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In this study, we develop a numerical optimization approach to address the challenge of optimal control in the spread of COVID-19. We evaluate the impact of various control strategies aimed at reducing the number of exposed and infectious individuals. Our novel approach employs Legendre wavelets, their derivative operational matrix, and a collocation method to transform the COVID-19 transmission optimal control model into a nonlinear programming (NLP) problem. To solve this problem, we employ a coronavirus optimization algorithm (COVIDOA) to determine the optimal control, state variables, and objective value. We investigate three control plans for this highly contagious disease, focusing on individual protection, rapid detection and treatment, detection with delay in treatment, and environmental viral dispersion as time-based control functions. These strategies are applied within an SEIR-type control model specific to COVID-19 in China, designed to mitigate disease spread. Lastly, we analyze the effects of various parameters within the COVID-19 spread model. Our numerical results highlight the significant impact of strategies that minimize the number of exposed and infectious individuals, particularly those related to rapid detection, detection delay, and environmental viral dispersion, in controlling and preventing the transmission of the COVID-19 virus., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Current global COVID-19 booster scheduling strategies mainly focus on vaccinating high-risk populations at predetermined intervals. However, these strategies overlook key data: the direct insights into individual immunity levels from active serological testing and the indirect information available either through sample-based sero-surveillance, or vital demographic, location, and epidemiological factors. Our research, employing an age-, risk-, and region-structured mathematical model of disease transmission-based on COVID-19 incidence and vaccination data from Israel between 15 May 2020 and 25 October 2021-reveals that a more comprehensive strategy integrating these elements can significantly reduce COVID-19 hospitalizations without increasing existing booster coverage. Notably, the effective use of indirect information alone can considerably decrease COVID-19 cases and hospitalizations, without the need for additional vaccine doses. This approach may also be applicable in optimizing vaccination strategies for other infectious diseases, including influenza., (© 2024. The Author(s).)

This paper explores the impact of various distancing measures on the spread of infectious diseases, focusing on the spread of COVID-19 in the Moroccan population as a case study. Contact matrices, generated through a social force model, capture population interactions within distinct activity locations and age groups. These matrices, tailored for each distancing scenario, have been incorporated into an SEIR model. The study models the region as a network of interconnected activity locations, enabling flexible analysis of the effects of different distancing measures within social contexts and between age groups. Additionally, the method assesses the influence of measures targeting potential superspreaders (i.e., agents with a very high contact rate) and explores the impact of inter-activity location flows, providing insights beyond scalar contact rates or survey-based contact matrices. The results suggest that implementing intra-activity location distancing measures significantly reduces in the number of infected individuals relative to the act of imposing restrictions on individuals with a high contact rate in each activity location. The combination of both measures proves more advantageous. On a regional scale, characterized as a network of interconnected activity locations, restrictions on the movement of individuals with high contact rates was found to result in a $ 2 \% $ reduction, while intra-activity location-based distancing measures was found to achieve a $ 44 \% $ reduction. The combination of these two measures yielded a $ 48\% $ reduction.

A local COVID-19 outbreak with two community clusters occurred in a large industrial city, Shaoxing, China, in December 2021 after serial interventions were imposed. We aimed to understand the reason by analysing the characteristics of the outbreak and evaluating the effects of phase-adjusted interventions. Publicly available data from 7 December 2021 to 25 January 2022 were collected to analyse the epidemiological characteristics of this outbreak. The incubation period was estimated using Hamiltonian Monte Carlo method. A well-fitted extended susceptible-exposed-infectious-recovered model was used to simulate the impact of different interventions under various combination of scenarios. There were 387 SARS-CoV-2-infected cases identified, and 8.3% of them were initially diagnosed as asymptomatic cases. The estimated incubation period was 5.4 (95% CI 5.2-5.7) days for all patients. Strengthened measures of comprehensive quarantine based on tracing led to less infections and a shorter duration of epidemic. With a same period of incubation, comprehensive quarantine was more effective in containing the transmission than other interventions. Our findings reveal an important role of tracing and comprehensive quarantine in blocking community spread when a cluster occurred. Regions with tense resources can adopt home quarantine as a relatively affordable and low-impact intervention measure compared with centralized quarantine.

Background: With the global spread of COVID-19, detecting high-risk countries/regions timely and dynamically is essential; therefore, we sought to develop automatic, quantitative and scalable analysis methods to observe and estimate COVID-19 spread worldwide and further generate reliable and timely decision-making support for public health management using a comprehensive modeling method based on multiple mathematical models., Methods: We collected global COVID-19 epidemic data reported from January 23 to September 30, 2020, to observe and estimate its possible spread trends. Countries were divided into three outbreak levels: high, middle, and low. Trends analysis was performed by calculating the growth rate, and then country grouping was implemented using group-based trajectory modeling on the three levels. Individual countries from each group were also chosen to further disclose the outbreak situations using two predicting models: the logistic growth model and the SEIR model., Results: All 187 observed countries' trajectory subgroups were identified using two grouping strategies: with and without population consideration. By measuring epidemic trends and predicting the epidemic size and peak of individual countries, our study found that the logistic growth model generally estimated a smaller epidemic size than the SEIR model. According to SEIR modeling, confirmed cases in each country would take an average of 9-12 months to reach the outbreak peak from the day the first case occurred. Additionally, the average number of cases at the peak time will reach approximately 10-20% of the countries' populations, and the countries with high trends and a high predicted size must pay special attention and implement public health interventions in a timely manner., Conclusions: We demonstrated comprehensive observations and predictions of the COVID-19 outbreak in 187 countries using a comprehensive modeling method. The methods proposed in this study can measure COVID-19 development from multiple perspectives and are generalizable to other epidemic diseases. Furthermore, the methods also provide reliable and timely decision-making support for public health management., (© 2023. The Author(s).)

This study aimed to predict the transmission trajectory of the 2019 Corona Virus Disease (COVID-19) and analyze the impact of preventive measures on the spread of the epidemic. Considering that tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than short-term predictions, an improved Susceptible-Exposed-Infected-Removed (SEIR) transmission dynamic model is established. The model depends on defining various parameters that describe both the virus and the population under study. However, it is likely that several of these parameters will exhibit significant variations among different states. Therefore, regression algorithms and heuristic algorithms were developed to effectively adapt the population-dependent parameters and ensure accurate fitting of the SEIR model to data for any specific state. In this study, we consider the second outbreak of COVID-19 in Italy as a case study, which occurred in August 2020. We divide the epidemic data from February to September of the same year into two distinct stages for analysis. The numerical results demonstrate that the improved SEIR model effectively simulates and predicts the transmission trajectories of the Italian epidemic during both periods before and after the second outbreak. By analyzing the impact of anti-epidemic measures on the spread of the disease, our findings emphasize the significance of implementing anti-epidemic preventive measures in COVID-19 modeling., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Lu, Zheng, Jia and Tian.)

