Quantifying the role of social distancing, personal protection and case detection in mitigating COVID-19 outbreak in Ontario, Canada

Behaviour quantification of public health policy adoption - the case of non-pharmaceutical measures during COVID-19

In this work, we provide estimates of non-pharmaceutical interventions (NPIs) adoption and its effects on the COVID-19 disease transmission across the province of Ontario, Canada, in 2020. Using freely available data, we estimate perceived risks of infection and a personal discomfort with complying with NPIs for Ontarians across 34 public health units. With the use of game theory, we model a time series of decision making processes in each public health region to extract an estimate of the adoption level of NPIs from March to December 2020. In conjunction with a susceptible-exposed-recovered-isolated compartmental model for Ontario, we are able to estimate a province-wide effectiveness level of NPIs. Last but not least, we show the model's versatility by applying it to Pennsylvania and Georgia in the United States.

Effective contact tracing for COVID-19: A systematic review

Contact tracing is commonly recommended to control outbreaks of COVID-19, but its effectiveness is unclear. Following PRISMA guidelines, we searched four databases using a range of terms related to contact tracing effectiveness for COVID-19. We found 343 papers; 32 were included. All were observational or modelling studies. Observational studies (n = 14) provided consistent, very-low certainty evidence that contact tracing (alone or in combination with other interventions) was associated with better control of COVID-19 (e.g. in Hong Kong, only 1084 cases and four deaths were recorded in the first 4.5 months of the pandemic). Modelling studies (n = 18) provided consistent, high-certainty evidence that under assumptions of prompt and thorough tracing with effective quarantines, contact tracing could stop the spread of COVID-19 (e.g. by reducing the reproduction number from 2.2 to 0.57). A cautious interpretation indicates that to stop the spread of COVID-19, public health practitioners have 2-3 days from the time a new case develops symptoms to isolate the case and quarantine at least 80% of its contacts.

Analysis, predicting, and controlling the COVID-19 pandemic in Iraq through SIR model

Using the standard SIR model with three unknown biological parameters, the COVID-19 pandemic in Iraq has been studied. The least squares method and real data on confirmed infections, deaths, and recoveries over a long time (455 days) were used to estimate these parameters. In this regards, first, we find the basic reproductive number R 0 is 0.9422661124 which indicates and predicts that the COVID-19 pandemic in Iraq will gradually subside until it is eradicated permanently with time. Additionally, we develop an optimal vaccination strategy with the goal of reducing COVID-19 infections and preventing their spread in Iraq, thereby putting a clear picture of control this pandemic.

A hybrid compartmental model with a case study of COVID-19 in Great Britain and Israel

Given the severe impact of COVID-19 on several societal levels, it is of crucial importance to model the impact of restriction measures on the pandemic evolution, so that governments are able to make informed decisions. Even though there have been countless attempts to propose diverse models since the rise of the outbreak, the increase in data availability and start of vaccination campaigns calls for updated models and studies. Furthermore, most of the works are focused on a very particular place or application and we strive to attain a more general model, resorting to data from different countries. In particular, we compare Great Britain and Israel, two highly different scenarios in terms of vaccination plans and social structure. We build a network-based model, complex enough to model different scenarios of government-mandated restrictions, but generic enough to be applied to any population. To ease the computational load we propose a decomposition strategy for our model.

A contact tracing SIR model for randomly mixed populations

Contact tracing is an important intervention measure to control infectious diseases. We present a new approach that borrows the edge dynamics idea from network models to track contacts included in a compartmental SIR model for an epidemic spreading in a randomly mixed population. Unlike network models, our approach does not require statistical information of the contact network, data that are usually not readily available. The model resulting from this new approach allows us to study the effect of contact tracing and isolation of diagnosed patients on the control reproduction number and number of infected individuals. We estimate the effects of tracing coverage and capacity on the effectiveness of contact tracing. Our approach can be extended to more realistic models that incorporate latent and asymptomatic compartments.

