A five-compartment model of age-specific transmissibility of SARS-CoV-2

Theoretical Epidemiology Needs Urgent Attention in China

The mathematical method to which theoretical epidemiology belongs is one of the three major methodologies in epidemiology. It is of great value in diagnosing infectious disease epidemic trends and evaluating the effectiveness of prevention and control measures. This paper aims to summarize the brief history of the development of theoretical epidemiology, common types of mathematical models, and key steps to develop a mathematical model. It also provides some thoughts and perspectives on the development and application of theoretical epidemiology in China.

Modeling the health impact of increasing vaccine coverage and nonpharmaceutical interventions against coronavirus disease 2019 in Ghana

Seroprevalence studies assessing community exposure to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Ghana concluded that population-level immunity remained low as of February 2021. Thus, it is important to demonstrate how increasing vaccine coverage reduces the economic and public health impacts associated with SARS-CoV-2 transmission. To that end, this study used a Susceptible-Exposed-Presymptomatic-Symptomatic-Asymptomatic-Recovered-Dead-Vaccinated compartmental model to simulate coronavirus disease 2019 (COVID-19) transmission and the role of public health interventions in Ghana. The impact of increasing vaccination rates and decline in transmission rates due to nonpharmaceutical interventions (NPIs) on cumulative infections and deaths averted was explored under different scenarios. Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) was used to investigate the uncertainty and sensitivity of the outcomes to the parameters. Simulation results suggest that increasing the vaccination rate to achieve 50% coverage was associated with almost 60,000 deaths and 25 million infections averted. In comparison, a 50% decrease in the transmission coefficient was associated with the prevention of about 150,000 deaths and 50 million infections. The LHS-PRCC results indicated that in the context of vaccination rate, cumulative infections and deaths averted were most sensitive to vaccination rate, waning immunity rates from vaccination, and waning immunity from natural infection. This study's findings illustrate the impact of increasing vaccination coverage and/or reducing the transmission rate by NPI adherence in the prevention of COVID-19 infections and deaths in Ghana.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Decay rate estimation of respiratory viruses in aerosols and on surfaces under different environmental conditions

Majority of the viral outbreaks are super-spreading events established within 2-10 h, dependent on a critical time interval for successful transmission between humans, which is governed by the decay rates of viruses. To evaluate the decay rates of respiratory viruses over a short span, we calculated their decay rate values for various surfaces and aerosols. We applied Bayesian regression and ridge regression and determined the best estimation for respiratory viruses, including severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), severe acute respiratory syndrome coronavirus (SARS-CoV), middle east respiratory syndrome coronavirus (MERS-CoV), influenza viruses, and respiratory syncytial virus (RSV); the decay rate values in aerosols for these viruses were 4.83 ± 5.70, 0.40 ± 0.24, 0.11 ± 0.04, 2.43 ± 5.94, and 1.00 ± 0.50 h^-1, respectively. The highest decay rate values for each virus type differed according to the surface type. According to the model performance criteria, the Bayesian regression model was better for SARS-CoV-2 and influenza viruses, whereas ridge regression was better for SARS-CoV and MERS-CoV. A simulation using a better estimation will help us find effective non-pharmaceutical interventions to control virus transmissions.

Age-specific transmission dynamics under suppression control measures during SARS-CoV-2 Omicron BA.2 epidemic

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 (R₀) was estimated with next generation matrix.

RESULTS

R₀ 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.

Contact pattern, current immune barrier, and pathogen virulence determines the optimal strategy of further vaccination

Background

The current outbreak of novel coronavirus disease 2019 has caused a serious disease burden worldwide. Vaccines are an important factor to sustain the epidemic. Although with a relatively high-vaccination worldwide, the decay of vaccine efficacy and the arising of new variants lead us to the challenge of maintaining a sufficient immune barrier to protect the population.