Background: From March to June 2022, an Omicron BA.2 epidemic occurred in Shanghai. We aimed to better understand the transmission dynamics and identify age-specific transmission characteristics for the epidemic., Methods: Data on COVID-19 cases were collected from the Shanghai Municipal Health Commission during the period from 20th February to 1st June. The effective reproductive number (R t ) and transmission distance between cases were calculated. An age-structured SEIR model with social contact patterns was developed to reconstruct the transmission dynamics and evaluate age-specific transmission characteristics. Least square method was used to calibrate the model. Basic reproduction number (R 0 ) was estimated with next generation matrix., Results: R 0 of Omicron variant was 7.9 (95% CI: 7.4 to 8.4). With strict interventions, R t had dropped quickly from 3.6 (95% CI: 2.7 to 4.7) on 4th March to below 1 on 18th April. The mean transmission distance of the Omicron epidemic in Shanghai was 13.4 km (95% CI: 11.1 to 15.8 km), which was threefold longer compared with that of epidemic caused by the wild-type virus in Wuhan, China. The model estimated that there would have been a total 870,845 (95% CI: 815,400 to 926,289) cases for the epidemic from 20th February to 15th June, and 27.7% (95% CI: 24.4% to 30.9%) cases would have been unascertained. People aged 50-59 years had the highest transmission risk 0.216 (95% CI: 0.210 to 0.222), and the highest secondary attack rate (47.62%, 95% CI: 38.71% to 56.53%)., Conclusions: The Omicron variant spread more quickly and widely than other variants and resulted in about one third cases unascertained for the recent outbreak in Shanghai. Prioritizing isolation and screening of people aged 40-59 might suppress the epidemic more effectively. Routine surveillance among people aged 40-59 years could also provide insight into the stage of the epidemic and the timely detection of new variants., Trial Registration: We did not involve clinical trial., (© 2023. The Author(s).)

Susceptible-exposed-infectious-recovered (SEIR) models were applied to assess the effectiveness of non-pharmaceutical interventions (NPIs) and to study the dynamic behavior of the COVID-19 pandemic. Recently, SEIR models have evolved to address the change of human mobility by some NPIs for predicting the new confirmed cases. However, the models have serious limitations when applied to Seoul. Seoul has two representative quarantine policies, i.e. social distancing and the ban on gatherings. Effects of the two policies need to be reflected in different functional forms in the model because changes in human mobility do not fully reflect the ban on gatherings. Thus we propose a modified SEIR model to assess the effectiveness of social distancing, ban on gatherings and vaccination strategies. The application of the modified SEIR model was illustrated by comparing the model output with real data., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Objective: After emergence of the COVID-19 pandemic and subsequent restrictions, countries worldwide have sought to reopen as quickly as possible. However, reopening involves the risk of epidemic rebound. In this study, we investigated the effective policy combination to ensure safe reopen., Methods: On the basis of the classical SEIR epidemic model, we constructed a COVID-19 system dynamics model, incorporating vaccination, border screening, and fever clinic unit monitoring policies. The case of China was used to validate the model and then to test policy combinations for safe reopening., Findings: Vaccination was found to be crucial for safe reopening. When the vaccination rate reached 60%, the daily number of newly confirmed COVID-19 cases began to drop significantly and stabilized around 1,400 [1/1,000,000]. The border screening policy alone only delayed epidemic spread for 8 days but did not reduce the number of infections. Fever clinic unit monitoring alone could reduce the peak of new confirmed cases by 44% when the case identification rate rose from 20 to 80%. When combining polices, once the vaccination rate reached 70%, daily new confirmed cases stabilized at 90 [0.64/1,000,000] with an 80% case identification rate at fever clinic units and border screening. For new variants, newly confirmed cases did not stabilize until the vaccination rate reached 90%., Conclusion: High vaccination rate is the base for reopening. Vaccination passport is less effective compared with a strong primary care monitoring system for early detection and isolation of the infected cases., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Huang, Qian, Shen, Chen, Zhao, Cao, Rich, Pastor Ansah and Wu.)

The global COVID-19 pandemic has taken a heavy toll on health, social, and economic costs since the end of 2019. Predicting the spread of a pandemic is essential to developing effective intervention policies. Since the beginning of this pandemic, many models have been developed to predict its pathways. However, the majority of these models assume homogeneous dynamics over the geographic space, while the pandemic exhibits substantial spatial heterogeneity. In addition, spatial interaction among territorial entities and variations in their magnitude impact the pandemic dynamics. In this study, we used a spatial extension of the SEIR-type epidemiological model to simulate and predict the 4-week number of COVID-19 cases in the Charlotte-Concord-Gastonia Metropolitan Statistical Area (MSA), USA. We incorporated a variety of covariates, including mobility, pharmaceutical, and non-pharmaceutical interventions, demographics, and weather data to improve the model's predictive performance. We predicted the number of COVID-19 cases for up to four weeks in the 10 counties of the studied MSA simultaneously over the time period 29 March 2020 to 13 March 2021, and compared the results with the reported number of cases using the root-mean-squared error (RMSE) metric. Our results highlight the importance of spatial heterogeneity and spatial interactions among locations in COVID-19 pandemic modeling.

Vaccination strategies to control COVID-19 have been ongoing worldwide since the end of 2020. Understanding their possible effect is key to prevent future disease spread. Using a modelling approach, this study intends to measure the impact of the COVID-19 Portuguese vaccination strategy on the effective reproduction number and explore three scenarios for vaccine effectiveness waning. Namely, the no-immunity-loss, 1-year and 3-years of immunity duration scenarios. We adapted an age-structured SEIR deterministic model and used Portuguese hospitalisation data for the model calibration. Results show that, although the Portuguese vaccination plan had a substantial impact in reducing overall transmission, it might not be sufficient to control disease spread. A significant vaccination coverage of those above 5 years old, a vaccine effectiveness against disease of at least 80% and softer non-pharmaceutical interventions (NPIs), such as mask usage and social distancing, would be necessary to control disease spread in the worst scenario considered. The immunity duration scenario of 1-year displays a resurgence of COVID-19 hospitalisations by the end of 2021, the same is observed in 3-year scenario although with a lower magnitude. The no-immunity-loss scenario presents a low increase in hospitalisations. In both the 1-year and 3-year scenarios, a vaccination boost of those above 65 years old would result in a 53% and 38% peak reduction of non-ICU hospitalisations, respectively. These results suggest that NPIs should not be fully phased-out but instead be combined with a fast booster vaccination strategy to reduce healthcare burden., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

A modified version of the SEIR model with the effects of vaccination and inter-state movement is proposed to simulate the spread of COVID-19 in Malaysia. A mathematical analysis of the proposed model was performed to derive the basic reproduction number. To enhance the model's forecasting capabilities, the model parameters were estimated using the Nelder-Mead simplex method by fitting the model outputs to the observed data. Our results showed a good fit between the model outputs and available data, where the model was then able to perform short-term predictions. In line with the rapid vaccination program, our model predicted that the COVID-19 cases in the country would decrease by the end of August. Furthermore, our findings indicated that relaxing travel restrictions from a highly vaccinated region to a low vaccinated region would result in an epidemic outbreak., (© 2022. Prof. Dr. Jan van der Hoeven stichting voor theoretische biologie.)