Prospective Case-control Study of Contact Tracing Speed for Emergency Department-based Contact Tracers

Introduction

In Snohomish County, WA, the time from obtaining a positive severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) test and initiating contact tracing is 4–6 days. We tested whether emergency department (ED)-based contact tracing reduces time to initiation and completion of contact tracing investigations.

Methods

All eligible coronavirus disease 2019 (COVID-19)-positive patients were offered enrollment in this prospective case-control study. Contact tracers were present in the ED from 7 AM to 2 AM for 60 consecutive days. Tracers conducted interviews using the Washington State Department of Health’s extended COVID-19 reporting form, which is also used by the Snohomish Health District (SHD).

Results

Eighty-one eligible SARS-CoV-2 positive patients were identified and 71 (88%) consented for the study. The mean time between positive COVID-19 test result and initiation of contact tracing investigation was 111 minutes with a median of 32 minutes (range: 1–1,203 minutes). The mean time from positive test result and completion of ED-based contact tracing investigation was 244 minutes with a median of 132 minutes (range: 23–1,233 minutes). In 100% of the enrolled cases, contact tracing was completed within 24 hours of a positive COVID-19 test result. For comparison, during this same period, SHD was able to complete contact tracing in 64% of positive cases within 24 hours of notification of a positive test result (P < 0.001). In the ED, each case identified a mean of 2.8 contacts as compared to 1.4 contacts identified by SHD-interviewed cases. There was no statistically significant difference between the percentage of contacts reached through ED contact tracing (82%) when compared to the usual practice (78%) (P = 0.16).

Conclusion

When contact tracing investigations occur at the point of diagnoses, the time to initiation and completion are reduced, there is higher enrollment, and more contacts are identified.

Human behaviour, NPI and mobility reduction effects on COVID-19 transmission in different countries of the world

BACKGROUND

The outbreak of Coronavirus disease, which originated in Wuhan, China in 2019, has affected the lives of billions of people globally. Throughout 2020, the reproduction number of COVID-19 was widely used by decision-makers to explain their strategies to control the pandemic.

METHODS

In this work, we deduce and analyze both initial and effective reproduction numbers for 12 diverse world regions between February and December of 2020. We consider mobility reductions, mask wearing and compliance with masks, mask efficacy values alongside other non-pharmaceutical interventions (NPIs) in each region to get further insights in how each of the above factored into each region's SARS-COV-2 transmission dynamic.

RESULTS

We quantify in each region the following reductions in the observed effective reproduction numbers of the pandemic: i) reduction due to decrease in mobility (as captured in Google mobility reports); ii) reduction due to mask wearing and mask compliance; iii) reduction due to other NPI's, over and above the ones identified in i) and ii).

CONCLUSION

In most cases mobility reduction coming from nationwide lockdown measures has helped stave off the initial wave in countries who took these types of measures. Beyond the first waves, mask mandates and compliance, together with social-distancing measures (which we refer to as other NPI's) have allowed some control of subsequent disease spread. The methodology we propose here is novel and can be applied to other respiratory diseases such as influenza or RSV.

Response to COVID-19 during the Tokyo Olympic Games: Did we properly assess the risk?

Background

The number of coronavirus disease 2019 (COVID-19) cases was expected to increase during the Tokyo Olympic Games because of the increased physical contact within and between the domestic population and international participants of the Games. The rapid rise of the Delta variant (B.1.617) in Japan meant that hosting the Olympic Games without any restrictions was likely to lead to an increase in cases. We aimed to quantitatively assess possible COVID-19 response strategies for the Olympic Games, comparing the prevalence of severe cases and the cumulative number of COVID-19 deaths via scenario analysis.

Methods

We used a discrete-time deterministic compartmental model structured by age group. Parameters were calibrated using the age-stratified COVID-19 incidence data in Osaka. Numerical simulations incorporated the planned Olympics Games and nationwide COVID-19 vaccination into the proposed model, alongside various subjects and types of countermeasures.

