Compartmental structures used in modeling COVID-19: a scoping review

Bayesian hierarchical spatiotemporal models for prediction of (under)reporting rates and cases: COVID-19 infection among the older people in the United States during the 2020-2022 pandemic

The gap between the reported and actual COVID-19 infection cases has been an issue of concern. Here, we present Bayesian hierarchical spatiotemporal disease mapping models for state-level predictions of COVID-19 infection risks and (under)reporting rates among people aged 65 and above during the first two years of the pandemic in the United States. With prior elicitation based on recent prevalence studies, the study suggests that the median state-level reporting rate of COVID-19 infection was 90% (interquartile range: [78%, 96%]). Our study uncovers spatiotemporal variations and dynamics in state-level infection risks and (under)reporting rates, suggesting time-varying associations between higher population density, higher percentage of minorities, and higher percentage of vaccination and increased risks of COVID-19 infection, as well as an association between more easily accessible tests and higher reporting rates. With sensitivity analyses, we highlight the impact and importance of incorporating covariates information and objective prior references for evaluating the issue of underreporting.

Autonomous and policy-induced behavior change during the COVID-19 pandemic: Towards understanding and modeling the interplay of behavioral adaptation

Changes in human behaviors, such as reductions of physical contacts and the adoption of preventive measures, impact the transmission of infectious diseases considerably. Behavioral adaptations may be the result of individuals aiming to protect themselves or mere responses to public containment measures, or a combination of both. What drives autonomous and policy-induced adaptation, how they are related and change over time is insufficiently understood. Here, we develop a framework for more precise analysis of behavioral adaptation, focusing on confluence, interactions and time variance of autonomous and policy-induced adaptation. We carry out an empirical analysis of Germany during the fall of 2020 and beyond. Subsequently, we discuss how behavioral adaptation processes can be better represented in behavioral-epidemiological models. We find that our framework is useful to understand the interplay of autonomous and policy-induced adaptation as a "moving target". Our empirical analysis suggests that mobility patterns in Germany changed significantly due to both autonomous and policy-induced adaption, with potentially weaker effects over time due to decreasing risk signals, diminishing risk perceptions and an erosion of trust in the government. We find that while a number of simulation and prediction models have made great efforts to represent behavioral adaptation, the interplay of autonomous and policy-induced adaption needs to be better understood to construct convincing counterfactual scenarios for policy analysis. The insights presented here are of interest to modelers and policy makers aiming to understand and account for behaviors during a pandemic response more accurately.

Prediction of cross-border spread of the COVID-19 pandemic: A predictive model for imported cases outside China

The COVID-19 pandemic has been present globally for more than three years, and cross-border transmission has played an important role in its spread. Currently, most predictions of COVID-19 spread are limited to a country (or a region), and models for cross-border transmission risk assessment remain lacking. Information on imported COVID-19 cases reported from March 2020 to June 2022 was collected from the National Health Commission of China, and COVID-19 epidemic data of the countries of origin of the imported cases were collected on data websites such as WHO and Our World in Data. It is proposed to establish a prediction model suitable for the prevention and control of overseas importation of COVID-19. Firstly, the SIR model was used to fit the epidemic infection status of the countries where the cases were exported, and most of the r2 values of the fitted curves obtained were above 0.75, which indicated that the SIR model could well fit different countries and the infection status of the region. After fitting the epidemic infection status data of overseas exporting countries, on this basis, a SIR-multiple linear regression overseas import risk prediction combination model was established, which can predict the risk of overseas case importation, and the established overseas import risk model overall P <0.05, the adjusted R2 = 0.7, indicating that the SIR-multivariate linear regression overseas import risk prediction combination model can obtain better prediction results. Our model effectively estimates the risk of imported cases of COVID-19 from abroad.

The unintended consequences of inconsistent closure policies and mobility restrictions during epidemics

Background

Controlling the spread of infectious diseases-even when safe, transmission-blocking vaccines are available-may require the effective use of non-pharmaceutical interventions (NPIs), e.g., mask wearing, testing, limits on group sizes, venue closure. During the SARS-CoV-2 pandemic, many countries implemented NPIs inconsistently in space and time. This inconsistency was especially pronounced for policies in the United States of America (US) related to venue closure.

Methods

Here, we investigate the impact of inconsistent policies associated with venue closure using mathematical modeling and high-resolution human mobility, Google search, and county-level SARS-CoV-2 incidence data from the USA. Specifically, we look at high-resolution location data and perform a US-county-level analysis of nearly 8 million SARS-CoV-2 cases and 150 million location visits, including 120 million church visitors across 184,677 churches, 14 million grocery visitors across 7662 grocery stores, and 13.5 million gym visitors across 5483 gyms.