The transmission of SARS-CoV-2 leads to devastating COVID-19 infections around the world, which has affected both human health and the development of industries dependent on social gatherings. Sports events are one of the subgroups facing great challenges. The uncertainty of COVID-19 transmission in large-scale sports events is a great barrier to decision-making with regard to reopening auditoriums. Policymakers and health experts are trying to figure out better policies to balance audience experiences and COVID-19 infection control. In this study, we employed the generalized SEIR model in conjunction with the Wells-Riley model to estimate the effects of vaccination, nucleic acid testing, and face mask wearing on audience infection control during the 2021 Chinese Football Association Super League from 20 April to 5 August. The generalized SEIR modeling showed that if the general population were vaccinated by inactive vaccines at an efficiency of 0.78, the total number of infectious people during this time period would decrease from 43,455 to 6,417. We assumed that the general population had the same odds ratio of entering the sports stadiums and becoming the audience. Their infection probabilities in the stadium were further estimated by the Wells-Riley model. The results showed that if all of the 30,000 seats in the stadium were filled by the audience, 371 audience members would have become infected during the 116 football games in the 2021 season. The independent use of vaccination and nucleic acid testing would have decreased this number to 79 and 118, respectively. The combined use of nucleic acid testing and vaccination or face mask wearing would have decreased this number to 14 and 34, respectively. The combined use of all three strategies could have further decreased this number to 0. According to the modeling results, policymakers can consider the combined use of vaccination, nucleic acid testing, and face mask wearing to protect audiences from infection when holding sports events, which could create a balance between audience experiences and COVID-19 infection control., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Liu, Zhou, Ding, Jia, Su, Ren, Hou, Zhang and Liu.)

Objectives: Waves of epidemics associated with Omicron variant of Coronavirus Disease 2019 (COVID-19) in major cities in China this year have been controlled. It is of great importance to study the transmission characteristics of these cases to support further interventions. Methods: We simulate the transmission trajectory and analyze the intervention influences of waves associated with Omicron variant in major cities in China using the Suspected-Exposed-Infectious-Removed (SEIR) model. In addition, we propose a model using a function between the maximum daily infections and the duration of the epidemic, calibrated with data from Chinese cities. Results: An infection period of 5 days and basic reproduction number R 0 between 2 and 8.72 are most appropriate for most cases in China. Control measures show a significant impact on reducing R 0 , and the earlier control measures are implemented, the shorter the epidemic will last. Our proposed model performs well in predicting the duration of the epidemic with an average error of 2.49 days. Conclusion: Our results show great potential in epidemic model simulation and predicting the end date of the Omicron epidemic effectively and efficiently., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Zheng and Wang.)

The COVID-19 global pandemic has had a significant impact on mass travel. We examined the risk of transmission of COVID-19 infection between subway commuters using the Susceptible Exposed Infected Recovered (SEIR) model. The model considered factors that may influence virus transmission, namely subway disinfection, ventilation capacity, average commuter spacing, single subway journey time, COVID-19 transmission capacity, and dynamic changes in passenger numbers. Based on these parameters, above a certain threshold (25 min), the risk of infection for susceptible people increased significantly as journey time increased. Average distance between commuters and levels of ventilation and disinfection were also important influencing factors. Meanwhile, the model also indicated that the risk of infection varied at different times of the day. Therefore, this paper recommends strengthening ventilation and disinfection in the carriages and limiting the time of single journeys, with an average distance of at least 1 m between passengers. In this light, subway commuters need to take proactive precautions to reduce their risk of COVID-19 infection. Also, the results show the importance of managing subway stations efficiently during epidemic and post-epidemic eras., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Human life is deeply influenced by infectious diseases. A vaccine, when available, is one of the most effective ways of controlling the spread of an epidemic. However, vaccine shortage and uncertain vaccine effectiveness in the early stage of vaccine production make vaccine allocation a critical issue. To tackle this issue, we propose a multi-objective framework to optimize the vaccine allocation strategy among different age groups during an epidemic under vaccine shortage in this study. Minimizing total disease onsets and total severe cases are the two objectives of this vaccine allocation optimization problem, and the multistage feature of vaccine allocation are considered in the framework. An improved Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the optimization problem. To evaluate the two objectives under different strategies, a deterministic age-stratified extended SEIR model is developed. In the proposed framework, different combinations of vaccine effectiveness and vaccine production capacity are investigated, and it is identified that for COVID-19 the optimal strategy is highly related to vaccine-related parameters. When the vaccine effectiveness is low, allocating most of vaccines to 0-19 age group or 65+ age group is a better choice under a low production capacity, while allocating most of vaccines to 20-49 age group or 50-64 age group is a better choice under a relatively high production capacity. When the vaccine effectiveness is high, a better strategy is to allocate vaccines to 65+ age group under a low production capacity, while to allocate vaccines to 20-49 age group under a relatively high production capacity., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Wu, Wang and Xu.)

We build a model that consider the falling antibody levels and vaccination to assess the impact of falling antibody levels and vaccination on the spread of the COVID-19 outbreak, and simulate the influence of vaccination rates and failure rates on the number of daily new cases in England. We get that the lower the vaccine failure rate, the fewer new cases. Over time, vaccines with low failure rates are more effective in reducing the number of cases than vaccines with high failure rates and the higher the vaccine efficiency and vaccination rate, the lower the epidemic peak. The peak arrival time is related to a boundary value. When the failure rate is less than this boundary value, the peak time will advance with the decrease of failure rate; when the failure rate is greater than this boundary value, the peak time is delayed with the decrease of failure rate. On the basis of improving the effectiveness of vaccines, increasing the vaccination rate has practical significance for controlling the spread of the epidemic.

The COVID-19 pandemic has proved to be one of the most disruptive public health emergencies in recent memory. Among non-pharmaceutical interventions, social distancing and lockdown measures are some of the most common tools employed by governments around the world to combat the disease. While mathematical models of COVID-19 are ubiquitous, few have leveraged network theory in a general way to explain the mechanics of social distancing. In this paper, we build on existing network models for heterogeneous, clustered networks with random link activation/deletion dynamics to put forth realistic mechanisms of social distancing using piecewise constant activation/deletion rates. We find our models are capable of rich qualitative behavior, and offer meaningful insight with relatively few intervention parameters. In particular, we find that the severity of social distancing interventions and when they begin have more impact than how long it takes for the interventions to take full effect., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022. Published by Elsevier Ltd.)

Objective: Since December 2019, a new coronavirus viral was initially detected in Wuhan, China. Population migration increases the risk of epidemic transmission. Here, the objective of study is to estimate the output risk quantitatively and evaluate the effectiveness of travel restrictions of Wuhan city., Methods: We proposed a modified susceptible-exposed-infectious-recovered (SEIR) dynamics model to predict the number of coronavirus disease 2019 (COVID-19) symptomatic and asymptomatic infections in Wuhan. And, subsequently, we estimated the export risk of COVID-19 epidemic from Wuhan to other provinces in China. Finally, we estimated the effectiveness of travel restrictions of Wuhan city quantitatively by the export risk on the assumption that the measure was postponed., Results: The export risks of COVID-19 varied from Wuhan to other provinces of China. The peak of export risk was January 21-23, 2020. With the travel restrictions of Wuhan delayed by 3, 5, and 7 d, the export risk indexes will increase by 38.50%, 55.89%, and 65.63%, respectively., Conclusions: The results indicate that the travel restrictions of Wuhan reduced the export risk and delayed the overall epidemic progression of the COVID-19 epidemic in China. The travel restrictions of Wuhan city may provide a reference for the control of the COVID-19 epidemic all over the world.