Results

Our model-informed approach suggested that having spectators at the Tokyo Olympic Games could lead to a surge in both cases and hospitalization. Projections for the scenario that explicitly incorporated the spread of the Delta variant (i.e., time-dependent increase in the relative transmissibility) showed that imposing stringent social distancing measures (Rt=0.7) for more than 8 weeks from the end of the Olympic Games might be required to suppress the prevalence of severe cases of COVID-19 to avoid overwhelming the intensive care unit capacity in Tokyo.

Conclusions

Our modeling analyses guided an optimal choice of COVID-19 response during and after the Tokyo Olympic Games, allowing the epidemic to be brought under control despite such a large mass gathering.

Mathematical modeling for novel coronavirus (COVID-19) and control

In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID-19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, 2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is ℛ₀ ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is ℛ₀ < 1. The model is locally asymptotically stable when ℛ₀ < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number ℛ₀ using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls.

The Collapse of Infectious Disease Diagnoses Commonly Due to Communicable Respiratory Pathogens During the Coronavirus Disease 2019 Pandemic: A Time Series and Hierarchical Clustering Analysis

Background

Nonpharmaceutical interventions such as physical distancing and mandatory masking were adopted in many jurisdictions during the coronavirus disease 2019 pandemic to decrease spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We determined the effects of these interventions on incidence of healthcare utilization for other infectious diseases.

Methods

Using a healthcare administrative dataset, we employed an interrupted time series analysis to measure changes in healthcare visits for various infectious diseases across the province of Ontario, Canada, from January 2017 to December 2020. We used a hierarchical clustering algorithm to group diagnoses that demonstrated similar patterns of change through the pandemic months.

Results

We found that visits for infectious diseases commonly caused by communicable respiratory pathogens (eg, acute bronchitis, acute sinusitis) formed distinct clusters from diagnoses that often originate from pathogens derived from the patient's own flora (eg, urinary tract infection, cellulitis). Moreover, infectious diagnoses commonly arising from communicable respiratory pathogens (hierarchical cluster 1: highly impacted diagnoses) were significantly decreased, with a rate ratio (RR) of 0.35 (95% confidence interval [CI], .30-.40; P < .001) after the introduction of public health interventions in April-December 2020, whereas infections typically arising from the patient's own flora (hierarchical cluster 3: minimally impacted diagnoses) did not demonstrate a sustained change in incidence (RR, 0.95 [95% CI, .90-1.01]; P = .085).

Conclusions

Public health measures to curtail the incidence of SARS-CoV-2 were widely effective against other communicable respiratory infectious diseases with similar modes of transmission but had little effect on infectious diseases not strongly dependent on person-to-person transmission.

Quarantine, physical distancing and social isolation measures in individuals potentially exposed to SARS-CoV-2 in community settings and health services: a scoping review

To provide a synthesis of diverse evidence on the impact of the non-therapeutic preventive measures, specifically quarantine, physical distancing and social isolation, on the control of COVID-19. A scoping review conducted in the PubMed, Embase, LILACS, CENTRAL and SCOPUS databases between 2019 and August 28th, 2020. The descriptors used were the following: "quarantine", "physical distancing", "social isolation", "COVID-19" and "SARS-Cov2". Studies that addressed the non-therapeutic preventive measures in people exposed to SARs-CoV-2 in community settings and health services were included. A total of 14,442 records identified through a database search were reduced to 346 studies and, after a standardized selection process, a total of 68 articles were selected for analysis. A total of 35 descriptive, cross-sectional or longitudinal observational studies were identified, as well as 3 reviews, in addition to 30 studies with mathematical modeling. The main intervention assessed was social distancing (56.6%), followed by lockdown (25.0%) and quarantine (18.4%). The main evidence analyzed points to the need for rapid responses to reduce the number of infections, deaths and hospital admissions, especially in intensive care unit beds.The current review revealed consistent reports that the quarantine, physical distancing and social isolation are effective strategies to contain spread of the new coronavirus.

Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control

This paper is devoted to answering some questions using a mathematical model by analyzing India’s first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value.

Analysis of a COVID-19 Epidemic Model with Seasonality

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number [Formula: see text] for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and there exists at least one positive periodic solution when [Formula: see text]. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of [Formula: see text]. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.