Results

Analyzing the interaction between venue closure and changing mobility using a mathematical model shows that, across a broad range of model parameters, inconsistent or partial closure can be worse in terms of disease transmission as compared to scenarios with no closures at all. Importantly, changes in mobility patterns due to epidemic control measures can lead to increase in the future number of cases. In the most severe cases, individuals traveling to neighboring jurisdictions with different closure policies can result in an outbreak that would otherwise have been contained. To motivate our mathematical models, we turn to mobility data and find that while stay-at-home orders and closures decreased contacts in most areas of the USA, some specific activities and venues saw an increase in attendance and an increase in the distance visitors traveled to attend. We support this finding using search query data, which clearly shows a shift in information seeking behavior concurrent with the changing mobility patterns.

Conclusions

While coarse-grained observations are not sufficient to validate our models, taken together, they highlight the potential unintended consequences of inconsistent epidemic control policies related to venue closure and stress the importance of balancing the societal needs of a population with the risk of an outbreak growing into a large epidemic.

Supplementary Information

The online version contains supplementary material available at 10.1186/s44263-023-00028-z.

Pharmaceutical and non-pharmaceutical interventions for controlling the COVID-19 pandemic

Disease spread can be affected by pharmaceutical interventions (such as vaccination) and non-pharmaceutical interventions (such as physical distancing, mask-wearing and contact tracing). Understanding the relationship between disease dynamics and human behaviour is a significant factor to controlling infections. In this work, we propose a compartmental epidemiological model for studying how the infection dynamics of COVID-19 evolves for people with different levels of social distancing, natural immunity and vaccine-induced immunity. Our model recreates the transmission dynamics of COVID-19 in Ontario up to December 2021. Our results indicate that people change their behaviour based on the disease dynamics and mitigation measures. Specifically, they adopt more protective behaviour when mandated social distancing measures are in effect, typically concurrent with a high number of infections. They reduce protective behaviour when vaccination coverage is high or when mandated contact reduction measures are relaxed, typically concurrent with a reduction of infections. We demonstrate that waning of infection and vaccine-induced immunity are important for reproducing disease transmission in autumn 2021.

An Epidemiological Analysis for Assessing and Evaluating COVID-19 Based on Data Analytics in Latin American Countries

This research provides a detailed analysis of the COVID-19 spread across 14 Latin American countries. Using time-series analysis and epidemic models, we identify diverse outbreak patterns, which seem not to be influenced by geographical location or country size, suggesting the influence of other determining factors. Our study uncovers significant discrepancies between the number recorded COVID-19 cases and the real epidemiological situation, emphasizing the crucial need for accurate data handling and continuous surveillance in managing epidemics. The absence of a clear correlation between the country size and the confirmed cases, as well as with the fatalities, further underscores the multifaceted influences on COVID-19 impact beyond population size. Despite the decreased real-time reproduction number indicating quarantine effectiveness in most countries, we note a resurgence in infection rates upon resumption of daily activities. These insights spotlight the challenge of balancing public health measures with economic and social activities. Our core findings provide novel insights, applicable to guiding epidemic control strategies and informing decision-making processes in combatting the pandemic.

A stochastic agent-based model to evaluate COVID-19 transmission influenced by human mobility

The COVID-19 pandemic has created an urgent need for mathematical models that can project epidemic trends and evaluate the effectiveness of mitigation strategies. A major challenge in forecasting the transmission of COVID-19 is the accurate assessment of the multiscale human mobility and how it impacts infection through close contacts. By combining the stochastic agent-based modeling strategy and hierarchical structures of spatial containers corresponding to the notion of geographical places, this study proposes a novel model, Mob-Cov, to study the impact of human traveling behavior and individual health conditions on the disease outbreak and the probability of zero-COVID in the population. Specifically, individuals perform power law-type local movements within a container and global transport between different-level containers. It is revealed that frequent long-distance movements inside a small-level container (e.g., a road or a county) and a small population size reduce both the local crowdedness and disease transmission. It takes only half of the time to induce global disease outbreaks when the population increases from 150 to 500 (normalized unit). When the exponent c 1 of the long-tail distribution of distance k moved in the same-level container, p ( k ) ∼ k - c 1 · level , increases, the outbreak time decreases rapidly from 75 to 25 (normalized unit). In contrast, travel between large-level containers (e.g., cities and nations) facilitates global spread of the disease and outbreak. When the mean traveling distance across containers 1 d increases from 0.5 to 1 (normalized unit), the outbreak occurs almost twice as fast. Moreover, dynamic infection and recovery in the population are able to drive the bifurcation of the system to a "zero-COVID" state or to a "live with COVID" state, depending on the mobility patterns, population number and health conditions. Reducing population size and restricting global travel help achieve zero-COVID-19. Specifically, when c 1 is smaller than 0.2, the ratio of people with low levels of mobility is larger than 80% and the population size is smaller than 400, zero-COVID can be achieved within fewer than 1000 time steps. In summary, the Mob-Cov model considers more realistic human mobility at a wide range of spatial scales, and has been designed with equal emphasis on performance, low simulation cost, accuracy, ease of use and flexibility. It is a useful tool for researchers and politicians to apply when investigating pandemic dynamics and when planning actions against disease.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11071-023-08489-5.