Objective: As a heavily populated megacity, Shanghai faces major epidemic risks. However, Shanghai's control of COVID-19 has been successful owing to both the strict government policy and wide community participation. Here, we investigated the impact of these stakeholders and examined who played a major role across different epidemic stages., Design: We extended the classic susceptible-exposed-infectious-recovered (SEIR) model considering the heterogeneous contact structure in four social sceneries, i.e., school, workplace, public entertainment venues, and neighborhood community, which could reflect the impact of lockdown policy and wide participation of residents happened at the community level., Result: The simulation results showed that without lockdown policy and only with community participation, the daily new confirmed cases would gradually increase to more than 7,000 [292/1,000,000] at the end of Sep. However, without community participation and only with a lockdown policy, the daily new confirmed cases sharply decreased to 30 [1.2/1,000,000] at the end of the 1st month and remained low for several months. However, when a lockdown policy was gradually lifted, the new confirmed cases increased exponentially, eventually reaching more than 17,000 [708/1,000,000]. Therefore, a government lockdown policy was necessary for the rapid control of COVID-19 during the outbreak stage while community participation is more important in keeping the number of new confirmed cases low during the reopening stage., Conclusion: Government lockdown policy and community participation play different roles in the control of COVID-19 at different stages of the epidemic: although the government played a leading role in setting up policies, the broader participation of community fever clinics (CFCs) and the general public were especially crucial in winning the battle against COVID-19 in the long run., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Qian, Huang, Zhao, Cheong, Cao, Xiong and Zhu.)

We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model., (© 2022. The Author(s).)

Objective: To evaluate epidemiological characteristics of the COVID-19 outbreak that resurged in Yangzhou and to simulate the impact of different control measures at different regional scales., Methods: We collected personal information from 570 laboratory-confirmed cases in Yangzhou from 28 July to 26 August 2021, and built a modified susceptible-exposed-infected-removed (SEIR) model and an agent-based model., Results: The SEIR model showed that for passengers from medium-high risk areas, pre-travel nucleic acid testing within 3 days could limit the total number of infected people in Yangzhou to 50; among elderly persons, a 60% increase in vaccination rates could reduce the estimated infections by 253. The agent-based model showed that when the population density of the chess and card room dropped by 40%, the number of infected people would decrease by 54 within 7 days. A ventilation increase in the chess and card room from 25 to 50% could reduce the total number of infections by 33 within 7 days; increasing the ventilation from 25 to 75% could reduce the total number of infections by 63 within 7 days., Conclusions: The SEIR model and agent-based model were used to simulate the impact of different control measures at different regional scales successfully. It is possible to provide references for epidemic prevention and control work., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Shen, Li, Wei, Zhao, Ye, Ma, Xiao, Jia, Zhou, Cui, Gong and Cao.)

The current novel Coronavirus Disease 2019 (COVID-19) is a multistage epidemic consisting of multiple rounds of alternating outbreak and containment periods that cannot be modeled with a conventional single-stage Suspected-Exposed-Infectious-Removed (SEIR) model. Seasonality and control measures could be the two most important driving factors of the multistage epidemic. Our goal is to formulate and incorporate the influences of seasonality and control measures into an epidemic model and interpret how these two factors interact to shape the multistage epidemic curves. New confirmed cases will be collected daily from seven Northern Hemisphere countries and five Southern Hemisphere countries from March 2020 to March 2021 to fit and validate the modified model. Results show that COVID-19 is a seasonal epidemic and that epidemic curves can be clearly distinguished in the two hemispheres. Different levels of control measures between different countries during different seasonal periods have different influences on epidemic transmission. Seasonality alone cannot cause the baseline reproduction number R 0 to fall below one and control measures must be taken. A superposition of a high level of seasonality and a low level of control measures can lead to a dramatically rapid increase in reported cases.

Insufficient testing capacity has been a critical bottleneck in the worldwide fight against COVID-19. Optimizing the deployment of limited testing resources has therefore emerged as a keystone problem in pandemic response planning. Here, we use a modified SEIR model to optimize testing strategies under a constraint of limited testing capacity. We define pre-symptomatic, asymptomatic, and symptomatic infected classes, and assume that positively tested individuals are immediately moved into quarantine. We further define two types of testing. Clinical testing focuses only on the symptomatic class. Non-clinical testing detects pre- and asymptomatic individuals from the general population, and a concentration parameter governs the degree to which such testing can be focused on high infection risk individuals. We then solve for the optimal mix of clinical and non-clinical testing as a function of both testing capacity and the concentration parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. At high but empirically observed testing capacities, a mix of clinical testing and non-clinical testing, even if extremely unfocused, becomes optimal. We further highlight the advantages of early implementation of testing programs, and of combining optimized testing with contact reduction interventions such as lockdowns, social distancing, and masking., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The COVID-19 pandemic, which began in December 2019, progressed in a complicated manner and thus caused problems worldwide. Seeking clues to the reasons for the complicated progression is necessary but challenging in the fight against the pandemic. We sought clues by investigating the relationship between reactions on social media and the COVID-19 epidemic in Japan. Twitter was selected as the social media platform for study because it has a large user base in Japan and because it quickly propagates short topic-focused messages ("tweets"). Analysis using Japanese Twitter data suggested that reactions on social media and the progression of the COVID-19 epidemic may have a close relationship. Analysis of the data for the past waves of COVID-19 in Japan revealed that the relevant reactions on Twitter and COVID-19 progression are related repetitive phenomena. We propose using observations of the reaction trend represented by tweet counts and the trend of COVID-19 epidemic progression in Japan and a deep neural network model to capture the relationship between social reactions and COVID-19 progression and to predict the future trend of COVID-19 progression. This trend prediction would then be used to set up a susceptible-exposed-infected-recovered model for simulating potential future COVID-19 cases. Experiments to evaluate the potential of using tweets to support the prediction of how an epidemic will progress demonstrated the value of using epidemic-related social media data. Our findings provide insights into the relationship between user reactions on social media, particularly Twitter, and epidemic progression, which can be used to fight pandemics., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Tran and Matsui.)