Mathematical modeling of the spread of the coronavirus under strict social restrictions

We formulate a simple susceptible-infectious-recovery (SIR) model to describe the spread of the coronavirus under strict social restrictions. The transmission rate in this model is exponentially decreasing with time. We find a formula for basic reproduction function and estimate the maximum number of daily infected individuals. We fit the model to induced death data in Italy, United States, Germany, France, India, Spain, and China over the period from the first reported death to August 7, 2020. We notice that the model has excellent fit to the disease death data in these countries. We estimate the model's parameters in each of these countries with 95% confidence intervals. We order the strength of social restrictions in these countries using the exponential rate. We estimate the time needed to reduce the basic reproduction function to one unit and use it to order the quality of social restrictions in these countries. The social restriction in China was the strictest and the most effective and in India was the weakest and the least effective. Policy-makers may apply the Chinese successful social restriction experiment and avoid the Indian unsuccessful one.

Long time frames to detect the impact of changing COVID-19 measures, Canada, March to July 2020

Background

Many countries have implemented population-wide interventions to control COVID-19, with varying extent and success. Many jurisdictions have moved to relax measures, while others have intensified efforts to reduce transmission.

Aim

We aimed to determine the time frame between a population-level change in COVID-19 measures and its impact on the number of cases.

Methods

We examined how long it takes for there to be a substantial difference between the number of cases that occur following a change in COVID-19 physical distancing measures and those that would have occurred at baseline. We then examined how long it takes to observe this difference, given delays and noise in reported cases. We used a susceptible-exposed-infectious-removed (SEIR)-type model and publicly available data from British Columbia, Canada, collected between March and July 2020.

Results

It takes 10 days or more before we expect a substantial difference in the number of cases following a change in COVID-19 control measures, but 20–26 days to detect the impact of the change in reported data. The time frames are longer for smaller changes in control measures and are impacted by testing and reporting processes, with delays reaching ≥ 30 days.

Conclusion

The time until a change in control measures has an observed impact is longer than the mean incubation period of COVID-19 and the commonly used 14-day time period. Policymakers and practitioners should consider this when assessing the impact of policy changes. Rapid, consistent and real-time COVID-19 surveillance is important to minimise these time frames.

Effectiveness of Contact Tracing for Viral Disease Mitigation and Suppression: Evidence-Based Review

BACKGROUND

Contact tracing in association with quarantine and isolation is an important public health tool to control outbreaks of infectious diseases. This strategy has been widely implemented during the current COVID-19 pandemic. The effectiveness of this nonpharmaceutical intervention is largely dependent on social interactions within the population and its combination with other interventions. Given the high transmissibility of SARS-CoV-2, short serial intervals, and asymptomatic transmission patterns, the effectiveness of contact tracing for this novel viral agent is largely unknown.

OBJECTIVE

This study aims to identify and synthesize evidence regarding the effectiveness of contact tracing on infectious viral disease outcomes based on prior scientific literature.

METHODS

An evidence-based review was conducted to identify studies from the PubMed database, including preprint medRxiv server content, related to the effectiveness of contact tracing in viral outbreaks. The search dates were from database inception to July 24, 2020. Outcomes of interest included measures of incidence, transmission, hospitalization, and mortality.

RESULTS

Out of 159 unique records retrieved, 45 (28.3%) records were reviewed at the full-text level, and 24 (15.1%) records met all inclusion criteria. The studies included utilized mathematical modeling (n=14), observational (n=8), and systematic review (n=2) approaches. Only 2 studies considered digital contact tracing. Contact tracing was mostly evaluated in combination with other nonpharmaceutical interventions and/or pharmaceutical interventions. Although some degree of effectiveness in decreasing viral disease incidence, transmission, and resulting hospitalizations and mortality was observed, these results were highly dependent on epidemic severity (R0 value), number of contacts traced (including presymptomatic and asymptomatic cases), timeliness, duration, and compliance with combined interventions (eg, isolation, quarantine, and treatment). Contact tracing effectiveness was particularly limited by logistical challenges associated with increased outbreak size and speed of infection spread.