Method

A case-contact tracking data in Hunan, China, is used to estimate the contact pattern of cases for scenarios including school, workspace, etc, rather than ordinary susceptible population. Based on the estimated vaccine coverage and efficacy, a multi-group vaccinated-exposed-presymptomatic-symptomatic-asymptomatic-removed model (VEFIAR) with 8 age groups, with each partitioned into 4 vaccination status groups is developed. The optimal dose-wise vaccinating strategy is optimized based on the currently estimated immunity barrier of coverage and efficacy, using the greedy algorithm that minimizes the cumulative cases, population size of hospitalization and fatality respectively in a certain future interval. Parameters of Delta and Omicron variants are used respectively in the optimization.

Results

The estimated contact matrices of cases showed a concentration on middle ages, and has compatible magnitudes compared to estimations from contact surveys in other studies. The VEFIAR model is numerically stable. The optimal controled vaccination strategy requires immediate vaccination on the un-vaccinated high-contact population of age 30-39 to reduce the cumulative cases, and is stable with different basic reproduction numbers ( R 0 ). As for minimizing hospitalization and fatality, the optimized strategy requires vaccination on the un-vaccinated of both aged 30-39 of high contact frequency and the vulnerable older.

Conclusion

The objective of reducing transmission requires vaccination in age groups of the highest contact frequency, with more priority for un-vaccinated than un-fully or fully vaccinated. The objective of reducing total hospitalization and fatality requires not only to reduce transmission but also to protect the vulnerable older. The priority changes by vaccination progress. For any region, if the local contact pattern is available, then with the vaccination coverage, efficacy, and disease characteristics of relative risks in heterogeneous populations, the optimal dose-wise vaccinating process will be obtained and gives hints for decision-making.

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.

Changes in life satisfaction, depression, general health and sleep quality of Spanish older women during COVID-19 lockdown and their relationship with lifestyle: an observational follow-up study

OBJETIVES

To analyse the effects of COVID-19 lockdown on mental well-being variables of older women, and to determine the influence of lifestyle and age on such effects. The hypothesis of the study was that all parameters related to mental well-being would worsen in older women during the COVID-19 lockdown.

DESIGN

Observational follow-up study. Pre lockdown measurements were taken before the lockdown. Post lockdown measurements were taken as soon as began the de-escalation.

SETTING

Senior centres in the Region of Murcia (Spain).

PARTICIPANTS

The sample was composed of 40 older women volunteers, over 54 years of age (mean age=62.35±8.15 years).

PRIMARY AND SECONDARY OUTCOME MEASURES

Pre lockdown and post lockdown evaluations were carried out face to face. The following questionnaires were completed: Satisfaction with Life Scale, The Center for Epidemiologic Studies Depression Scale, The Short Form 36 Health Survey, The Pittsburgh Sleep Quality Index, the Global Physical Activity Questionnaire and Prevention with Mediterranean Diet.

RESULTS

Post lockdown, a worsening was found in the variables of life satisfaction (p=0.001); depression (p<0.001), quality of life in physical role (p=0.006), pain (p=0.004), emotional role (p<0.001) and mental health (p<0.001); and sleep quality (p=0.018), sleep latency (p=0.004), sleep disturbances (p=0.002) and global sleep quality score (p=0.002). It was found how age influenced the variables of pain (p=0.003) and social role (p=0.047), as well as the influence of a healthy lifestyle on the variables analysed (F=6.214; p=0.017). Adherence to the Mediterranean diet was shown to be a protective factor against increased depression (p=0.03). Spending time sitting was shown to be a risk factor for physical role health (p=0.002), as was advanced age on health due to worsening pain (p=0.005), or an unhealthy lifestyle on increased consumption of sleeping aids (p=0.017).

CONCLUSION

The lockdown had a great negative impact on Spanish older women on mental well-being variables.

TRIAL REGISTRATION NUMBER

NCT04958499.

Using simulation modelling and systems science to help contain COVID-19: A systematic review

This study systematically reviews applications of three simulation approaches, that is, system dynamics model (SDM), agent-based model (ABM) and discrete event simulation (DES), and their hybrids in COVID-19 research and identifies theoretical and application innovations in public health. Among the 372 eligible papers, 72 focused on COVID-19 transmission dynamics, 204 evaluated both pharmaceutical and non-pharmaceutical interventions, 29 focused on the prediction of the pandemic and 67 investigated the impacts of COVID-19. ABM was used in 275 papers, followed by 54 SDM papers, 32 DES papers and 11 hybrid model papers. Evaluation and design of intervention scenarios are the most widely addressed area accounting for 55% of the four main categories, that is, the transmission of COVID-19, prediction of the pandemic, evaluation and design of intervention scenarios and societal impact assessment. The complexities in impact evaluation and intervention design demand hybrid simulation models that can simultaneously capture micro and macro aspects of the socio-economic systems involved.