Background: With the global spreading of Coronavirus disease (COVID-19), many primary care medical workers have been infected, particularly in the early stages of this pandemic. Although extensive studies have explored the COVID-19 transmission patterns and (non-) pharmaceutical intervention to protect the general public, limited research has analysed the measures to prevent nosocomial transmission based upon detailed interpersonal contacts between medical staff and patients., Aim: This paper aims to develop and evaluate proactive prevention measures to contain the nosocomial transmission of COVID-19. The specific objectives are (1) to understand the virus transmission via interpersonal contacts among medical staff and patients; (2) to define proactive measures to reduce the risk of infection of medical staff and (3) evaluate the effectiveness of these measures to control the COVID-19 epidemic in hospitals., Methods: We observed the operation of a typical primary hospital in China to understand the interpersonal contacts among medical staff and patients. We defined effective distance as the indicator for risk of transmission. Then three proactive measures were proposed based upon the observations, including a medical staff rotation system, the establishment of a separate fever clinic and medical staff working alone. Finally, the impacts of these measures are evaluated with a modified Susceptible-Exposure-Infected-Removed model accommodating the situation of hospitals and asymptomatic and latent infection of COVID-19. The case study was conducted with the hospital observed in December 2019 and February 2020., Findings: The implementation of the medical staff rotation system has the most significant impact on containing the epidemic. The establishment of a separate fever clinic and medical staff working alone also benefits from inhibiting the epidemic outbreak. The simulation finds that if effective prevention and control measures are not taken in time, it will lead to a surge of infection cases in all asymptomatic probabilities and incubation periods.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has the potential for rapid transmission in congregate settings. We describe the multidisciplinary response to an outbreak of coronavirus disease (COVID-19) in a large homeless shelter in Chicago, Illinois, USA. The response to the outbreak included 4 rounds of mass PCR testing of all staff and residents and subsequent isolation of persons who tested positive for SARS-CoV-2. We further describe the dynamics of the shelter outbreak by fitting a modified susceptible-exposed-infectious-recovered compartmental model incorporating the widespread SARS-CoV-2 testing and isolation measures implemented in this shelter. Our model demonstrates that rapid transmission of COVID-19 in the shelter occurred before the outbreak was detected; rates of transmission declined after widespread testing and isolation measures were put in place. Overall, we demonstrate the feasibility of mass PCR testing and isolation in congregate settings and suggest the necessity of prompt response to suspected COVID-19 outbreaks in homeless shelters.

Background: As one of the strategies to mitigate the COVID-19 pandemic, social distancing (SD) measures are recommended to control disease spread and reduce the attack rate. Therefore, this study aims to estimate the costs and effects of SD measures through school closures, workforce, and community contact reductions for mitigating the COVID-19 pandemic in Indonesia., Methods: Two mitigation scenarios of SD for 1 month and continuous SD were compared with the baseline (no intervention). A modified Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model accounting for disease spread during the latent period was applied by considering a 1-year time horizon. The costs of healthcare, school closures, and productivity loss due to disease as well as intervention were considered to estimate the total pandemic cost among all scenarios., Results: In a comparison with the baseline, the result showed that total savings in scenarios of SD for 1 month and continuous SD was approximately $415 billion and $699 billion, respectively, while the averted deaths were 4.6 million and 8.5 million, respectively. Sensitivity analysis showed that basic reproduction number, infectious period, daily wage, incubation period, daily ICU admission cost, and case fatality rate were the most influential parameters affecting the savings and the number of averted deaths., Conclusions: SD measures through school closures, workforce, and community contact reductions were concluded to be cost-saving. Increasing the duration of social distancing tends to increase both the savings and the number of averted deaths., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

In this work we use simple mathematical models to study the impact of vaccination against COVID-19 in Portugal. First, we fit a SEIR type model without vaccination to the Portuguese data on confirmed cases of COVID-19 by the date of symptom onset, from the beginning of the epidemic until the 23rd January of 2021, to estimate changes in the transmission intensity. Then, by including vaccination in the model we develop different scenarios for the fade-out of the non pharmacological intervention (NPIs) as vaccine coverage increases in the population according to Portuguese vaccination goals. We include a feedback function to mimic the implementation and relaxation of NPIs, according to some disease incidence thresholds defined by the Portuguese health authorities.

Background: From 2 January to 14 February 2021, a local outbreak of COVID-19 occurred in Shijiazhuang, the capital city of Hebei Province, with a population of 10 million. We analyzed the characteristics of the local outbreak of COVID-19 in Shijiazhuang and evaluated the effects of serial interventions., Methods: Publicly available data, which included age, sex, date of diagnosis, and other patient information, were used to analyze the epidemiological characteristics of the COVID-19 outbreak in Shijiazhuang. The maximum likelihood method and Hamiltonian Monte Carlo method were used to estimate the serial interval and incubation period, respectively. The impact of incubation period and different interventions were simulated using a well-fitted SEIR +q model., Results: From 2 January to 14 February 2021, there were 869 patients with symptomatic COVID-19 in Shijiazhuang, and most cases (89.6%) were confirmed before 20 January. Overall, 40.2% of the cases were male, 16.3% were aged 0 to 19 years, and 21.9% were initially diagnosed as asymptomatic but then became symptomatic. The estimated incubation period was 11.6 days (95% CI 10.6, 12.7 days) and the estimated serial interval was 6.6 days (0.025 th , 0.975 th : 0.6, 20.0 days). The results of the SEIR +q model indicated that a longer incubation period led to a longer epidemic period. If the comprehensive quarantine measures were reduced by 10%, then the nucleic acid testing would need to increase by 20% or more to minimize the cumulative number of cases., Conclusions: Incubation period was longer than serial interval suggested that more secondary transmission may occur before symptoms onset. The long incubation period made it necessary to extend the isolation period to control the outbreak. Timely contact tracing and implementation of a centralized quarantine quickly contained this epidemic in Shijiazhuang. Large-scale nucleic acid testing also helped to identify cases and reduce virus transmission., (© 2021. The Author(s).)

Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number R eff t below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The emergence of novel SARS-CoV-2 variants of concern (VOC), in late 2020, with selective transmission advantage and partial immunity escape potential, has been driving further evolution in the pandemic. The timing of mutational evolution and its limits are thus of paramount importance in preparedness planning. Here, we present a model predicting the pattern of epidemic growth including the emergence of variants through mutation. It is based on the SEIR (Susceptible, Exposed, Infected, Removed) model, but its equations are modified according to the transmission parameters of novel variants. Since more transmissible strains will drive a further increase in the number of cases, they will also lead to further novel mutations. As one cannot predict whether there is a viral mutational evolutionary limit, we model a cascade that could lead to hyper-exponential growth (HEG) involving the emergence of even more transmissible mutants that could overwhelm any systematic response. Our results are consistent with the timing, since the beginning of the pandemic, of the concurrent and independent emergence of the VOCs. The current dominance of the Delta variant and the need for additional public health measures indicates some of the risks of a possible HEG. We examine conditions that favor the expected appearance of similar variants, thus enabling better preparedness and more targeted research., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Epidemic spreading causes severe challenges to the global public health system, and global and local interventions are considered an effective way to contain such spreading, including school closures (local), border control (global), etc. However, there is little study on comparing the efficiency of global and local interventions on epidemic spreading. Here, we develop a new model based on the Susceptible-Exposed-Infectious-Recovered (SEIR) model with an additional compartment called "quarantine status". We simulate various kinds of outbreaks and interventions. Firstly, we predict, consistent with previous studies, interventions reduce epidemic spreading to 16% of its normal level. Moreover, we compare the effect of global and local interventions and find that local interventions are more effective than global ones. We then study the relationships between incubation period and interventions, finding that early implementation of rigorous intervention significantly reduced the scale of the epidemic. Strikingly, we suggest a Pareto optimal in the intervention when resources were limited. Finally, we show that combining global and local interventions is the most effective way to contain the pandemic spreading if initially infected individuals are concentrated in localized regions. Our work deepens our understandings of the role of interventions on the pandemic, and informs an actionable strategy to contain it.

