Containing the Transmission of COVID-19: A Modeling Study in 160 Countries

Mathematical Assessment of the Role of Human Behavior Changes on SARS-CoV-2 Transmission Dynamics in the United States

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020-June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).

Relationship of various COVID-19 antibody titer with individual characteristics and prediction of future epidemic trend in Xiamen City, China

Background

Reinfection of coronavirus disease 2019 (COVID-19) has raised concerns about how reliable immunity from infection and vaccination is. With mass testing for the virus halted, understanding the current prevalence of COVID-19 is crucial. This study investigated 1,191 public health workers at the Xiamen Center for Disease Control, focusing on changes in antibody titers and their relationship with individual characteristics.

Methods

The study began by describing the epidemiological characteristics of the study participants. Multilinear regression (MLR) models were employed to explore the associations between individual attributes and antibody titers. Additionally, group-based trajectory models (GBTMs) were utilized to identify trajectories in antibody titer changes. To predict and simulate future epidemic trends and examine the correlation of antibody decay with epidemics, a high-dimensional transmission dynamics model was constructed.

Results

Analysis of epidemiological characteristics revealed significant differences in vaccination status between infected and non-infected groups (χ2=376.706, P<0.05). However, the distribution of antibody titers among the infected and vaccinated populations was not significantly different. The MLR model identified age as a common factor affecting titers of immunoglobulin G (IgG), immunoglobulin M (IgM), and neutralizing antibody (NAb), while other factors showed varying impacts. History of pulmonary disease and hospitalization influenced IgG titer, and factors such as gender, smoking, family history of pulmonary diseases, and hospitalization impacted NAb titers. Age was the sole determinant of IgM titers in this study. GBTM analysis indicated a "gradual decline type" trajectory for IgG (95.65%), while IgM and NAb titers remained stable over the study period. The high-dimensional transmission dynamics model predicted and simulated peak epidemic periods in Xiamen City, which correlated with IgG decay. Age-group-specific simulations revealed a higher incidence and infection rate among individuals aged 30-39 years during both the second and third peaks, followed by those aged 40-49, 50-59, 18-29, and 70-79 years.

Conclusions

Our study shows that antibody titer could be influenced by age, previous pulmonary diseases as well as smoking. Furthermore, the decline in IgG titers is consistent with epidemic trends. These findings emphasize the need for further exploration of these factors and the development of optimized self-protection countermeasures against reinfection.

Assessing the Impact of Vaccination on the Dynamics of COVID-19 in Africa: A Mathematical Modeling Study

Several effective COVID-19 vaccines are administered to combat the COVID-19 pandemic globally. In most African countries, there is a comparatively limited deployment of vaccination programs. In this work, we develop a mathematical compartmental model to assess the impact of vaccination programs on curtailing the burden of COVID-19 in eight African countries considering SARS-CoV-2 cumulative case data for each country for the third wave of the COVID-19 pandemic. The model stratifies the total population into two subgroups based on individual vaccination status. We use the detection and death rates ratios between vaccinated and unvaccinated individuals to quantify the vaccine's effectiveness in reducing new COVID-19 infections and death, respectively. Additionally, we perform a numerical sensitivity analysis to assess the combined impact of vaccination and reduction in the SARS-CoV-2 transmission due to control measures on the control reproduction number (Rc). Our results reveal that on average, at least 60% of the population in each considered African country should be vaccinated to curtail the pandemic (lower the Rc below one). Moreover, lower values of Rc are possible even when there is a low (10%) or moderate (30%) reduction in the SARS-CoV-2 transmission rate due to NPIs. Combining vaccination programs with various levels of reduction in the transmission rate due to NPI aids in curtailing the pandemic. Additionally, this study shows that vaccination significantly reduces the severity of the disease and death rates despite low efficacy against COVID-19 infections. The African governments need to design vaccination strategies that increase vaccine uptake, such as an incentive-based approach.

A Strategy Formulation Framework for Efficient Screening during the Early Stage of a Pandemic

For viruses that can be transmitted by contacts of people, efficiently screening infected individuals is beneficial for controlling outbreaks rapidly and avoiding widespread diffusion, especially during the early stage of a pandemic. The process of virus transmission can be described as virus diffusion in complex networks such as trajectory networks. We propose a strategy formulation framework (SFF) for generating various screening strategies to identify influential nodes in networks. We propose two types of metrics to measure the nodes' influence and three types of screening modes. Then, we can obtain six combinations, i.e., six strategies. To verify the efficiencies of the strategies, we build a scenario model based on the multi-agent modelling. In this model, people can move according to their self-decisions, and a virtual trajectory network is generated by their contacts. We found that (1) screening people will have a better performance based on their contact paths if there is no confirmed case yet, and (2) if the first confirmed case has been discovered, it is better to screen people sequentially by their influences. The proposed SFF and strategies can provide support for decision makers, and the proposed scenario model can be applied to simulate and forecast the virus-diffusion process.