COVID-19 in children: epidemic issues and candidate vaccines

A large-scale vaccination of coronavirus disease-19 (COVID-19) in adults has been conducted for nearly a year, and there is a growing recognition that immunization for children is also essential. It has been months since emergency use of pediatric COVID-19 vaccine was approved, we reviewed the prevalence and transmission of COVID-19 in children. The prevalence of COVID-19 in children is reduced due to vaccination even in a Delta prevalent period, so an increase in the vaccination rate is needed in children. Although the precise role of children in the transmission requires more research to uncover, they likely played a significant role, according to the available literature. We also described four candidate COVID-19 vaccines for children on their safety and immunogenicity and the impact of severe acute respiratory syndrome coronavirus 2 variants on childhood vaccination. Safety issues on pediatric vaccines post-approval, like adverse events following immunization and adverse events of special interest require studies on long-term and effective regulatory mechanisms.

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.

Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain.

Computing R0 of dynamic models by a definition-based method

Objectives

Computing the basic reproduction number (R₀) in deterministic dynamical models is a hot topic and is frequently demanded by researchers in public health. The next-generation methods (NGM) are widely used for such computation, however, the results of NGM are usually not to be the true R₀ but only a threshold quantity with little interpretation. In this paper, a definition-based method (DBM) is proposed to solve such a problem.

Methods

Start with the definition of R₀, consider different states that one infected individual may develop into, and take expectations. A comparison with NGM has proceeded. Numerical verification is performed using parameters fitted by data of COVID-19 in Hunan Province.

Results

DBM and NGM give identical expressions for single-host models with single-group and interactive R_ij of single-host models with multi-groups, while difference arises for models partitioned into subgroups. Numerical verification showed the consistencies and differences between DBM and NGM, which supports the conclusion that R₀ derived by DBM with true epidemiological interpretations are better.

Conclusions

DBM is more suitable for single-host models, especially for models partitioned into subgroups. However, for multi-host dynamic models where the true R₀ is failed to define, we may turn to the NGM for the threshold R₀.

Shigellosis seasonality and transmission characteristics in different areas of China: A modelling study

Objective

In China, the burden of shigellosis is unevenly distributed, notably across various ages and geographical areas. Shigellosis temporal trends appear to be seasonal. We should clarify seasonal warnings and regional transmission patterns.

Method

This study adopted a Logistic model to assess the seasonality and a dynamics model to compare the transmission in different areas. The next-generation matrix was used to calculate the effective reproduction number (R_eff) to quantify the transmissibility.

Results

In China, the rate of shigellosis fell from 35.12 cases per 100,000 people in 2005 to 7.85 cases per 100,000 people in 2017, peaking in June and August. After simulation by the Logistic model, the ‘peak time’ is mainly concentrated from mid-June to mid-July. China's ‘early warning time’ is primarily focused on from April to May. We predict the ‘peak time’ of shigellosis is the 6.30th month and the ‘early warning time’ is 3.87th month in 2021. According to the dynamics model results, the water/food transfer pathway has been mostly blocked off. The transmissibility of different regions varies greatly, such as the mean R_eff of Longde County (3.76) is higher than Xiamen City (3.15), higher than Chuxiong City (2.52), and higher than Yichang City (1.70).

Conclusion

The ‘early warning time’ for shigellosis in China is from April to May every year, and it may continue to advance in the future, such as the early warning time in 2021 is in mid-March. Furthermore, we should focus on preventing and controlling the person-to-person route of shigellosis and stratified deploy prevention and control measures according to the regional transmission.