CONCLUSIONS

Timely deployment of contact tracing strategically layered with other nonpharmaceutical interventions could be an effective public health tool for mitigating and suppressing infectious outbreaks by decreasing viral disease incidence, transmission, and resulting hospitalizations and mortality.

Optimal Reopening Pathways With COVID-19 Vaccine Rollout and Emerging Variants of Concern

We developed a stochastic optimization technology based on a COVID-19 transmission dynamics model to determine optimal pathways from lockdown toward reopening with different scales and speeds of mass vaccine rollout in order to maximize social economical activities while not overwhelming the health system capacity in general, hospitalization beds, and intensive care units in particular. We used the Province of Ontario, Canada as a case study to demonstrate the methodology and the optimal decision trees; but our method and algorithm are generic and can be adapted to other settings. Our model framework and optimization strategies take into account the likely range of social contacts during different phases of a gradual reopening process and consider the uncertainties of these contact rates due to variations of individual behaviors and compliance. The results show that, without a mass vaccination rollout, there would be multiple optimal pathways should this strategy be adopted right after the Province's lockdown and stay-at-home order; however, once reopening has started earlier than the timing determined in the optimal pathway, an optimal pathway with similar constraints no longer exists, and sub-optimal pathways with increased demand for intensive care units can be found, but the choice is limited and the pathway is narrow. We also simulated the situation when the reopening starts after the mass vaccination has been rolled out, and we concluded that optimal pathways toward near pre-pandemic activity level is feasible given an accelerated vaccination rollout plan, with the final activity level being determined by the vaccine coverage and the transmissibility of the dominating strain.

Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave

In this work, we employ a data-fitted compartmental model to visualize the progression and behavioral response to COVID-19 that match provincial case data in Ontario, Canada from February to June of 2020. This is a "rear-view mirror" glance at how this region has responded to the 1st wave of the pandemic, when testing was sparse and NPI measures were the only remedy to stave off the pandemic. We use an SEIR-type model with age-stratified subpopulations and their corresponding contact rates and asymptomatic rates in order to incorporate heterogeneity in our population and to calibrate the time-dependent reduction of Ontario-specific contact rates to reflect intervention measures in the province throughout lockdown and various stages of social-distancing measures. Cellphone mobility data taken from Google, combining several mobility categories, allows us to investigate the effects of mobility reduction and other NPI measures on the evolution of the pandemic. Of interest here is our quantification of the effectiveness of Ontario's response to COVID-19 before and after provincial measures and our conclusion that the sharp decrease in mobility has had a pronounced effect in the first few weeks of the lockdown, while its effect is harder to infer once other NPI measures took hold.

Merits and Limitations of Mathematical Modeling and Computational Simulations in Mitigation of COVID-19 Pandemic: A Comprehensive Review

Mathematical models have assisted in describing the transmission and propagation dynamics of various viral diseases like MERS, measles, SARS, and Influenza; while the advanced computational technique is utilized in the epidemiology of viral diseases to examine and estimate the influences of interventions and vaccinations. In March 2020, the World Health Organization (WHO) has declared the COVID-19 as a global pandemic and the rate of morbidity and mortality triggers unprecedented public health crises throughout the world. The mathematical models can assist in improving the interventions, key transmission parameters, public health agencies, and countermeasures to mitigate this pandemic. Besides, the mathematical models were also used to examine the characteristics of epidemiological and the understanding of the complex transmission mechanism. Our literature study found that there were still some challenges in mathematical modeling for the case of ecology, genetics, microbiology, and pathology pose; also, some aspects like political and societal issues and cultural and ethical standards are hard to be characterized. Here, the recent mathematical models about COVID-19 and their prominent features, applications, limitations, and future perspective are discussed and reviewed. This review can assist in further improvement of mathematical models that will consider the current challenges of viral diseases.

Mathematical modeling and analysis of the novel Coronavirus using Atangana-Baleanu derivative

The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana-Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard-Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.