Booster Dose Vaccination and Dynamics of COVID-19 Pandemic in the Fifth Wave: An Efficient and Simple Mathematical Model for Disease Progression

Background: Mathematical studies exploring the impact of booster vaccine doses on the recent COVID-19 waves are scarce, leading to ambiguity regarding the significance of booster doses. Methods: A mathematical model with seven compartments was used to determine the basic and effective reproduction numbers and the proportion of infected people during the fifth wave of COVID-19. Using the next-generation matrix, we computed the effective reproduction parameter, Rt. Results: During the fifth COVID-19 wave, the basic reproductive number in Thailand was calculated to be R0= 1.018691. Analytical analysis of the model revealed both local and global stability of the disease-free equilibrium and the presence of an endemic equilibrium. A dose-dependent decrease in the percentage of infected individuals was observed in the vaccinated population. The simulation results matched the real-world data of the infected patients, establishing the suitability of the model. Furthermore, our analysis suggested that people who had received vaccinations had a better recovery rate and that the death rate was the lowest among those who received the booster dose. The booster dose reduced the effective reproduction number over time, suggesting a vaccine efficacy rate of 0.92. Conclusion: Our study employed a rigorous analytical approach to accurately describe the dynamics of the COVID-19 fifth wave in Thailand. Our findings demonstrated that administering a booster dose can significantly increase the vaccine efficacy rate, resulting in a lower effective reproduction number and a reduction in the number of infected individuals. These results have important implications for public health policymaking, as they provide useful information for the more effective forecasting of the pandemic and improving the efficiency of public health interventions. Moreover, our study contributes to the ongoing discourse on the effectiveness of booster doses in mitigating the impact of the COVID-19 pandemic. Essentially, our study suggests that administering a booster dose can substantially reduce the spread of the virus, supporting the case for widespread booster dose campaigns.

Transmission trends of the global COVID-19 pandemic with combined effects of adaptive behaviours and vaccination

We developed a mechanism model which allows for simulating the novel coronavirus (COVID-19) transmission dynamics with the combined effects of human adaptive behaviours and vaccination, aiming at predicting the end time of COVID-19 infection in global scale. Based on the surveillance information (reported cases and vaccination data) between 22 January 2020 and 18 July 2022, we validated the model by Markov Chain Monte Carlo (MCMC) fitting method. We found that (1) if without adaptive behaviours, the epidemic could sweep the world in 2022 and 2023, causing 3.098 billion of human infections, which is 5.39 times of current number; (2) 645 million people could be avoided from infection due to vaccination; and (3) in current scenarios of protective behaviours and vaccination, infection cases would increase slowly, levelling off around 2023, and it would end completely in June 2025, causing 1.024 billion infections, with 12.5 million death. Our findings suggest that vaccination and the collective protection behaviour remain the key determinants against the global process of COVID-19 transmission.

Asymptotic Analysis of Optimal Vaccination Policies

Targeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivation of the leading-order optimal vaccination policy under multi-group susceptible-infected-recovered dynamics in two different cases. Firstly, it considers the case of a small vulnerable subgroup in a population and shows that (in the asymptotic limit) it is optimal to vaccinate this group first, regardless of the properties of the other groups. Then, it considers the case of a small vaccine supply and transforms the optimal vaccination problem into a simple knapsack problem by linearising the final size equations. Both of these cases are then explored further through numerical examples, which show that these solutions are also directly useful for realistic parameter values. Moreover, the findings of this paper give some general principles for optimal vaccination policies which will help policy-makers and the public to understand the reasoning behind optimal vaccination programs in more generic cases.