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable whenR 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

Epidemiological Characteristics and Transmissibility for SARS-CoV-2 of Population Level and Cluster Level in a Chinese City

Background

To date, there is a lack of sufficient evidence on the type of clusters in which severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is most likely to spread. Notably, the differences between cluster-level and population-level outbreaks in epidemiological characteristics and transmissibility remain unclear. Identifying the characteristics of these two levels, including epidemiology and transmission dynamics, allows us to develop better surveillance and control strategies following the current removal of suppression measures in China.

Methods

We described the epidemiological characteristics of SARS-CoV-2 and calculated its transmissibility by taking a Chinese city as an example. We used descriptive analysis to characterize epidemiological features for coronavirus disease 2019 (COVID-19) incidence database from 1 Jan 2020 to 2 March 2020 in Chaoyang District, Beijing City, China. The susceptible-exposed-infected-asymptomatic-recovered (SEIAR) model was fitted with the dataset, and the effective reproduction number (R_eff) was calculated as the transmissibility of a single population. Also, the basic reproduction number (R₀) was calculated by definition for three clusters, such as household, factory and community, as the transmissibility of subgroups.

Results

The epidemic curve in Chaoyang District was divided into three stages. We included nine clusters (subgroups), which comprised of seven household-level and one factory-level and one community-level cluster, with sizes ranging from 2 to 17 cases. For the nine clusters, the median incubation period was 17.0 days [Interquartile range (IQR): 8.4–24.0 days (d)], and the average interval between date of onset (report date) and diagnosis date was 1.9 d (IQR: 1.7 to 6.4 d). At the population level, the transmissibility of the virus was high in the early stage of the epidemic (R_eff = 4.81). The transmissibility was higher in factory-level clusters (R₀ = 16) than in community-level clusters (R₀ = 3), and household-level clusters (R₀ = 1).

Conclusions

In Chaoyang District, the epidemiological features of SARS-CoV-2 showed multi-stage pattern. Many clusters were reported to occur indoors, mostly from households and factories, and few from the community. The risk of transmission varies by setting, with indoor settings being more severe than outdoor settings. Reported household clusters were the predominant type, but the population size of the different types of clusters limited transmission. The transmissibility of SARS-CoV-2 was different between a single population and its subgroups, with cluster-level transmissibility higher than population-level transmissibility.

The influence of a transport process on the epidemic threshold

By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the transport process that gives rise to a multiplex network model. In addition to a static layer, the (multiplex) epidemic network consists of a second dynamic layer in which any two individuals are connected for the time they occupy the same site during a random walk they perform on a separate transport network. We develop a mean-field description of the stochastic network model and study the influence the transport process has on the epidemic threshold. We show that any transport process generally lowers the epidemic threshold because of the additional connections it generates. In contrast, considering also random walks of fractional order that in some sense are a more realistic model of human mobility, we find that these non-local transport dynamics raise the epidemic threshold in comparison to a classical local random walk. We also test our model on a realistic transport network (the Munich U-Bahn network), and carefully compare mean-field solutions with stochastic trajectories in a range of scenarios.

Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.

The optimal vaccination strategy to control COVID-19: a modeling study in Wuhan City, China

Background

Reaching optimal vaccination rates is an essential public health strategy to control the coronavirus disease 2019 (COVID-19) pandemic. This study aimed to simulate the optimal vaccination strategy to control the disease by developing an age-specific model based on the current transmission patterns of COVID-19 in Wuhan City, China.

Methods

We collected two indicators of COVID-19, including illness onset data and age of confirmed case in Wuhan City, from December 2, 2019, to March 16, 2020. The reported cases were divided into four age groups: group 1, ≤ 14 years old; group 2, 15 to 44 years old; group 3, 44 to 64 years old; and group 4, ≥ 65 years old. An age-specific susceptible-exposed-symptomatic-asymptomatic-recovered/removed model was developed to estimate the transmissibility and simulate the optimal vaccination strategy. The effective reproduction number (R_eff) was used to estimate the transmission interaction in different age groups.

