitivity analysis was performed on the parameters that control these habits to further validate the results.

RESULTS

We found that observing physical distance is the dominant habit in reducing disease transmission, although adopting either or both of the other two habits is necessary to some extent to suppress a new outbreak entirely. When physical distance is not observed, adherence to the use of masks or handwashing has a significant decrease in infections and mortality, but the epidemic still unfolds. We also found that in all scenarios, the combined effect of adhering to the three habits is more powerful than adopting them separately.

CONCLUSIONS

Our findings suggest that a broad adherence of the population to voluntary self-care habits would help contain unfold of new outbreaks. The purpose of our model is illustrative and contributes to ratify the importance of urging citizens to adopt the amalgam of personal care habits as a primary collective protection measure to prevent communities from returning to confinements, while immunisation is carried out in late stages of the pandemic.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between ‘spatial' and ‘non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic

The role of school-based contacts in the epidemiology of SARS-CoV-2 is incompletely understood. We use an age-structured transmission model fitted to age-specific seroprevalence and hospital admission data to assess the effects of school-based measures at different time points during the COVID-19 pandemic in the Netherlands. Our analyses suggest that the impact of measures reducing school-based contacts depends on the remaining opportunities to reduce non-school-based contacts. If opportunities to reduce the effective reproduction number (Re) with non-school-based measures are exhausted or undesired and Re is still close to 1, the additional benefit of school-based measures may be considerable, particularly among older school children. As two examples, we demonstrate that keeping schools closed after the summer holidays in 2020, in the absence of other measures, would not have prevented the second pandemic wave in autumn 2020 but closing schools in November 2020 could have reduced Re below 1, with unchanged non-school-based contacts.

Strategy to reduce adverse health outcomes in subjects highly vulnerable to COVID-19: results from a population-based study in Northern Italy

OBJECTIVES

This study describes a new strategy to reduce the impact of COVID-19 on the elderly and other clinically vulnerable subjects, where general practitioners (GPs) play an active role in managing high-risk patients, reducing adverse health outcomes.

DESIGN

Retrospective cohort study.

SETTING

Population-based study including subjects resident in the province of Milan and Lodi.

PARTICIPANTS

127 735 residents older than 70 years, with specific chronic conditions.

INTERVENTIONS

We developed a predictive algorithm for overall mortality risk based on demographic and clinical characteristics. All residents older than 70 years were classified as being at low or high risk of death from COVID-19 infection according to the algorithm. The high-risk group was assigned to their GPs for telephone triage and consultation. The high-risk cohort was divided into two groups based on GP intervention: patients who were not contacted and patients who were contacted by their GPs.

OUTCOME MEASURES

Overall mortality, COVID-19 morbidity and hospitalisation.

RESULTS

Patients with increased risk of death from COVID-19 were 127 735; 495 669 patients were not at high risk and were not included in the intervention. Out of the high-risk subjects, 79 110 were included but not contacted by their GPs, while 48 625 high-risk subjects were included and contacted. Overall mortality, morbidity and hospitalisation was higher in high-risk patients compared with low-risk populations. High-risk patients contacted by their GPs had a 50% risk reduction in COVID-19 mortality, and a 70% risk reduction in morbidity and hospitalisation for COVID-19 compared with non-contacted patients.

CONCLUSIONS

The study showed that, during the COVID-19 outbreak, involvement of GPs and changes in care management of high-risk groups produced a significant reduction in all adverse health outcomes.

Sensitivity analysis of the infection transmissibility in the UK during the COVID-19 pandemic

The coronavirus (COVID-19) outbreak started in December 2019 and rapidly spread around the world affecting millions of people. With the growth of infection rate, many countries adopted different policies to control the spread of the disease. The UK implemented strict rules instructing individuals to stay at home except in some special circumstances starting from 23 March 2020. Accordingly, this study focuses on sensitivity analysis of transmissibility of the infection as the effects of removing restrictions, for example by returning different occupational groups to their normal working environment and its effect on the reproduction number in the UK. For this reason, available social contact matrices are adopted for the population of UK to account for the average number of contacts. Different scenarios are then considered to analyse the variability of total contacts on the reproduction number in the UK as a whole and each of its four nations. Our data-driven retrospective analysis shows that if more than 38.5% of UK working-age population return to their normal working environment, the reproduction number in the UK is expected to be higher than 1. However, analysis of each nation, separately, shows that local reproduction number in each nation may be different and requires more adequate analysis. Accordingly, we believe that using statistical methods and historical data can provide good estimation of local transmissibility and reproduction number in any region. As a consequence of this analysis, efforts to reduce the restrictions should be implemented locally via different control policies. It is important that these policies consider the social contacts, population density, and the occupational groups that are specific to each region.

Trade-offs between mobility restrictions and transmission of SARS-CoV-2

In their response to the COVID-19 outbreak, governments face the dilemma to balance public health and economy. Mobility plays a central role in this dilemma because the movement of people enables both economic activity and virus spread. We use mobility data in the form of counts of travellers between regions, to extend the often-used SEIR models to include mobility between regions. We quantify the trade-off between mobility and infection spread in terms of a single parameter, to be chosen by policy makers, and propose strategies for restricting mobility so that the restrictions are minimal while the infection spread is effectively limited. We consider restrictions where the country is divided into regions, and study scenarios where mobility is allowed within these regions, and disallowed between them. We propose heuristic methods to approximate optimal choices for these regions. We evaluate the obtained restrictions based on our trade-off. The results show that our methods are especially effective when the infections are highly concentrated, e.g. around a few municipalities, as resulting from superspreading events that play an important role in the spread of COVID-19. We demonstrate our method in the example of the Netherlands. The results apply more broadly when mobility data are available.

What the reproductive number R0 can and cannot tell us about COVID-19 dynamics

The reproductive number R (or R0, the initial reproductive number in an immune-naïve population) has long been successfully used to predict the likelihood of pathogen invasion, to gauge the potential severity of an epidemic, and to set policy around interventions. However, often ignored complexities have generated confusion around use of the metric. This is particularly apparent with the emergent pandemic virus SARS-CoV-2, the causative agent of COVID-19. We address some misconceptions about the predictive ability of the reproductive number, focusing on how it changes over time, varies over space, and relates to epidemic size by referencing the mathematical definition of R and examples from the current pandemic. We hope that a better appreciation of the uses, nuances, and limitations of R and R0 facilitates a better understanding of epidemic spread, epidemic severity, and the effects of interventions in the context of SARS-CoV-2.

Parameter Estimation of Compartmental Epidemiological Model Using Harmony Search Algorithm and Its Variants

Epidemiological models play a vital role in understanding the spread and severity of a pandemic of infectious disease, such as the COVID-19 global pandemic. The mathematical modeling of infectious diseases in the form of compartmental models are often employed in studying the probable outbreak growth. Such models heavily rely on a good estimation of the epidemiological parameters for simulating the outbreak trajectory. In this paper, the parameter estimation is formulated as an optimization problem and a metaheuristic algorithm is applied, namely Harmony Search (HS), in order to obtain the optimized epidemiological parameters. The application of HS in epidemiological modeling is demonstrated by implementing ten variants of HS algorithm on five COVID-19 data sets that were calibrated with the prototypical Susceptible-Infectious-Removed (SIR) compartmental model. Computational experiments indicated the ability of HS to be successfully applied to epidemiological modeling and as an efficacious estimator for the model parameters. In essence, HS is proposed as a potential alternative estimation tool for parameters of interest in compartmental epidemiological models.