A comparative study on the three calculation methods for reproduction numbers of COVID-19

Objective

This study uses four COVID-19 outbreaks as examples to calculate and compare merits and demerits, as well as applicational scenarios, of three methods for calculating reproduction numbers.

Method

The epidemiological characteristics of the COVID-19 outbreaks are described. Through the definition method, the next-generation matrix-based method, and the epidemic curve and serial interval (SI)-based method, corresponding reproduction numbers were obtained and compared.

Results

Reproduction numbers (R eff ), obtained by the definition method of the four regions, are 1.20, 1.14, 1.66, and 1.12. Through the next generation matrix method, in region H R eff = 4.30, 0.44; region P R eff = 6.5, 1.39, 0; region X R eff = 6.82, 1.39, 0; and region Z R eff = 2.99, 0.65. Time-varying reproduction numbers (R t ), which are attained by SI of onset dates, are decreasing with time. Region H reached its highest R t = 2.8 on July 29 and decreased to R t < 1 after August 4; region P reached its highest R t = 5.8 on September 9 and dropped to R t < 1 by September 14; region X had a fluctuation in the R t and R t < 1 after September 22; R t in region Z reached a maximum of 1.8 on September 15 and decreased continuously to R t < 1 on September 19.

Conclusion

The reproduction number obtained by the definition method is optimal in the early stage of epidemics with a small number of cases that have clear transmission chains to predict the trend of epidemics accurately. The effective reproduction number R eff , calculated by the next generation matrix, could assess the scale of the epidemic and be used to evaluate the effectiveness of prevention and control measures used in epidemics with a large number of cases. Time-varying reproduction number R t , obtained via epidemic curve and SI, can give a clear picture of the change in transmissibility over time, but the conditions of use are more rigorous, requiring a greater sample size and clear transmission chains to perform the calculation. The rational use of the three methods for reproduction numbers plays a role in the further study of the transmissibility of COVID-19.

Intensity and lag-time of non-pharmaceutical interventions on COVID-19 dynamics in German hospitals

Introduction

Evaluating the potential effects of non-pharmaceutical interventions on COVID-19 dynamics is challenging and controversially discussed in the literature. The reasons are manifold, and some of them are as follows. First, interventions are strongly correlated, making a specific contribution difficult to disentangle; second, time trends (including SARS-CoV-2 variants, vaccination coverage and seasonality) influence the potential effects; third, interventions influence the different populations and dynamics with a time delay.

Methods

In this article, we apply a distributed lag linear model on COVID-19 data from Germany from January 2020 to June 2022 to study intensity and lag time effects on the number of hospital patients and the number of prevalent intensive care patients diagnosed with polymerase chain reaction tests. We further discuss how the findings depend on the complexity of accounting for the seasonal trends.

Results and discussion

Our findings show that the first reducing effect of non-pharmaceutical interventions on the number of prevalent intensive care patients before vaccination can be expected not before a time lag of 5 days; the main effect is after a time lag of 10-15 days. In general, we denote that the number of hospital and prevalent intensive care patients decrease with an increase in the overall non-pharmaceutical interventions intensity with a time lag of 9 and 10 days. Finally, we emphasize a clear interpretation of the findings noting that a causal conclusion is challenging due to the lack of a suitable experimental study design.

Optimal control strategies of SARS-CoV-2 Omicron supported by invasive and dynamic models

BACKGROUND

There is a raising concern of a higher infectious Omicron BA.2 variant and the latest BA.4, BA.5 variant, made it more difficult in the mitigation process against COVID-19 pandemic. Our study aimed to find optimal control strategies by transmission of dynamic model from novel invasion theory.

METHODS

Based on the public data sources from January 31 to May 31, 2022, in four cities (Nanjing, Shanghai, Shenzhen and Suzhou) of China. We segmented the theoretical curves into five phases based on the concept of biological invasion. Then, a spatial autocorrelation analysis was carried out by detecting the clustering of the studied areas. After that, we choose a mathematical model of COVID-19 based on system dynamics methodology to simulate numerous intervention measures scenarios. Finally, we have used publicly available migration data to calculate spillover risk.

RESULTS

Epidemics in Shanghai and Shenzhen has gone through the entire invasion phases, whereas Nanjing and Suzhou were all ended in the establishment phase. The results indicated that Rt value and public health and social measures (PHSM)-index of the epidemics were a negative correlation in all cities, except Shenzhen. The intervention has come into effect in different phases of invasion in all studied cities. Until the May 31, most of the spillover risk in Shanghai remained above the spillover risk threshold (18.81-303.84) and the actual number of the spillovers (0.94-74.98) was also increasing along with the time. Shenzhen reported Omicron cases that was only above the spillover risk threshold (17.92) at the phase of outbreak, consistent with an actual partial spillover. In Nanjing and Suzhou, the actual number of reported cases did not exceed the spillover alert value.

CONCLUSIONS

Biological invasion is positioned to contribute substantively to understanding the drivers and mechanisms of the COVID-19 spread and outbreaks. After evaluating the spillover risk of cities at each invasion phase, we found the dynamic zero-COVID strategy implemented in four cities successfully curb the disease epidemic peak of the Omicron variant, which was highly correlated to the way to perform public health and social measures in the early phases right after the invasion of the virus.

Mathematical Models Supporting Control of COVID-19

Mathematical models have played an important role in the management of the coronavirus disease 2019 (COVID-19) pandemic. The aim of this review is to describe the use of COVID-19 mathematical models, their classification, and the advantages and disadvantages of different types of models. We conducted subject heading searches of PubMed and China National Knowledge Infrastructure with the terms "COVID-19," "Mathematical Statistical Model," "Model," "Modeling," "Agent-based Model," and "Ordinary Differential Equation Model" and classified and analyzed the scientific literature retrieved in the search. We categorized the models as data-driven or mechanism-driven. Data-driven models are mainly used for predicting epidemics, and have the advantage of rapid assessment of disease instances. However, their ability to determine transmission mechanisms is limited. Mechanism-driven models include ordinary differential equation (ODE) and agent-based models. ODE models are used to estimate transmissibility and evaluate impact of interventions. Although ODE models are good at determining pathogen transmission characteristics, they are less suitable for simulation of early epidemic stages and rely heavily on availability of first-hand field data. Agent-based models consider influences of individual differences, but they require large amounts of data and can take a long time to develop fully. Many COVID-19 mathematical modeling studies have been conducted, and these have been used for predicting trends, evaluating interventions, and calculating pathogen transmissibility. Successful infectious disease modeling requires comprehensive considerations of data, applications, and purposes.

Natural history and cycle threshold values analysis of COVID-19 in Xiamen City, China

Objective

This study elaborated the natural history parameters of Delta variant, explored the differences in detection cycle thresholds (Ct) among cases.

Methods

Natural history parameters were calculated based on the different onset time and exposure time of the cases. Intergenerational relationships between generations of cases were calculated. Differences in Ct values of cases by gender, age, and mode of detection were analyzed statistically to assess the detoxification capacity of cases.

Results

The median incubation period was 4 days; the detection time for cases decreased from 25 to 7 h as the outbreak continued. The average generation time (GT), time interval between transmission generations (TG) and serial interval (SI) were 3.6 ± 2.6 days, 1.67 ± 2.11 days and 1.7 ± 3.0 days. Among the Ct values, we found little differences in testing across companies, but there were some differences in the gender of detected genes. The Ct values continuous to decreased with age, but increased when the age was greater than 60.

Conclusion

This epidemic was started from aggregation of factories. It is more reasonable to use SI to calculate the effective reproduction number and the time-varying reproduction number. And the analysis of Ct values can improve the positive detection rate and improve prevention and control measures.

Model-Based Evaluation of Transmissibility and Intervention Measures for a COVID-19 Outbreak in Xiamen City, China

Background

In September 2021, there was an outbreak of coronavirus disease 2019 (COVID-19) in Xiamen, China. Various non-pharmacological interventions (NPIs) and pharmacological interventions (PIs) have been implemented to prevent and control the spread of the disease. This study aimed to evaluate the effectiveness of various interventions and to identify priorities for the implementation of prevention and control measures.

Methods

The data of patients with COVID-19 were collected from 8 to 30 September 2021. A Susceptible-Exposed-Infectious-Recovered (SEIR) dynamics model was developed to fit the data and simulate the effectiveness of interventions (medical treatment, isolation, social distancing, masking, and vaccination) under different scenarios. The effective reproductive number (R_eff) was used to assess the transmissibility and transmission risk.