Results

A total of 47 722 new cases were reported in Wuhan City from December 2, 2019, to March 16, 2020. Before the travel ban of Wuhan City, the highest transmissibility was observed among age group 2 (R_eff = 4.28), followed by group 2 to 3 (R_eff = 2.61), and group 2 to 4 (R_eff = 1.69). China should vaccinate at least 85% of the total population to interrupt transmission. The priority for controlling transmission should be to vaccinate 5% to 8% of individuals in age group 2 per day (ultimately vaccinated 90% of age group 2), followed by 10% of age group 3 per day (ultimately vaccinated 90% age group 3). However, the optimal vaccination strategy for reducing the disease severity identified individuals ≥ 65 years old as a priority group, followed by those 45–64 years old.

Conclusions

Approximately 85% of the total population (nearly 1.2 billion people) should be vaccinated to build an immune barrier in China to safely consider removing border restrictions. Based on these results, we concluded that 90% of adults aged 15–64 years should first be vaccinated to prevent transmission in China.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-021-00922-4.

Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R 0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.

Feasibility of Booster Vaccination in High-Risk Populations for Controlling Coronavirus Variants - China, 2021

Introduction

Vaccination booster shots are completely necessary for controlling breakthrough infections of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in China. The study aims to estimate effectiveness of booster vaccines for high-risk populations (HRPs).

Methods

A vaccinated Susceptible-Exposed-Symptomatic-Asymptomatic-Recovered/Removed (SEIAR) model was developed to simulate scenarios of effective reproduction number (R_eff) from 4 to 6. Total number of infectious and asymptomatic cases were used to evaluated vaccination effectiveness.

Results

Our model showed that we could not prevent outbreaks when covering 80% of HRPs with booster unless R_eff=4.0 or the booster vaccine had efficacy against infectivity and susceptibility of more than 90%. The results were consistent when the outcome index was confirmed cases or asymptomatic cases.

Conclusions

An ideal coronavirus disease 2019 (COVID-19) booster vaccination strategy for HRPs would be expected to reach the initial goal to control the transmission of the Delta variant in China. Accordingly, the recommendation for the COVID-19 booster vaccine should be implemented in HRPs who are already vaccinated and could prevent transmission to other groups.

Predicting Hospital Resource Use During COVID-19 Surges: A Simple but Flexible Discretely Integrated Condition Event Simulation of Individual Patient-Hospital Trajectories

OBJECTIVES

To assist with planning hospital resources, including critical care (CC) beds, for managing patients with COVID-19.

METHODS

An individual simulation was implemented in Microsoft Excel using a discretely integrated condition event simulation. Expected daily cases presented to the emergency department were modeled in terms of transitions to and from ward and CC and to discharge or death. The duration of stay in each location was selected from trajectory-specific distributions. Daily ward and CC bed occupancy and the number of discharges according to care needs were forecast for the period of interest. Face validity was ascertained by local experts and, for the case study, by comparing forecasts with actual data.

RESULTS

To illustrate the use of the model, a case study was developed for Guy's and St Thomas' Trust. They provided inputs for January 2020 to early April 2020, and local observed case numbers were fit to provide estimates of emergency department arrivals. A peak demand of 467 ward and 135 CC beds was forecast, with diminishing numbers through July. The model tended to predict higher occupancy in Level 1 than what was eventually observed, but the timing of peaks was quite close, especially for CC, where the model predicted at least 120 beds would be occupied from April 9, 2020, to April 17, 2020, compared with April 7, 2020, to April 19, 2020, in reality. The care needs on discharge varied greatly from day to day.

CONCLUSIONS

The DICE simulation of hospital trajectories of patients with COVID-19 provides forecasts of resources needed with only a few local inputs. This should help planners understand their expected resource needs.

Modelling the Emerging COVID-19 Epidemic and Estimating Intervention Effectiveness - Taiwan, China, 2021

INTRODUCTION

The coronavirus disease 2019 (COVID-19) pandemic recently affected Taiwan, China. This study aimed to calculate the transmissibility of COVID-19 to predict trends and evaluate the effects of interventions.

METHODS

The data of reported COVID-19 cases was collected from April 20 to May 26, 2021, which included daily reported data (Scenario I) and reported data after adjustment (Scenario II). A susceptible-exposed-symptomatic-asymptomatic-recovered model was developed to fit the data. The effective reproductive number (Reff ) was used to estimate the transmissibility of COVID-19.