By the end of February 2021, COVID-19 had spread to over 230 countries, with more than 100 million confirmed cases and 2.5 million deaths. To control infection spread with the least disruption to economic and societal activities, it is crucial to implement the various interventions effectively. In this study, we developed an agent-based SEIR model, using real demographic and geographic data from Hong Kong, to analyse the efficiency of various intervention strategies in preventing infection by the SARS-CoV-2 virus. Close contact route including short-range airborne is considered as the main transmission routes for COVID-19 spread. Contact tracing is not that useful if all other interventions have been fully deployed. The number of infected individuals could be halved if people reduced their close contact rate by 25%. For reducing transmission, students should be prioritized for vaccination rather than retired older people and preschool aged children. Home isolation, and taking the nucleic acid test (NAT) as soon as possible after symptom onset, are much more effective interventions than wearing masks in public places. Temperature screening in public places only disrupted the infection spread by a small amount when other interventions have been fully implemented. Our results may be useful for other highly populated cities, when choosing their intervention strategies to prevent outbreaks of COVID-19 and similar diseases., (Copyright © 2021 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

We investigate the impact of the delay in compulsory mask wearing on the spread of COVID-19 in the community, set in the Singapore context. By using modified SEIR-based compartmental models, we focus on macroscopic population-level analysis of the relationships between the delay in compulsory mask wearing and the maximum infection, through a series of scenario-based analysis. Our analysis suggests that collective masking can meaningfully reduce the transmission of COVID-19 in the community, but only if implemented within a critical time window of approximately before 80-100 days delay after the first infection is detected, coupled with strict enforcement to ensure compliance throughout the duration. We also identify a delay threshold of about 100 days that results in masking enforcement having little significant impact on the Maximum Infected Values. The results therefore highlight the necessity for rapid implementation of compulsory mask wearing to curb the spread of the pandemic.

The COVID-19 pandemic continues to present enormous challenges for colleges and universities and strategies for save reopening remain a topic of ongoing debate. Many institutions that reopened cautiously in the fall experienced a massive wave of infections and colleges were soon declared as the new hotspots of the pandemic. However, the precise effects of college outbreaks on their immediate neighborhood remain largely unknown. Here we show that the first two weeks of instruction present a high-risk period for campus outbreaks and that these outbreaks tend to spread into the neighboring communities. By integrating a classical mathematical epidemiology model and Bayesian learning, we learned the dynamic reproduction number for 30 colleges from their daily case reports. Of these 30 institutions, 14 displayed a spike of infections within the first two weeks of class, with peak seven-day incidences well above 1,000 per 100,000, an order of magnitude larger than the nation-wide peaks of 70 and 150 during the first and second waves of the pandemic. While most colleges were able to rapidly reduce the number of new infections, many failed to control the spread of the virus beyond their own campus: Within only two weeks, 17 campus outbreaks translated directly into peaks of infection within their home counties. These findings suggests that college campuses are at risk to develop an extreme incidence of COVID-19 and become superspreaders for neighboring communities. We anticipate that tight test-trace-quarantine strategies, flexible transition to online instruction, and-most importantly-compliance with local regulations will be critical to ensure a safe campus reopening after the winter break.

Objective: There has been much discussion and debate around the underreporting of COVID-19 infections and deaths in India. In this short report we first estimate the underreporting factor for infections from publicly available data released by the Indian Council of Medical Research on reported number of cases and national seroprevalence surveys. We then use a compartmental epidemiologic model to estimate the undetected number of infections and deaths, yielding estimates of the corresponding underreporting factors. We compare the serosurvey based ad hoc estimate of the infection fatality rate (IFR) with the model-based estimate. Since the first and second waves in India are intrinsically different in nature, we carry out this exercise in two periods: the first wave (April 1, 2020-January 31, 2021) and part of the second wave (February 1, 2021-May 15, 2021). The latest national seroprevalence estimate is from January 2021, and thus only relevant to our wave 1 calculations., Results: Both wave 1 and wave 2 estimates qualitatively show that there is a large degree of "covert infections" in India, with model-based estimated underreporting factor for infections as 11.11 (95% credible interval (CrI) 10.71-11.47) and for deaths as 3.56 (95% CrI 3.48-3.64) for wave 1. For wave 2, underreporting factor for infections escalate to 26.77 (95% CrI 24.26-28.81) and to 5.77 (95% CrI 5.34-6.15) for deaths. If we rely on only reported deaths, the IFR estimate is 0.13% for wave 1 and 0.03% for part of wave 2. Taking underreporting of deaths into account, the IFR estimate is 0.46% for wave 1 and 0.18% for wave 2 (till May 15). Combining waves 1 and 2, as of May 15, while India reported a total of nearly 25 million cases and 270 thousand deaths, the estimated number of infections and deaths stand at 491 million (36% of the population) and 1.21 million respectively, yielding an estimated (combined) infection fatality rate of 0.25%. There is considerable variation in these estimates across Indian states. Up to date seroprevalence studies and mortality data are needed to validate these model-based estimates.

Objective: To simulate the different prevalence of corona virus disease 2019 (COVID-19) in Beijing as the spreading and the outbreak city and analyze the response capacity of its medical resources of fever clinics, and to provide a scientific basis for optimizing the spatial layout in Beijing under severe epidemics., Methods: The study obtained epidemiological indicators for COVID-19, factors about medical resources and population movement as parameters for the SEIR model and utilized the model to predict the maximum number of infections on a single day at different control levels in Beijing, simulated as an epidemic spreading city and an epidemic outbreak city respectively. The modified two-step floating catchment area method under ArcGIS 10.6 environment was used to analyze spatial accessibility to fever clinics services for the patients in Beijing., Results: According to the results of the SEIR model, the highest number of infections in a single day in Beijing simulated as an epidemic spreading city at low, medium and high levels of prevention and control were 8 514, 183, and 68 cases, the highest number of infections in a single day in Beijing simulated as an outbreak city was 22 803, 10 868 and 3 725 cases, respectively. The following result showed that Beijing was simulated as an epidemic spreading city: among the 585 communities in Beijing, under the low level of prevention and control, there were 17 communities (2.91%) with excellent accessibility to fever clinics, and that of 41 communities (7.01%) with fever clinics was good. Spatial accessibility of fever clinics in 56 communities (9.57%) was ranked average, and 62 communities' (10.60%) accessibility was fair and 409 communities (69.91%) had poor accessibility; at the medium level of prevention and control, only the west region of Fangshan District and Mentougou District, the north region of Yanqing District, Huairou District and Miyun District had poor accessibility; under the high level of prevention and control, 559 communities' (95.56%) had excellent accessibility. The accessibility in 24 communities (4.10%) was good and in 2 communities (0.34%) was average. In brief, the existing fever clinics could meet the common demand. Beijing was simulated as an outbreak city: under the low level of prevention and control, only 1 community (0.17%) had excellent accessibility to fever clinics, and 5 communities (0.86%) had good accessibility. The accessibility of fever clinics in 10 communities (1.71%) was average and in 12 communities (2.05%) was fair. The accessibility of fever clinics in 557 communities (95.21%), nearly all areas of Beijing, was poor; under the middle and high level of prevention and control, the accessibility of ecological conservation areas was also relatively poor., Conclusion: The distribution of fever clinic resources in Beijing is uneven. When Beijing is simulated as an epidemic spreading city: under the high level of prevention and control, the number of fever clinics can be appropriately reduced to avoid cross-infection; at the medium level of prevention and control, the fever clinics can basically meet the needs of patients with fever in Beijing, but the accessibility of fever clinics in ecological conservation areas is insufficient, and priority should be given to the construction of fever clinics in public hospitals above the second level in the ecological conservation areas. When the level of prevention and control is low, the accessibility of fever clinics in ecological conservation areas is poor. Priority should be given to the construction of fever clinics in ecological conservation areas, and temporary fever sentinels can be established to relieve the pressure of fever clinics. When Beijing is simulated as an outbreak city and has low prevention and control, due to a large number of infections, it is necessary to upgrade the prevention and control level to reduce the flow of people to curb the development of the epidemic.

