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The reproduction number serves as a fundamental metric in the examination of infectious disease outbreaks, epidemics, and pandemics. Despite an array of available methods for estimating equation M2, both newcomers and established public health professionals often encounter difficulties in comprehending the circumstances for their use and their constrictions. Consequently, this review intends to offer elementary guidance on equation M3’s selection and estimation approaches. To facilitate our review, we executed an extensive search on PubMed and Web of Science applying the following search approach: [“Basic Reproduction Number/classification”(Mesh)] AND [“Basic Reproduction Number/prevention and control”(Mesh)] OR [“Basic Reproduction Number/statistics and numerical data”(Mesh)]. Our search parameters were restricted to articles published from January 2013 to January 2023. This search rendered a total of 7,094 articles, of which we selected 60 that met our inclusion standards for further analysis.

Objectives To evaluate the impact of early implementation of public health and social measures (PHSMs) on contact rates over time and explore contact behavior of asymptomatic versus symptomatic cases. Methods We used the largest contact tracing data in China thus far to estimate the mean contacts over time by age groups and contact settings. We used bootstrap with replacement to quantify the uncertainty of contact matrixes. The Pearson correlation was performed to demonstrate the number of contacts over time in relation to the evolution of restrictions. In addition, we analyzed the index cases with a high number of contacts and index cases that produced a high number of secondary cases. Results Rapidly adapted PHSMs can reduce the mean contact rates in public places while increasing the mean contact rates within households. The mean contact rates were 11.81 (95% confidence interval, 11.61-12.01) for asymptomatic (at the time of investigation) cases and 6.70 (95% confidence interval, 6.54-6.87) for symptomatic cases. The percentage of asymptomatic cases (at the time of investigation) meeting >50 close contacts make up more than 65% of the overall cases. The percentage of asymptomatic cases producing >10 secondary cases account for more than 80% of the overall cases. Conclusion PHSMs may increase the contacts within the household, necessitating the need for pertinent prevention strategies at home. Asymptomatic cases can contribute significantly to Omicron transmission. By making asymptomatic people aware that they are already contagious, hence limiting their social contacts, it is possible to lower the transmission risk.

Mpox has high transmissibility in MSM, which required minimize the risk of infection and exposure to high-risk populations. Community prevention and control is the top priority of interventions to contain the spread of mpox.

Since the epidemic of the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2), many governments have used reverse transcription polymerase chain reaction (RT-PCR) to detect the virus. However, there are fewer measures of CT values information based on RT-PCR results, and the relationship between CT values and factors from consecutive tests is not clear enough. So in this study, we analyzed the connection between CT values and the factors based on cohort data from Delta variant of SARS-CoV-2 in Hunan Province. Previous studies have showed that the mean age of the cases was 33.34 years (±18.72 years), with a female predominance (55.03%, n=71), and the greatest proportion of clinical symptoms were of the common type (60.47%, n=78). There were statistical differences between the N and ORF1ab genes in the CT values for the cases. Based on the analysis of the association between CT values and the factors, the lowest CT values were obtained for the unvaccinated, older and clinically symptomatic group at 3 to 10 days, the maximum peak of viral load occurred. Therefore, it is recommended to use patient information to focus on older, clinically symptomatic, unvaccinated patients and to intervene promptly upon admission.

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 ( R0 ). 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.

The world has undergone five waves of COVID-19 pandemics, with a sixth wave likely to be led by China as policies in China begin to relax. We reproduced the multiple Omicron waves in Singapore using a multi-dimensional model. Our model shows that the simulated epidemic curve matches the publicly reported data. And we simulated the Omicron wave after reopening in Xiamen, a city with a population size and age structure similar to Singapore based on Singapore’s experience during Omicron wave. We advocate that cities in China emulate Singapore’s response to the Omicron wave through dynamic PHSMs adjustment, thereby reducing the disease and healthcare system burden.

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 (Reff), 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 Reff = 4.30, 0.44; region P Reff = 6.5, 1.39, 0; region X Reff = 6.82, 1.39, 0; and region Z Reff = 2.99, 0.65. Time-varying reproduction numbers (Rt), which are attained by SI of onset dates, are decreasing with time. Region H reached its highest Rt = 2.8 on July 29 and decreased to Rt < 1 after August 4; region P reached its highest Rt = 5.8 on September 9 and dropped to Rt < 1 by September 14; region X had a fluctuation in the Rt and Rt < 1 after September 22; Rt in region Z reached a maximum of 1.8 on September 15 and decreased continuously to Rt < 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 Reff, 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 Rt, 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.

In order to reduce individual variations and estimate the positive duration (Ct value < 30), B-spline basis functions (using the 4th-degree basis function) were selected to model the change of Ct value after infected (Table S1, Supplementary materials 3). In our model, ORF gene expression was slightly higher than N gene expression, with a longer positive duration (9.85 vs. 8.80 days) (Fig. 1D). Pre-symptomatic positive duration was 0.5 days and 0.15 days for N gene and ORF gene, respectively (Fig. 1D). For N gene expression, the positive duration after receiving booster dose was 9.55 days, which was slightly shorter than fully vaccinated (10.15 days) and unfully vaccinated (10.70 days) (Fig. 1E). And similar results were observed for ORF gene expression in Fig. 1F (mean duration: 8.65 vs. 9.00 vs. 9.40 days). This is consistent with what was previously described in Table 1, completed full vaccination and received booster reduces the duration of positivity, regardless of N gene or ORF gene expression.

The results showed the mean value of median Rt value for MPX of 1.36 (SD: 0.21) and the median R0 value of 1.63 (IQR: 1.34–1.72) where the R0 values we calculated were higher than the estimates listed on the WHO official website.

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.

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

Our findings imply that Omicron’s transmissibility is 1.5–1.8 times higher than that of Delta in terms of viral transmission. This is lower than the value reported by other studies, which claim that Omicron has a transmissibility 2.5 to 4 higher than that of Delta. This might be attributable to the rising rate of fully vaccinated and booster-vaccinated people. Meanwhile, the geographic variability is also linked to inconsistencies in the implementation of COVID-19 prevention and control measures in different regions. We also saw that the transmissibility of the two Omicron sub-lineages differed, with Omicron BA.2 being 1.2 times more transmissible than BA.1, which is similar to the results of several studies that suggest that BA.2 is 30 to 40 percent more infectious than BA.1. In comparison to Delta, applying a dynamic zero-COVID policy for interrupting Omicron transmission may necessitate greater preventative and control efforts.


Objectives: Computing the basic reproduction number (R 0) 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 R 0 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 R 0, 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 R 0 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 R 0 is failed to define, we may turn to the NGM for the threshold R 0.