RESULTS

A total of 4,854 cases were collected for the modelling. In Scenario I, the intervention has already taken some effects from May 17 to May 26 (the Reff reduced to 2.1). When the Reff was set as 0.1, the epidemic was projected to end on July 4, and a total of 1,997 cases and 855 asymptomatic individuals would have been reported. In Scenario II, the interventions were projected as having been effective from May 24 to May 26 (the Reff reduced to 0.4). When the Reff was set as 0.1, the epidemic was projected to end on July 1, and a total of 1,482 cases and 635 asymptomatic individuals would have been reported.

CONCLUSION

The epidemic of COVID-19 was projected to end after at least one month, even if the most effective interventions were applied in Taiwan, China. Although there were some positive effects of intervention in Taiwan, China.

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

Background: It is much valuable to evaluate the comparative effectiveness of the coronavirus disease 2019 (COVID-19) prevention and control in the non-pharmacological intervention phase of the pandemic across countries and identify useful experiences that could be generalized worldwide. Methods: In this study, we developed a susceptible-exposure-infectious-asymptomatic-removed (SEIAR) model to fit the daily reported COVID-19 cases in 160 countries. The time-varying reproduction number (R t ) that was estimated through fitting the mathematical model was adopted to quantify the transmissibility. We defined a synthetic index (I AC ) based on the value of R t to reflect the national capability to control COVID-19. Results: The goodness-of-fit tests showed that the SEIAR model fitted the data of the 160 countries well. At the beginning of the epidemic, the values of R t of countries in the European region were generally higher than those in other regions. Among the 160 countries included in the study, all European countries had the ability to control the COVID-19 epidemic. The Western Pacific Region did best in continuous control of the epidemic, with a total of 73.76% of countries that can continuously control the COVID-19 epidemic, while only 43.63% of the countries in the European Region continuously controlled the epidemic, followed by the Region of Americas with 52.53% of countries, the Southeast Asian Region with 48% of countries, the African Region with 46.81% of countries, and the Eastern Mediterranean Region with 40.48% of countries. Conclusion: Large variations in controlling the COVID-19 epidemic existed across countries. The world could benefit from the experience of some countries that demonstrated the highest containment capabilities.

Feasibility of controlling hepatitis E in Jiangsu Province, China: a modelling study

BACKGROUND

Hepatitis E, an acute zoonotic disease caused by the hepatitis E virus (HEV), has a relatively high burden in developing countries. The current research model on hepatitis E mainly uses experimental animal models (such as pigs, chickens, and rabbits) to explain the transmission of HEV. Few studies have developed a multi-host and multi-route transmission dynamic model (MHMRTDM) to explore the transmission feature of HEV. Hence, this study aimed to explore its transmission and evaluate the effectiveness of intervention using the dataset of Jiangsu Province.

METHODS

We developed a dataset comprising all reported HEV cases in Jiangsu Province from 2005 to 2018. The MHMRTDM was developed according to the natural history of HEV cases among humans and pigs and the multi-transmission routes such as person-to-person, pig-to-person, and environment-to-person. We estimated the key parameter of the transmission using the principle of least root mean square to fit the curve of the MHMRTDM to the reported data. We developed models with single or combined countermeasures to assess the effectiveness of interventions, which include vaccination, shortening the infectious period, and cutting transmission routes. The indicator, total attack rate (TAR), was adopted to assess the effectiveness.

RESULTS

From 2005 to 2018, 44 923 hepatitis E cases were reported in Jiangsu Province. The model fits the data well (R2 = 0.655, P < 0.001). The incidence of the disease in Jiangsu Province and its cities peaks are around March; however, transmissibility of the disease peaks in December and January. The model showed that the most effective intervention was interrupting the pig-to-person route during the incidence trough of September, thereby reducing the TAR by 98.11%, followed by vaccination (reducing the TAR by 76.25% when the vaccination coefficient is 100%) and shortening the infectious period (reducing the TAR by 50.05% when the infectious period is shortened to 15 days).

CONCLUSIONS

HEV could be controlled by interrupting the pig-to-person route, shortening the infectious period, and vaccination. Among these interventions, the most effective was interrupting the pig-to-person route.