Mathematical analysis of a stochastic model for spread of Coronavirus

This paper is associated to investigate a stochastic SEIAQHR model for transmission of Coronavirus disease 2019 that is a recent great crisis in numerous societies. This stochastic pandemic model is established due to several safety protocols, for instance social-distancing, mask and quarantine. Three white noises are added to three of the main parameters of the system to represent the impact of randomness in the environment on the considered model. Also, the unique solvability of the presented stochastic model is proved. Moreover, a collocation approach based on the Legendre polynomials is presented to obtain the numerical solution of this system. Finally, some simulations are provided to survey the obtained results of this pandemic model and to identify the theoretical findings.

Modeling transmission dynamics of severe acute respiratory syndrome coronavirus 2 in São Paulo, Brazil

INTRODUCTION

Severe acute respiratory syndrome coronavirus 2 has been transmitted to more than 200 countries, with 92.5 million cases and 1,981,678 deaths.

METHODS

This study applied a mathematical model to estimate the increase in the number of cases in São Paulo state, Brazil during four epidemic periods and the subsequent 300 days. We used different types of dynamic transmission models to measure the effects of social distancing interventions, based on local contact patterns. Specifically, we used a model that incorporated multiple transmission pathways and an environmental class that represented the pathogen concentration in the environmental reservoir and also considered the time that an individual may sustain a latent infection before becoming actively infectious. Thus, this model allowed us to show how the individual quarantine and active monitoring of contacts can influence the model parameters and change the rate of exposure of susceptible individuals to those who are infected.

RESULTS

The estimated basic reproductive number, R o , was 3.59 (95% confidence interval [CI]: 3.48 - 3.72). The mathematical model data prediction coincided with the real data mainly when the social distancing measures were respected. However, a lack of social distancing measures caused a significant increase in the number of infected individuals. Thus, if social distancing measures are not respected, we estimated a difference of at least 100,000 cases over the next 300 days.

CONCLUSIONS

Although the predictive capacity of this model was limited by the accuracy of the available data, our results showed that social distancing is currently the best non-pharmacological measure.

[Covid-19 in the Northeast of Brazil: from lockdown to the relaxation of social distancing measures]

Even in the period when the Covid-19 pandemic was on the rise in the Northeast of Brazil, the relaxation of social distancing measures was introduced. The scope of the study is to assess, in the light of the epidemiological-sanitary situation in the region, the suitability of relaxation of social distancing measures. Based on the WHO guidelines for relaxation of social distancing, operational indicators were created and analyzed for each guideline in the context of the Northeast. To analyze the behavior of the epidemic, according to selected indicators, Joinpoint trend analysis techniques, heat maps, rate ratios and time trends between capitals and the state interior were compared. The weekly growth peak of the epidemic occurred in May-July 2020 (epidemiological weeks 19 to 31). In most capitals, there was no simultaneous downward trend in the number of cases and deaths in the 14 days prior to flexibilization. In all states the number of tests performed was insufficient. In epidemiological week 24, the state percentages of ICU/Covid-19 bed occupancy were close to or above 70%. The epidemiological situation of the nine Northeastern state capitals analyzed here did not meet criteria and parameters recommended by the World Health Organization for the relaxation of social distancing measures.

Modeling and analysis of the dynamics of novel coronavirus (COVID-19) with Caputo fractional derivative

The new emerged infectious disease that is known the coronavirus disease (COVID-19), which is a high contagious viral infection that started in December 2019 in China city Wuhan and spread very fast to the rest of the world. This infection caused million of infected cases globally and still pose an alarming situation for human lives. Pakistan in Asian countries is considered the third country with higher number of cases of coronavirus with more than 200,000. Recently, many mathematical models have been considered to better understand the coronavirus infection. Most of these models are based on classical integer-order derivative which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using the non-integer Caputo derivative. In the absence of vaccine or therapy, the role of non-pharmaceutical interventions (NPIs) is examined on the dynamics of theCOVID-19 outbreak in Pakistan. First, we construct the model in integer sense and then apply the fractional operator to have a generalized model. The generalized model is then used to present the detailed theoretical results. We investigate the stability of the model for the case of fractional model using a nonlinear fractional Lyapunov function of Goh-Voltera type. Furthermore, we estimate the values of parameters with the help of least square curve fitting tool for the COVID-19 data recorded in Pakistan since March 1 till June 30, 2020 and show that our considered model give an accurate prediction to the real COVID-19 statistical cases. Finally, numerical simulations are presented using estimated parameters for various values of the fractional order of the Caputo derivative. From the simulation results it is found that the fractional order provides more insights about the disease dynamics.