Background: There are few studies demonstrating how the effectiveness of various extents of non-pharmaceutical interventions (NPIs) before and after vaccination periods. The study aimed to demonstrate such an effectiveness in the alteration of the epidemic curves from theory to practice., Methods: The empirical data on the daily reported COVID-19 cases were extracted from open source. A computer simulation design in conjunction with the susceptible-exposed-infected-recovered (SEIR) type model was applied to evaluating confinement measures in Italy with adjustment for underreported cases; isolation and quarantine in Taiwan; and NPIs and vaccination in Israel., Results: In Italy scenario, the extents of confinement measures were 34% before the end of March and then scaled up to 70% after then. Both figures were reduced to 22-69% after adjusting for underreported cases. Approximately 44% of confinement measures were implemented in the second surge of pandemic in Italy. Fitting the observational data on Taiwan assuming the initial outbreak similar to Wuhan, China, 44% of isolation and quarantine were estimated before March 23rd, 2020. Isolation and quarantine were scaled up to 90% and at least 60% to contain community-acquired outbreaks from March 24th, 2020 onwards. Given 15% monthly vaccination rate from December 2020 in Israel, the effectiveness estimates of reducing the infected toll were 36%, 56%, and 85% for NPIs alone, vaccination alone, and both combined, respectively., Conclusion: We demonstrated how various NPIs stamp out and delay the epidemic curve of COVID-19. The optimal implementation of these NPIs has to be planned before wide vaccine uptake worldwide., Competing Interests: Declaration of competing interest The authors have no conflicts of interest relevant to this article., (Copyright © 2021. Published by Elsevier B.V.)

It is of critical importance to estimate changing disease-transmission rates and their dependence on population mobility. A common approach to this problem involves fitting daily transmission rates using a susceptible-exposed-infected-recovered-(SEIR) model (regularizing to avoid overfitting) and then computing the relationship between the estimated transmission rate and mobility. Unfortunately, there are often several very different transmission-rate trajectories that can fit the reported cases well, meaning that the choice of regularization determines the final solution (and thus the mobility-transmission rate relationship) selected by the SEIR model. Moreover, the classical approaches to regularization-penalizing the derivative of the transmission rate trajectory-do not correspond to realistic properties of pandemic spread. Consequently, models fitted using derivative-based regularization are often biased toward underestimating the current transmission rate and future deaths. In this work, we propose mobility-driven regularization of the SEIR transmission rate trajectory. This method rectifies the artificial regularization problem, produces more accurate and unbiased forecasts of future deaths, and estimates a highly interpretable relationship between mobility and the transmission rate. For this analysis, mobility data related to the coronavirus disease 2019 pandemic was collected by Safegraph (San Francisco, California) from major US cities between March and August 2020., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Objectives: While highly effective in preventing SARS-CoV-2 spread, national lockdowns come with an enormous economic price. Few countries have adopted an alternative "testing, tracing, and isolation" approach to selectively isolate people at high exposure risk, thereby minimizing the economic impact. To assist policy makers, we performed a cost-effectiveness analysis of these 2 strategies., Methods: A modified Susceptible, Exposed, Infectious, Recovered, and Deceased (SEIRD) model was employed to assess the situation in Israel, a small country with ∼9 million people. The incremental cost-effectiveness ratio (ICER) of these strategies as well as the expected number of infected individuals and deaths were calculated., Results: A nationwide lockdown is expected to save, on average, 274 (median 124, interquartile range: 71-221) lives compared to the "testing, tracing, and isolation" approach. However, the ICER will be, on average, $45 104 156 (median $49.6 million, interquartile range: 22.7-220.1) to prevent 1 case of death., Conclusion: A national lockdown has a moderate advantage in saving lives with tremendous costs and possible overwhelming economic effects. These findings should assist decision makers dealing with additional waves of this pandemic., (Copyright © 2020 ISPOR–The Professional Society for Health Economics and Outcomes Research. Published by Elsevier Inc. All rights reserved.)

At the beginning of 2020, the global outbreak of the novel coronavirus COVID-19 posed a huge challenge to the governance capabilities of public health in various countries. In this paper, the SEIR model is used to fit the number of confirmed cases in each province in China, and the reduction rate of the basic reproduction number is used to measure the actual score of the control effect of COVID-19. The potential capacity of prevention and control of epidemics, in theory, is constructed, and we use the difference between theoretical ability and actual score to measure the ability of governance of public health. We found that there were significant differences between actual effect and theoretical ability in various regions, and governance capabilities were an important reason leading to this difference, which was not consistent with the level of economic development. The balance of multiple objectives, the guiding ideology of emphasizing medical treatment over prevention, the fragmentation of the public health system, and the insufficiency of prevention and control ability in primary public health systems seriously affected the government's ability to respond to public health emergencies.

The spreading of infectious diseases including COVID-19 depends on human interactions. In an environment where behavioral patterns and physical contacts are constantly evolving according to new governmental regulations, measuring these interactions is a major challenge. Mobility has emerged as an indicator for human activity and, implicitly, for human interactions. Here, we study the coupling between mobility and COVID-19 dynamics and show that variations in global air traffic and local driving mobility can be used to stratify different disease phases. For ten European countries, our study shows a maximal correlation between driving mobility and disease dynamics with a time lag of [Formula: see text] days. Our findings suggest that trends in local mobility allow us to forecast the outbreak dynamics of COVID-19 for a window of two weeks and adjust local control strategies in real time.

The coronavirus disease 2019 (COVID-19) outbreak caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) began in December 2019 and was basically under control in April 2020 in Wuhan. To explore the impact of intervention measures on the COVID-19 epidemic, we established susceptible-exposed-infectious-recovered (SEIR) models to predict the epidemic characteristics of COVID-19 at four different phases (beginning, outbreak, recession, and plateau) from January 1st to March 30th, 2020. We found that the infection rate rapidly grew up to 0.3647 at Phase II from 0.1100 at Phase I and went down to 0.0600 and 0.0006 at Phase III and IV, respectively. The reproduction numbers of COVID-19 were 10.7843, 13.8144, 1.4815, and 0.0137 at Phase I, II, III, and IV, respectively. These results suggest that intensive interventions, including compulsory home isolation and rapid improvement of medical resources, can effectively reduce the COVID-19 transmission. Furthermore, the predicted COVID-19 epidemic trend by our models was close to the actual epidemic trend in Wuhan. Our phase-based SEIR models demonstrate that intensive intervention measures can effectively control COVID-19 spread even without specific medicines and vaccines against this disease., (© 2021 Wiley Periodicals LLC.)