Relative transmissibility of shigellosis among different age groups: A modeling study in Hubei Province, China

Shigellosis is a heavy disease burden in China especially in children aged under 5 years. However, the age-related factors involved in transmission of shigellosis are unclear. An age-specific Susceptible-Exposed-Infectious/Asymptomatic-Recovered (SEIAR) model was applied to shigellosis surveillance data maintained by Hubei Province Centers for Disease Control and Prevention from 2005 to 2017. The individuals were divided into four age groups (≤ 5 years, 6-24 years, 25-59 years, and ≥ 60 years). The effective reproduction number (Reff), including infectivity (RI) and susceptibility (RS) was calculated to assess the transmissibility of different age groups. From 2005 to 2017, 130,768 shigellosis cases were reported in Hubei Province. The SEIAR model fitted well with the reported data (P < 0.001). The highest transmissibility (Reff) was from ≤ 5 years to the 25-59 years (mean: 0.76, 95% confidence interval [CI]: 0.34-1.17), followed by from the 6-24 years to the 25-59 years (mean: 0.69, 95% CI: 0.35-1.02), from the ≥ 60 years to the 25-59 years (mean: 0.58, 95% CI: 0.29-0.86), and from the 25-59 years to 25-59 years (mean: 0.50, 95% CI: 0.21-0.78). The highest infectivity was in ≤ 5 years (RI = 1.71), and was most commonly transmitted to the 25-59 years (45.11%). The highest susceptibility was in the 25-59 years (RS = 2.51), and their most common source was the ≤ 5 years (30.15%). Furthermore, "knock out" simulation predicted the greatest reduction in the number of cases occurred by when cutting off transmission routes among ≤ 5 years and from 25-59 years to ≤ 5 years. Transmission in ≤ 5 years occurred mainly within the group, but infections were most commonly introduced by individuals in the 25-59 years. Infectivity was highest in the ≤ 5 years and susceptibility was highest in the 25-59 years. Interventions to stop transmission should be directed at these age groups.

The epidemiological characteristics and effectiveness of countermeasures to contain coronavirus disease 2019 in Ningbo City, Zhejiang Province, China

A novel coronavirus (SARS-CoV-2) has spread worldwide and led to high disease burden around the world. This study aimed to explore the key parameters of SARS-CoV-2 infection and to assess the effectiveness of interventions to control the coronavirus disease 2019 (COVID-19). A susceptible-exposed-infectious-asymptomatic-recovered (SEIAR) model was developed for the assessment. The information of each confirmed case and asymptomatic infection was collected from Ningbo Center for Disease Control and Prevention (CDC) to calculate the key parameters of the model in Ningbo City, China. A total of 157 confirmed COVID-19 cases (including 51 imported cases and 106 secondary cases) and 30 asymptomatic infections were reported in Ningbo City. The proportion of asymptomatic infections had an increasing trend. The proportion of elder people in the asymptomatic infections was lower than younger people, and the difference was statistically significant (Fisher's Exact Test, P = 0.034). There were 22 clusters associated with 167 SARS-CoV-2 infections, among which 29 cases were asymptomatic infections, accounting for 17.37%. We found that the secondary attack rate (SAR) of asymptomatic infections was almost the same as that of symptomatic cases, and no statistical significance was observed (χ2 = 0.052, P = 0.819) by Kruskal-Wallis test. The effective reproduction number (Reff) was 1.43, which revealed that the transmissibility of SARS-CoV-2 was moderate. If the interventions had not been strengthened, the duration of the outbreak would have lasted about 16 months with a simulated attack rate of 44.15%. The total attack rate (TAR) and duration of the outbreak would increase along with the increasing delay of intervention. SARS-CoV-2 had moderate transmissibility in Ningbo City, China. The proportion of asymptomatic infections had an increase trend. Asymptomatic infections had the same transmissibility as symptomatic infections. The integrated interventions were implemented at different stages during the outbreak, which turned out to be exceedingly effective in China.