Results

A total of 236 cases of COVID-19 were reported in Xiamen. The epidemic curve was divided into three phases (R_eff = 6.8, 1.5, and 0). Notably, the cumulative number of cases was reduced by 99.67% due to the preventive and control measures implemented by the local government. In the effective containment stage, the number of cases could be reduced to 115 by intensifying the implementation of interventions. The total number of cases (TN) could be reduced by 29.66–95.34% when patients voluntarily visit fever clinics. When only two or three of these measures are implemented, the simulated TN may be greater than the actual number. As four measures were taken simultaneously, the TN may be <100, which is 57.63% less than the actual number. The simultaneous implementation of five interventions could rapidly control the transmission and reduce the number of cases to fewer than 25.

Conclusion

With the joint efforts of the government and the public, the outbreak was controlled quickly and effectively. Authorities could promptly cut the transmission chain and control the spread of the disease when patients with fever voluntarily went to the hospital. The ultimate effect of controlling the outbreak through only one intervention was not obvious. The combined community control and mask wearing, along with other interventions, could lead to rapid control of the outbreak and ultimately lower the total number of cases. More importantly, this would mitigate the impact of the outbreak on society and socioeconomics.

Mathematical modeling and stability analysis of the time-delayed SAIM model for COVID-19 vaccination and media coverage

Since the COVID-19 outbreak began in early 2020, it has spread rapidly and threatened public health worldwide. Vaccination is an effective way to control the epidemic. In this paper, we model a SAIM equation. Our model involves vaccination and the time delay for people to change their willingness to be vaccinated, which is influenced by media coverage. Second, we theoretically analyze the existence and stability of the equilibria of our model. Then, we study the existence of Hopf bifurcation related to the two equilibria and obtain the normal form near the Hopf bifurcating critical point. Third, numerical simulations based two groups of values for model parameters are carried out to verify our theoretical analysis and assess features such as stable equilibria and periodic solutions. To ensure the appropriateness of model parameters, we conduct a mathematical analysis of official data. Next, we study the effect of the media influence rate and attenuation rate of media coverage on vaccination and epidemic control. The analysis results are consistent with real-world conditions. Finally, we present conclusions and suggestions related to the impact of media coverage on vaccination and epidemic control.

The Second Wave of COVID-19 in South and Southeast Asia and the Effects of Vaccination

Background: By February 2021, the overall impact of coronavirus disease 2019 (COVID-19) in South and Southeast Asia was relatively mild. Surprisingly, in early April 2021, the second wave significantly impacted the population and garnered widespread international attention. Methods: This study focused on the nine countries with the highest cumulative deaths from the disease as of August 17, 2021. We look at COVID-19 transmission dynamics in South and Southeast Asia using the reported death data, which fits a mathematical model with a time-varying transmission rate. Results: We estimated the transmission rate, infection fatality rate (IFR), infection attack rate (IAR), and the effects of vaccination in the nine countries in South and Southeast Asia. Our study suggested that the IAR is still low in most countries, and increased vaccination is required to prevent future waves. Conclusion: Implementing non-pharmacological interventions (NPIs) could have helped South and Southeast Asia keep COVID-19 under control in 2020, as demonstrated in our estimated low-transmission rate. We believe that the emergence of the new Delta variant, social unrest, and migrant workers could have triggered the second wave of COVID-19.

Forecast of the COVID-19 trend in India: A simple modelling approach

By February 2021, the overall impact of the COVID-19 pandemic in India had been relatively mild in terms of total reported cases and deaths. Surprisingly, the second wave in early April becomes devastating and attracts worldwide attention. Multiple factors (e.g., Delta variants with increased transmissibility) could have driven the rapid growth of the epidemic in India and led to a large number of deaths within a short period. We aim to reconstruct the transmission rate, estimate the infection fatality rate and forecast the epidemic size. We download the reported COVID-19 mortality data in India and formulate a simple mathematical model with a flexible transmission rate. We use iterated filtering to fit our model to deaths data. We forecast the infection attack rate in a month ahead. Our model simulation matched the reported deaths well and is reasonably close to the results of the serological study. We forecast that the infection attack rate (IAR) could have reached 43% by July 24, 2021, under the current trend. Our estimated infection fatality rate is about 0.07%. Under the current trend, the IAR will likely reach a level of 43% by July 24, 2021. Our estimated infection fatality rate appears unusually low, which could be due to a low case to infection ratio reported in previous study. Our approach is readily applicable in other countries and with other types of data (e.g., excess deaths).