Nonlinear model predictive control with logic constraints for COVID-19 management

The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model, and it is able to handle complex, possibly time-dependent constraints, logical relations between model variables and multiple predefined discrete levels of interventions. A state observer is also constructed for the computation of non-measured variables from the number of hospitalized patients. Five control scenarios with different cost functions and constraints are studied through numerical simulations, including an output feedback configuration with uncertain parameters. It is visible from the results that, depending on the cost function associated with different policy aims, the obtained controls correspond to mitigation and suppression strategies, and the constructed control inputs are similar to real-life government responses. The results also clearly show the key importance of early intervention, the continuous tracking of the susceptible population and that of future work in determining the true costs of restrictive control measures and their quantitative effects.

Quantifying the shift in social contact patterns in response to non-pharmaceutical interventions

Social contact mixing plays a critical role in influencing the transmission routes of infectious diseases. Moreover, quantifying social contact mixing patterns and their variations in a rapidly evolving pandemic intervened by changing public health measures is key for retroactive evaluation and proactive assessment of the effectiveness of different age- and setting-specific interventions. Contact mixing patterns have been used to inform COVID-19 pandemic public health decision-making; but a rigorously justified methodology to identify setting-specific contact mixing patterns and their variations in a rapidly developing pandemic, which can be informed by readily available data, is in great demand and has not yet been established. Here we fill in this critical gap by developing and utilizing a novel methodology, integrating social contact patterns derived from empirical data with a disease transmission model, that enables the usage of age-stratified incidence data to infer age-specific susceptibility, daily contact mixing patterns in workplace, household, school and community settings; and transmission acquired in these settings under different physical distancing measures. We demonstrated the utility of this methodology by performing an analysis of the COVID-19 epidemic in Ontario, Canada. We quantified the age- and setting (household, workplace, community, and school)-specific mixing patterns and their evolution during the escalation of public health interventions in Ontario, Canada. We estimated a reduction in the average individual contact rate from 12.27 to 6.58 contacts per day, with an increase in household contacts, following the implementation of control measures. We also estimated increasing trends by age in both the susceptibility to infection by SARS-CoV-2 and the proportion of symptomatic individuals diagnosed. Inferring the age- and setting-specific social contact mixing and key age-stratified epidemiological parameters, in the presence of evolving control measures, is critical to inform decision- and policy-making for the current COVID-19 pandemic.

Assessing the impact of varying levels of case detection and contact tracing on COVID-19 transmission in Canada during lifting of restrictive closures using a dynamic compartmental model

BACKGROUND

The coronavirus disease 2019 (COVID-19) pandemic began with a detected cluster of pneumonia cases in Wuhan, China in December 2019. Endemic transmission was recognized in Canada in early February 2020, making it urgent for public health stakeholders to have access to robust and reliable tools to support decision-making for epidemic management. The objectives of this paper are to present one of these tools-an aged-stratified dynamic compartmental model developed by the Public Health Agency of Canada in collaboration with Statistics Canada-and to model the impact of non-pharmaceutical interventions on the attack rate of COVID-19 infection in Canada.

METHODS

This model simulates the impact of different levels of non-pharmaceutical interventions, including case detection/isolation, contact tracing/quarantine and changes in the level of physical distancing in Canada, as restrictive closures began to be lifted in May 2020.

RESULTS

This model allows us to highlight the importance of a relatively high level of detection and isolation of cases, as well as tracing and quarantine of individuals in contact with those cases, in order to avoid a resurgence of the epidemic in Canada as restrictive closures are lifted. Some level of physical distancing by the public will also likely need to be maintained.

CONCLUSION

This study underlines the importance of a cautious approach to lifting restrictive closures in this second phase of the epidemic. This approach includes efforts by public health to identify cases and trace contacts, and to encourage Canadians to get tested if they are at risk of having been infected and to maintain physical distancing in public areas.

Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study

Coronavirus disease (COVID-19) is the biggest public health challenge the world is facing in recent days. Since there is no effective vaccine and treatment for this virus, therefore, the only way to mitigate this infection is the implementation of non-pharmaceutical interventions such as social-distancing, community lockdown, quarantine, hospitalization or self-isolation and contact-tracing. In this paper, we develop a mathematical model to explore the transmission dynamics and possible control of the COVID-19 pandemic in Pakistan, one of the Asian countries with a high burden of disease with more than 200,000 confirmed infected cases so far. Initially, a mathematical model without optimal control is formulated and some of the basic necessary analysis of the model, including stability results of the disease-free equilibrium is presented. It is found that the model is stable around the disease-free equilibrium both locally and globally when the basic reproduction number is less than unity. Despite the basic analysis of the model, we further consider the confirmed infected COVID-19 cases documented in Pakistan from March 1, till May 28, 2020 and estimate the model parameters using the least square fitting tools from statistics and probability theory. The results show that the model output is in good agreement with the reported COVID-19 infected cases. The approximate value of the basic reproductive number based on the estimated parameters is R 0 ≈ 1.87 . The effect of low (or mild), moderate, and comparatively strict control interventions like social-distancing, quarantine rate, (or contact-tracing of suspected people) and hospitalization (or self-isolation) of testing positive COVID-19 cases are shown graphically. It is observed that the most effective strategy to minimize the disease burden is the implementation of maintaining a strict social-distancing and contact-tracing to quarantine the exposed people. Furthermore, we carried out the global sensitivity analysis of the most crucial parameter known as the basic reproduction number using the Latin Hypercube Sampling (LHS) and the partial rank correlation coefficient (PRCC) techniques. The proposed model is then reformulated by adding the time-dependent control variables u ₁(t) for quarantine and u ₂(t) for the hospitalization interventions and present the necessary optimality conditions using the optimal control theory and Pontryagin's maximum principle. Finally, the impact of constant and optimal control interventions on infected individuals is compared graphically.

The COVID-19 Pandemic Vulnerability Index (PVI) Dashboard: Monitoring county-level vulnerability using visualization, statistical modeling, and machine learning

BACKGROUND

While the COVID-19 pandemic presents a global challenge, the U.S. response places substantial responsibility for both decision-making and communication on local health authorities, necessitating tools to support decision-making at the community level.

OBJECTIVES

We created a Pandemic Vulnerability Index (PVI) to support counties and municipalities by integrating baseline data on relevant community vulnerabilities with dynamic data on local infection rates and interventions. The PVI visually synthesizes county-level vulnerability indicators, enabling their comparison in regional, state, and nationwide contexts.

METHODS

We describe the data streams used and how these are combined to calculate the PVI, detail the supporting epidemiological modeling and machine-learning forecasts, and outline the deployment of an interactive web Dashboard. Finally, we describe the practical application of the PVI for real-world decision-making.

RESULTS

Considering an outlook horizon from 1 to 28 days, the overall PVI scores are significantly associated with key vulnerability-related outcome metrics of cumulative deaths, population adjusted cumulative deaths, and the proportion of deaths from cases. The modeling results indicate the most significant predictors of case counts are population size, proportion of black residents, and mean PM2.5. The machine learning forecast results were strongly predictive of observed cases and deaths up to 14 days ahead. The modeling reinforces an integrated concept of vulnerability that accounts for both dynamic and static data streams and highlights the drivers of inequities in COVID-19 cases and deaths. These results also indicate that local areas with a highly ranked PVI should take near-term action to mitigate vulnerability.

DISCUSSION

The COVID-19 PVI Dashboard monitors multiple data streams to communicate county-level trends and vulnerabilities and facilitates decision-making and communication among government officials, scientists, community leaders, and the public to enable effective and coordinated action to combat the pandemic.