Modeling social interaction and metapopulation mobility of the COVID-19 pandemic in main cities of highly populated Java Island, Indonesia: An agent-based modeling approach

Introduction

Coronavirus transmission is strongly influenced by human mobilities and interactions within and between different geographical regions. Human mobility within and between cities is motivated by several factors, including employment, cultural-driven, holidays, and daily routines.

Method

We developed a sustained metapopulation (SAMPAN) model, an agent-based model (ABM) for simulating the effect of individual mobility and interaction behavior on the spreading of COVID-19 viruses across main cities on Java Island, Indonesia. The model considers social classes and social mixing affecting the mobility and interaction behavior within a sub-population of a city in the early pandemic. Travelers’ behavior represents the mobility among cities from central cities to other cities and commuting behavior from the surrounding area of each city.

Results

Local sensitivity analysis using one factor at a time was performed to test the SAMPAN model, and we have identified critical parameters for the model. While validation was carried out for the Jakarta area, we are confident in implementing the model for a larger area with the concept of metapopulation dynamics. We included the area of Bogor, Depok, Bekasi, Bandung, Semarang, Surakarta, Yogyakarta, Surabaya, and Malang cities which have important roles in the COVID-19 pandemic spreading on this island.

Discussion

Our SAMPAN model can simulate various waves during the first year of the pandemic caused by various phenomena of large social mobilities and interactions, particularly during religious occasions and long holidays.

Estimation of monkeypox spread in a nonendemic country considering contact tracing and self-reporting: A stochastic modeling study

In May 2022, monkeypox started to spread in nonendemic countries. To investigate contact tracing and self-reporting of the primary case in the local community, a stochastic model is developed. An algorithm based on Gillespie's stochastic chemical kinetics is used to quantify the number of infections, contacts, and duration from the arrival of the primary case to the detection of the index case (or until there are no more local infections). Different scenarios were set considering the delay in contact tracing and behavior of infectors. We found that the self-reporting behavior of a primary case is the most significant factor affecting outbreak size and duration. Scenarios with a self-reporting primary case have an 86% reduction in infections (average: 5-7, in a population of 10 000) and contacts (average: 27-72) compared with scenarios with a non-self-reporting primary case (average number of infections and contacts: 27-72 and 197-537, respectively). Doubling the number of close contacts per day is less impactful compared with the self-reporting behavior of the primary case as it could only increase the number of infections by 45%. Our study emphasizes the importance of the prompt detection of the primary case.

Simulating and Forecasting the COVID-19 Spread in a U.S. Metropolitan Region with a Spatial SEIR Model

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.

Modeling the effects of vaccination, nucleic acid testing, and face mask wearing interventions against COVID-19 in large sports events

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.

Optimization of COVID-19 prevention and control measures during the Beijing 2022 Winter Olympics: a model-based study

Background

The continuous mutation of severe acute respiratory syndrome coronavirus 2 has made the coronavirus disease 2019 (COVID-19) pandemic complicated to predict and posed a severe challenge to the Beijing 2022 Winter Olympics and Winter Paralympics held in February and March 2022.

Methods

During the preparations for the Beijing 2022 Winter Olympics, we established a dynamic model with pulse detection and isolation effect to evaluate the effect of epidemic prevention and control measures such as entry policies, contact reduction, nucleic acid testing, tracking, isolation, and health monitoring in a closed-loop management environment, by simulating the transmission dynamics in assumed scenarios. We also compared the importance of each parameter in the combination of intervention measures through sensitivity analysis.

Results

At the assumed baseline levels, the peak of the epidemic reached on the 57th day. During the simulation period (100 days), 13,382 people infected COVID-19. The mean and peak values of hospitalized cases were 2650 and 6746, respectively. The simulation and sensitivity analysis showed that: (1) the most important measures to stop COVID-19 transmission during the event were daily nucleic acid testing, reducing contact among people, and daily health monitoring, with cumulative infections at 0.04%, 0.14%, and 14.92% of baseline levels, respectively (2) strictly implementing the entry policy and reducing the number of cases entering the closed-loop system could delay the peak of the epidemic by 9 days and provide time for medical resources to be mobilized; (3) the risk of environmental transmission was low.

Conclusions

Comprehensive measures under certain scenarios such as reducing contact, nucleic acid testing, health monitoring, and timely tracking and isolation could effectively prevent virus transmission. Our research results provided an important reference for formulating prevention and control measures during the Winter Olympics, and no epidemic spread in the closed-loop during the games indirectly proved the rationality of our research results.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-022-01019-2.