The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

Effectiveness of potential antiviral treatments in COVID-19 transmission control: a modelling study

BACKGROUND

Novel coronavirus disease 2019 (COVID-19) causes an immense disease burden. Although public health countermeasures effectively controlled the epidemic in China, non-pharmaceutical interventions can neither be maintained indefinitely nor conveniently implemented globally. Vaccination is mainly used to prevent COVID-19, and most current antiviral treatment evaluations focus on clinical efficacy. Therefore, we conducted population-based simulations to assess antiviral treatment effectiveness among different age groups based on its clinical efficacy.

METHODS

We collected COVID-19 data of Wuhan City from published literature and established a database (from 2 December 2019 to 16 March 2020). We developed an age-specific model to evaluate the effectiveness of antiviral treatment in patients with COVID-19. Efficacy was divided into three types: (1) viral activity reduction, reflected as transmission rate decrease [reduction was set as v (0-0.8) to simulate hypothetical antiviral treatments]; (2) reduction in the duration time from symptom onset to patient recovery/removal, reflected as a 1/γ decrease (reduction was set as 1-3 days to simulate hypothetical or real-life antiviral treatments, and the time of asymptomatic was reduced by the same proportion); (3) fatality rate reduction in severely ill patients (fc) [reduction (z) was set as 0.3 to simulate real-life antiviral treatments]. The population was divided into four age groups (groups 1, 2, 3 and 4), which included those aged ≤ 14; 15-44; 45-64; and ≥ 65 years, respectively. Evaluation indices were based on outbreak duration, cumulative number of cases, total attack rate (TAR), peak date, number of peak cases, and case fatality rate (f).

RESULTS

Comparing the simulation results of combination and single medication therapy s, all four age groups showed better results with combination medication. When 1/γ = 2 and v = 0.4, age group 2 had the highest TAR reduction rate (98.48%, 56.01-0.85%). When 1/γ = 2, z = 0.3, and v = 0.1, age group 1 had the highest reduction rate of f (83.08%, 0.71-0.12%).

CONCLUSIONS

Antiviral treatments are more effective in COVID-19 transmission control than in mortality reduction. Overall, antiviral treatments were more effective in younger age groups, while older age groups showed higher COVID-19 prevalence and mortality. Therefore, physicians should pay more attention to prevention of viral spread and patients deaths when providing antiviral treatments to patients of older age groups.

Evaluating the effectiveness of measures to control the novel coronavirus disease 2019 in Jilin Province, China

BACKGROUND

Based on differences in populations and prevention and control measures, the spread of new coronary pneumonia in different countries and regions also differs. This study aimed to calculate the transmissibility of coronavirus disease 2019 (COVID-19), and to evaluate the effectiveness of measures to control the disease in Jilin Province, China.

METHODS

The data of reported COVID-19 cases were collected, including imported and local cases from Jilin Province as of March 14, 2019. A Susceptible-Exposed-Infectious-Asymptomatic-Recovered/Removed (SEIAR) model was developed to fit the data, and the effective reproduction number (Reff) was calculated at different stages in the province. Finally, the effectiveness of the measures was assessed.

RESULTS

A total of 97 COVID-19 infections were reported in Jilin Province, among which 45 were imported infections (including one asymptomatic infection) and 52 were local infections (including three asymptomatic infections). The model fit the reported data well (R2 = 0.593, P < 0.001). The Reff of COVID-19 before and after February 1, 2020 was 1.64 and 0.05, respectively. Without the intervention taken on February 1, 2020, the predicted cases would have reached a peak of 177,011 on October 22, 2020 (284 days from the first case). The projected number of cases until the end of the outbreak (on October 9, 2021) would have been 17,129,367, with a total attack rate of 63.66%. Based on the comparison between the predicted incidence of the model and the actual incidence, the comprehensive intervention measures implemented in Jilin Province on February 1 reduced the incidence of cases by 99.99%. Therefore, according to the current measures and implementation efforts, Jilin Province can achieve good control of the virus's spread.

CONCLUSIONS

COVID-19 has a moderate transmissibility in Jilin Province, China. The interventions implemented in the province had proven effective; increasing social distancing and a rapid response by the prevention and control system will help control the spread of the disease.

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

Background

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

Methods

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

Results

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

Conclusion

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