Background: The effect of the COVID-19 outbreak has led policymakers around the world to attempt transmission control. However, lockdown and shutdown interventions have caused new social problems and designating policy resumption for infection control when reopening society remains a crucial issue. We investigated the effects of different resumption strategies on COVID-19 transmission using a modeling study setting., Methods: We employed a susceptible-exposed-infectious-removed model to simulate COVID-19 outbreaks under five reopening strategies based on China's business resumption progress. The effect of each strategy was evaluated using the peak values of the epidemic curves vis-à-vis confirmed active cases and cumulative cases. Two-sample t-test was performed in order to affirm that the pick values in different scenarios are different., Results: We found that a hierarchy-based reopen strategy performed best when current epidemic prevention measures were maintained save for lockdown, reducing the peak number of active cases and cumulative cases by 50 and 44%, respectively. However, the modeled effect of each strategy decreased when the current intervention was lifted somewhat. Additional attention should be given to regions with significant numbers of migrants, as the potential risk of COVID-19 outbreaks amid society reopening is intrinsically high., Conclusions: Business resumption strategies have the potential to eliminate COVID-19 outbreaks amid society reopening without special control measures. The proposed resumption strategies focused mainly on decreasing the number of imported exposure cases, guaranteeing medical support for epidemic control, or decreasing active cases.

Various measures have been taken in different countries to mitigate the Covid-19 epidemic. But, throughout the world, many citizens don't understand well how these measures are taken and even question the decisions taken by their government. Should the measures be more (or less) restrictive? Are they taken for a too long (or too short) period of time? To provide some quantitative elements of response to these questions, we consider the well-known SEIR model for the Covid-19 epidemic propagation and propose a pragmatic model of the government decision-making operation. Although simple and obviously improvable, the proposed model allows us to study the tradeoff between health and economic aspects in a pragmatic and insightful way. Assuming a given number of phases for the epidemic (namely, 4 in this paper) and a desired tradeoff between health and economic aspects, it is then possible to determine the optimal duration of each phase and the optimal severity level (i.e., the target transmission rate) for each of them. The numerical analysis is performed for the case of France but the adopted approach can be applied to any country. One of the takeaway messages of this analysis is that being able to implement the optimal 4-phase epidemic management strategy in France would have led to 1.05 million of infected people and a GDP loss of 231 billions € instead of 6.88 millions of infected and a loss of 241 billions €. This indicates that, seen from the proposed model perspective, the effectively implemented epidemic management strategy is good economically, whereas substantial improvements might have been obtained in terms of health impact. Our analysis indicates that the lockdown/severe phase should have been more severe but shorter, and the adjustment phase occurred earlier. Due to the natural tendency of people to deviate from the official rules, updating measures every month over the whole epidemic episode seems to be more appropriate., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Lasaulce, Zhang, Varma and Morărescu.)

Background and objective Many countries around the world experienced a high increase in the number of COVID-19 cases after a few weeks of the first case, and along with it, excessive pressure on the healthcare systems. While medicines, drugs, and vaccines against the COVID-19 are being developed, social isolation has become the most used method for controlling the virus spreading. With the social isolation, authorities aimed to slow down the spreading, avoiding saturation of the healthcare system, and allowing that all critical COVID-19 cases could be appropriately treated. By tuning the proposed model to fit Brazil's initial COVID-19 data, the objectives of the paper are to analyze the impact of the social isolation features on the population dynamics; simulate the number of deaths due to COVID-19 and due to the lack of healthcare infrastructure; study combinations of the features for the healthcare system does not collapse; and analyze healthcare system responses for the crisis. Methods In this paper, a Susceptible-Exposed-Infected-Removed model is described in terms of probabilistic cellular automata and ordinary differential equations for the transmission of COVID-19, flexible enough for simulating different scenarios of social isolation according to the following features: the start day for the social isolation after the first death, the period for the social isolation campaign, and the percentage of the population committed to the campaign. Results Results showed that efforts in the social isolation campaign must be concentrated both on the isolation percentage and campaign duration to delay the healthcare system failure. For the hospital situation in Brazil at the beginning of the pandemic outbreak, a rate of 200 purchases per day of intensive care units and mechanical ventilators is the minimum rate to prevent the collapse of the healthcare system. Conclusions By using the model for different scenarios, it is possible to estimate the impact of social isolation campaign adhesion. For instance, if the social isolation percentage increased from 40% to 50% in Brazil, the purchase rate of 150 intensive care units and mechanical ventilators per day would be enough to prevent the healthcare system to collapse. Moreover, results showed that a premature relaxation of the social isolation campaign can lead to subsequent waves of contamination., Competing Interests: Declaration of Competing Interest The author declares that there are no conflicts of interest regarding the publication of this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

We present a classic SEIR model taking into account the daily movements of individuals in different places. The model also takes into account partial confinement of individuals. This model is coupled with a model of protection against the epidemic by the use of masks. We are studying the effects of combined confinement and protection measures on the dynamics of the epidemic. We consider a constant proportion of asymptomatic people. We assume that symptomatic infected people may change their urban travel behavior due to the disease which causes them to travel less to places where they used to move and to stay at home more often. We present a sensitivity study with respect to the parameters. We show that the combination of the use of masks with almost complete release of confinement makes it possible to avoid the occurrence of a secondary peak of the epidemic. The model predicts that a total release of confinement can be successful for an epidemic of [Formula: see text] if on average a proportion of [Formula: see text] of the population wears masks of [Formula: see text] efficacy. However, if [Formula: see text] of the population remains confined, the same goal can be achieved with a proportion of [Formula: see text] of the population wearing masks with efficacy of the order of [Formula: see text].

Western countries are experiencing surges in COVID-19 cases and deaths due to increasing public transportation during holiday seasons. This study aimed to explore whether mainland China will face an epidemic rebound during the Spring Festival holiday, when millions of Chinese people travel across the country, and investigate which nucleic acid testing (NAT) strategy is optimal to contain the epidemic. A microsimulation model was used to simulate SARS-CoV-2 transmission among railway travelers and evaluated the effects of various NAT strategies. An extended susceptible-exposed-infectious-recovered (SEIR) model was built to forecast local transmission during the Spring Festival period under different scenarios of testing strategies. The total number of infections, testing burden, and medical expenditure were calculated to devise an optimal strategy during the Spring Festival travel rush. Assuming the daily incidence of 20 per 10 million persons, our model simulated that there would be 97 active infections on the day of travel among 10 million railway passengers without NAT and symptom screening. Pre-travel testing could reduce the number of active infections. Compared with no NAT, testing passengers from risk tier 2-4 regions 3 days before travelling could significantly reduce the risk of transmission, and it is more economical and efficient than testing for all passengers.

In this paper, deterministic and stochastic models are proposed to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp disease threshold: the disease dies out if $ \mathcal{R}_0\le 1 $ and persists if $ \mathcal{R}_0 > 1 $. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when $ \mathcal{R}_0 > 1 $. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly.