SARS-CoV-2 Transmission in Alberta, British Columbia, and Ontario, Canada, January 2020-January 2022

We estimated COVID-19 transmission potential and case burden by variant type in Alberta, British Columbia, and Ontario, Canada, during January 23, 2020-January 27, 2022; we also estimated the effectiveness of public health interventions to reduce transmission. We estimated time-varying reproduction number (Rt) over 7-day sliding windows and nonoverlapping time-windows determined by timing of policy changes. We calculated incidence rate ratios (IRRs) for each variant and compared rates to determine differences in burden among provinces. Rt corresponding with emergence of the Delta variant increased in all 3 provinces; British Columbia had the largest increase, 43.85% (95% credible interval [CrI] 40.71%-46.84%). Across the study period, IRR was highest for Omicron (8.74 [95% CrI 8.71-8.77]) and burden highest in Alberta (IRR 1.80 [95% CrI 1.79-1.81]). Initiating public health interventions was associated with lower Rt and relaxing restrictions and emergence of new variants associated with increases in Rt.

Substantial transmission of SARS-CoV-2 through casual contact in retail stores: Evidence from matched administrative microdata on card payments and testing

This paper presents quasiexperimental evidence of Covid-19 transmission through casual contact between customers in retail stores. For a large sample of individuals in Denmark, we match card payment data, indicating exactly where and when each individual made purchases, with Covid-19 test data, indicating when each individual was tested and whether the test was positive. The resulting dataset identifies more than 100,000 instances where an infected individual made a purchase in a store and, in each instance, allows us to track the infection dynamics of other individuals who made purchases in the same store around the same time. We estimate transmissions by comparing the infection rate of exposed customers, who made a purchase within 5 min of an infected individual, and nonexposed customers, who made a purchase in the same store 16 to 30 min before. We find that exposure to an infected individual in a store increases the infection rate by around 0.12 percentage points (P < 0.001) between day 3 and day 7 after exposure. The estimates imply that transmissions in stores contributed around 0.04 to the reproduction number for the average infected individual and significantly more in the period where Omicron was the dominant variant.

Estimating the reproduction number and transmission heterogeneity from the size distribution of clusters of identical pathogen sequences

Quantifying transmission intensity and heterogeneity is crucial to ascertain the threat posed by infectious diseases and inform the design of interventions. Methods that jointly estimate the reproduction number R and the dispersion parameter k have however mainly remained limited to the analysis of epidemiological clusters or contact tracing data, whose collection often proves difficult. Here, we show that clusters of identical sequences are imprinted by the pathogen offspring distribution, and we derive an analytical formula for the distribution of the size of these clusters. We develop and evaluate an inference framework to jointly estimate the reproduction number and the dispersion parameter from the size distribution of clusters of identical sequences. We then illustrate its application across a range of epidemiological situations. Finally, we develop a hypothesis testing framework relying on clusters of identical sequences to determine whether a given pathogen genetic subpopulation is associated with increased or reduced transmissibility. Our work provides tools to estimate the reproduction number and transmission heterogeneity from pathogen sequences without building a phylogenetic tree, thus making it easily scalable to large pathogen genome datasets.

Time Scales of Human Mpox Transmission in The Netherlands

Mpox has spread rapidly to many countries in nonendemic regions. After reviewing detailed exposure histories of 109 pairs of mpox cases in the Netherlands, we identified 34 pairs where transmission was likely and the infectee reported a single potential infector with a mean serial interval of 10.1 days (95% credible interval, 6.6-14.7 days). Further investigation into pairs from 1 regional public health service revealed that presymptomatic transmission may have occurred in 5 of 18 pairs. These findings emphasize that precaution remains key, regardless of the presence of recognizable symptoms of mpox.

Season of death, pathogen persistence and wildlife behaviour alter number of anthrax secondary infections from environmental reservoirs

An important part of infectious disease management is predicting factors that influence disease outbreaks, such as R, the number of secondary infections arising from an infected individual. Estimating R is particularly challenging for environmentally transmitted pathogens given time lags between cases and subsequent infections. Here, we calculated R for Bacillus anthracis infections arising from anthrax carcass sites in Etosha National Park, Namibia. Combining host behavioural data, pathogen concentrations and simulation models, we show that R is spatially and temporally variable, driven by spore concentrations at death, host visitation rates and early preference for foraging at infectious sites. While spores were detected up to a decade after death, most secondary infections occurred within 2 years. Transmission simulations under scenarios combining site infectiousness and host exposure risk under different environmental conditions led to dramatically different outbreak dynamics, from pathogen extinction (R < 1) to explosive outbreaks (R > 10). These transmission heterogeneities may explain variation in anthrax outbreak dynamics observed globally, and more generally, the critical importance of environmental variation underlying host-pathogen interactions. Notably, our approach allowed us to estimate the lethal dose of a highly virulent pathogen non-invasively from observational studies and epidemiological data, useful when experiments on wildlife are undesirable or impractical.

Impact of public health policy and mobility change on transmission potential of severe acute respiratory syndrome coronavirus 2 in Rhode Island, March 2020 - November 2021

To study the SARS-CoV-2 transmission potential in Rhode Island (RI) and its association with policy changes and mobility changes, the time-varying reproduction number, Rt, was estimated. The daily incident case counts (16 March 2020, through 30 November 2021) were bootstrapped within a 15-day sliding window and multiplied by Poisson-distributed multipliers (λ = 4, sensitivity analysis: 11) to generate 1000 estimated infection counts, to which EpiEstim was applied to generate Rt time series. The median Rt percentage change when policies changed was estimated. The time lag correlations were assessed between the 7-day moving average of the relative changes in Google mobility data in the first 90 days, and Rt and estimated infection count, respectively. There were three major pandemic waves in RI in 2020-2021: spring 2020, winter 2020-2021 and fall-winter 2021. The median Rt fluctuated within the range of 0.5-2 from April 2020 to November 2021. Mask mandate (18 April 2020) was associated with a decrease in Rt (-25.99%, 95% CrI: -37.42%, -14.30%). Termination of mask mandates on 6 July 2021 was associated with an increase in Rt (36.74%, 95% CrI: 27.20%, 49.13%). Positive correlations were found between changes in grocery and pharmacy, Rt retail and recreation, transit, and workplace visits, for both Rt and estimated infection count, respectively. Negative correlations were found between changes in residential area visits for both Rt and estimated infection count, respectively. Public health policies enacted in RI were associated with changes in the pandemic trajectory. This ecological study provides further evidence of how non-pharmaceutical interventions and vaccination slowed COVID-19 transmission in RI.

Wastewater-based reproduction numbers and projections of COVID-19 cases in three areas in Japan, November 2021 to December 2022

BackgroundWastewater surveillance has expanded globally as a means to monitor spread of infectious diseases. An inherent challenge is substantial noise and bias in wastewater data because of the sampling and quantification process, limiting the applicability of wastewater surveillance as a monitoring tool.AimTo present an analytical framework for capturing the growth trend of circulating infections from wastewater data and conducting scenario analyses to guide policy decisions.MethodsWe developed a mathematical model for translating the observed SARS-CoV-2 viral load in wastewater into effective reproduction numbers. We used an extended Kalman filter to infer underlying transmissions by smoothing out observational noise. We also illustrated the impact of different countermeasures such as expanded vaccinations and non-pharmaceutical interventions on the projected number of cases using three study areas in Japan during 2021-22 as an example.ResultsObserved notified cases were matched with the range of cases estimated by our approach with wastewater data only, across different study areas and virus quantification methods, especially when the disease prevalence was high. Estimated reproduction numbers derived from wastewater data were consistent with notification-based reproduction numbers. Our projections showed that a 10-20% increase in vaccination coverage or a 10% reduction in contact rate may suffice to initiate a declining trend in study areas.ConclusionOur study demonstrates how wastewater data can be used to track reproduction numbers and perform scenario modelling to inform policy decisions. The proposed framework complements conventional clinical surveillance, especially when reliable and timely epidemiological data are not available.

The reproduction number and its probability distribution for stochastic viral dynamics

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

Mathematical model on HIV and nutrition

HIV continues to be a major global health issue, having claimed millions of lives in the last few decades. While several empirical studies support the fact that proper nutrition is useful in the fight against HIV, very few studies have focused on developing and using mathematical modelling approaches to assess the association between HIV, human immune response to the disease, and nutrition. We develop a within-host model for HIV that captures the dynamic interactions between HIV, the immune system and nutrition. We find that increased viral activity leads to increased serum protein levels. We also show that the viral production rate is positively correlated with HIV viral loads, as is the enhancement rate of protein by virus. Although our numerical simulations indicate a direct correlation between dietary protein intake and serum protein levels in HIV-infected individuals, further modelling and clinical studies are necessary to gain comprehensive understanding of the relationship.

Unveiling invisible farm-to-farm PRRSV-2 transmission links and routes through transmission tree and network analysis

The United States (U.S.) swine industry has struggled to control porcine reproductive and respiratory syndrome (PRRS) for decades, yet the causative virus, PRRSV-2, continues to circulate and rapidly diverges into new variants. In the swine industry, the farm is typically the epidemiological unit for monitoring, prevention, and control; breaking transmission among farms is a critical step in containing disease spread. Despite this, our understanding of farm transmission still is inadequate, precluding the development of tailored control strategies. Therefore, our objective was to infer farm-to-farm transmission links, estimate farm-level transmissibility as defined by reproduction numbers (R), and identify associated risk factors for transmission using PRRSV-2 open reading frame 5 (ORF5) gene sequences, animal movement records, and other data from farms in a swine-dense region of the U.S. from 2014 to 2017. Timed phylogenetic and transmission tree analyses were performed on three sets of sequences (n = 206) from 144 farms that represented the three largest genetic variants of the virus in the study area. The length of inferred pig-to-pig infection chains that corresponded to pairs of farms connected via direct animal movement was used as a threshold value for identifying other feasible transmission links between farms; these links were then transformed into farm-to-farm transmission networks and calculated farm-level R-values. The median farm-level R was one (IQR = 1-2), whereas the R value of 28% of farms was more than one. Exponential random graph models were then used to evaluate the influence of farm attributes and/or farm relationships on the occurrence of farm-to-farm transmission links. These models showed that, even though most transmission events cannot be directly explained by animal movement, movement was strongly associated with transmission. This study demonstrates how integrative techniques may improve disease traceability in a data-rich era by providing a clearer picture of regional disease transmission.

A Mathematical Model to Study the Potential Hepatitis B Virus Infections and Effects of Vaccination Strategies in China

MOTIVATIONS

Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV). Approximately 390,000 people in China die from HBV-related diseases each year. Around 86 million individuals suffer from infections of the hepatitis B virus, accounting for about 6% of the total population in the region. There are approximately 30 million chronic infections. From 2002 to 2007, China's government took part in "The Global Alliance for Vaccines and Immunization (GAVI)" initiative, which helped reduce cases of chronic HBV infections among children. However, incidences of hepatitis B remain persistently high in China. Accurately estimating the number of potential HBV infections is crucial for preventing and controlling the transmission of the hepatitis B virus. Up until now, there were no studies of potentially infectious hepatitis B virus infections.

METHODS

this study was based on data from the National Bureau of Statistics of China from 2003 to 2021; a dynamic model was built, which included a compartment for potentially infectious hepatitis B virus infections. The parameters in the model were fitted using a combination of nonlinear least-squares and genetic algorithm methods.

RESULTS

the calculated reproduction number for hepatitis B virus transmission within the population is Rc = 1.741. Considering the existing vaccine inefficiency rate of 0.1, the model estimates there are 449,535 (95%CI [415,651, 483,420]) potentially infectious hepatitis B virus infections, constituting 30.49% of total hepatitis B cases. Date fitting using MATLAB reveals that increasing the rate of hepatitis B vaccinations can effectively reduce the number of infections.

CONCLUSIONS

the results reveal that the number of potential infectious hepatitis B virus infections is so high that the number of hepatitis B patients persistently rises in China. To better control the transmission of the hepatitis B virus, an optional prevention and control strategy is needed to increase the vaccination of different age groups, and it is necessary to help the public correctly understand the transmission of hepatitis B and ensure adequate protection.

Mathematical Modeling of SARS-CoV-2 Transmission between Minks and Humans Considering New Variants and Mink Culling

We formulated and studied mathematical models to investigate control strategies for the outbreak of the disease caused by SARS-CoV-2, considering the transmission between humans and minks. Two novel models, namely SEIR and SVEIR, are proposed to incorporate human-to-human, human-to-mink, and mink-to-human transmission. We derive formulas for the reproduction number R0 for both models using the next-generation matrix technique. We fitted our model to the daily number of COVID-19-infected cases among humans in Denmark as an example, and using the best-fit parameters, we calculated the values of R0 to be 1.58432 and 1.71852 for the two-strain and single-strain models, respectively. Numerical simulations are conducted to investigate the impact of control measures, such as mink culling or vaccination strategies, on the number of infected cases in both humans and minks. Additionally, we investigated the possibility of the mutated virus in minks being transmitted to humans. Our results indicate that to control the disease and spread of SARS-CoV-2 mutant strains among humans and minks, we must minimize the transmission and contact rates between mink farmers and other humans by quarantining such individuals. In order to reduce the virus mutation rate in minks, culling or vaccination strategies for infected mink farms must also be implemented. These measures are essential in managing the spread of SARS-CoV-2 and its variants, protecting public health, and mitigating the potential risks associated with human-to-mink transmission.

Contribution of cats and dogs to SARS-CoV-2 transmission in households

Introduction

SARS-CoV-2 is known to jump across species. The occurrence of transmission in households between humans and companion animals has been shown, but the contribution of companion animals to the overall transmission within a household is unknown. The basic reproduction number (R₀) is an important indicator to quantify transmission. For a pathogen with multiple host species, such as SARS-CoV-2, the basic reproduction number needs to be calculated from the partial reproduction numbers for each combination of host species.

Method

In this study, the basic and partial reproduction numbers for SARS-CoV-2 were estimated by reanalyzing a survey of Dutch households with dogs and cats and minimally one SARS-CoV-2-infected human.

Results

For households with cats, a clear correlation between the number of cats and the basic reproduction number (Spearman's correlation: p 0.40, p-value: 1.4 × 10^-5) was identified, while for dogs, the correlation was smaller and not significant (Spearman's correlation: p 0.12, p-value: 0.21). Partial reproduction numbers from cats or dogs to humans were 0.3 (0.0-2.0) and 0.3 (0.0-3.5) and from humans to cats or dogs were 0.6 (0.4-0.8) and 0.6 (0.4-0.9).

Discussion

Thus, the estimations of within-household transmission indicated the likelihood of transmission from these companion animals to humans and vice versa, but the observational nature of this study limited the ability to establish conclusive evidence. This study's findings support the advice provided during the pandemic to COVID-19 patients to maintain distance from companion animals as a precautionary measure and given the possibility of transmission, although there is an overall relatively limited impact on the pandemic when compared to human-to-human transmission.

Estimates of Serial Interval and Reproduction Number of Sudan Virus, Uganda, August-November 2022

We estimated the mean serial interval for Sudan virus in Uganda to be 11.7 days (95 CI% 8.2-15.8 days). Estimates for the 2022 outbreak indicate a mean basic reproduction number of 2.4-2.7 (95% CI 1.7-3.5). Estimated net reproduction numbers across districts suggest a marked spatial heterogeneity.

Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays

BACKGROUND

Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus.

METHODS

The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed.

RESULTS

Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done.

CONCLUSIONS

The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.

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

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

Monkeypox: a review of epidemiological modelling studies and how modelling has led to mechanistic insight

Human monkeypox (mpox) virus is a viral zoonosis that belongs to the Orthopoxvirus genus of the Poxviridae family, which presents with similar symptoms as those seen in human smallpox patients. Mpox is an increasing concern globally, with over 80,000 cases in non-endemic countries as of December 2022. In this review, we provide a brief history and ecology of mpox, its basic virology, and the key differences in mpox viral fitness traits before and after 2022. We summarize and critique current knowledge from epidemiological mathematical models, within-host models, and between-host transmission models using the One Health approach, where we distinguish between models that focus on immunity from vaccination, geography, climatic variables, as well as animal models. We report various epidemiological parameters, such as the reproduction number, R0, in a condensed format to facilitate comparison between studies. We focus on how mathematical modelling studies have led to novel mechanistic insight into mpox transmission and pathogenesis. As mpox is predicted to lead to further infection peaks in many historically non-endemic countries, mathematical modelling studies of mpox can provide rapid actionable insights into viral dynamics to guide public health measures and mitigation strategies.

Analysis of a multi-type resurgence of Mycobacterium bovis in cattle and badgers in Southwest France, 2007-2019

Although control measures to tackle bovine tuberculosis (bTB) in cattle have been successful in many parts of Europe, this disease has not been eradicated in areas where Mycobacterium bovis circulates in multi-host systems. Here we analyzed the resurgence of 11 M. bovis genotypes (defined based on spoligotyping and MIRU-VNTR) detected in 141 farms between 2007 and 2019, in an area of Southwestern France where wildlife infection was also detected from 2012 in 65 badgers. We used a spatially-explicit model to reconstruct the simultaneous diffusion of the 11 genotypes in cattle farms and badger populations. Effective reproduction number R was estimated to be 1.34 in 2007-2011 indicating a self-sustained M. bovis transmission by a maintenance community although within-species Rs were both < 1, indicating that neither cattle nor badger populations acted as separate reservoir hosts. From 2012, control measures were implemented, and we observed a decrease of R below 1. Spatial contrasts of the basic reproduction ratio suggested that local field conditions may favor (or penalize) local spread of bTB upon introduction into a new farm. Calculation of generation time distributions showed that the spread of M. bovis has been more rapid from cattle farms (0.5-0.7 year) than from badger groups (1.3-2.4 years). Although eradication of bTB appears possible in the study area (since R < 1), the model suggests it is a long-term prospect, because of the prolonged persistence of infection in badger groups (2.9-5.7 years). Supplementary tools and efforts to better control bTB infection in badgers (including vaccination for instance) appear necessary.

Correlation of viral loads in disease transmission could affect early estimates of the reproduction number

Early estimates of the transmission properties of a newly emerged pathogen are critical to an effective public health response, and are often based on limited outbreak data. Here, we use simulations to investigate how correlations between the viral load of cases in transmission chains can affect estimates of these fundamental transmission properties. Our computational model simulates a disease transmission mechanism in which the viral load of the infector at the time of transmission influences the infectiousness of the infectee. These correlations in transmission pairs produce a population-level convergence process during which the distributions of initial viral loads in each subsequent generation converge to a steady state. We find that outbreaks arising from index cases with low initial viral loads give rise to early estimates of transmission properties that could be misleading. These findings demonstrate the potential for transmission mechanisms to affect estimates of the transmission properties of newly emerged viruses in ways that could be operationally significant to a public health response.

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.

Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19

It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

In this study, a mathematical model for studying the dynamics of monkeypox virus transmission with non-pharmaceutical intervention is created, examined, and simulated using real-time data. Positiveness, invariance, and boundedness of the solutions are thus examined as fundamental features of mathematical models. The equilibrium points and the prerequisites for their stability are achieved. The basic reproduction number and thus the virus transmission coefficient ℜ0 were determined and quantitatively used to study the global stability of the model's steady state. Furthermore, this study considered the sensitivity analysis of the parameters according to ℜ0. The most sensitive variables that are important for infection control are determined using the normalized forward sensitivity index. Data from the United Kingdom collected between May and August 2022, which also aid in demonstrating the usefulness and practical application of the model to the spread of the disease in the United Kingdom, were used. In addition, using the Caputo-Fabrizio operator, Krasnoselskii's fixed point theorem has been used to analyze the existence and uniqueness of the solutions to the suggested model. The numerical simulations are presented to assess the system dynamic behavior. More vulnerability was observed when monkeypox virus cases first appeared recently as a result of numerical calculations. We advise the policymakers to consider these elements to control monkeypox transmission. Based on these findings, we hypothesized that another control parameter could be the memory index or fractional order.

Estimation of the serial interval of monkeypox during the early outbreak in 2022

With increased transmissibility and novel transmission mode, monkeypox poses new threats to public health globally in the background of the ongoing COVID-19 pandemic. Estimates of the serial interval, a key epidemiological parameter of infectious disease transmission, could provide insights into the virus transmission risks. As of October 2022, little was known about the serial interval of monkeypox due to the lack of contact tracing data. In this study, public-available contact tracing data of global monkeypox cases were collected and 21 infector-infectee transmission pairs were identified. We proposed a statistical method applied to real-world observations to estimate the serial interval of the monkeypox. We estimated a mean serial interval of 5.6 days with the right truncation and sampling bias adjusted and calculated the reproduction number of 1.33 for the early monkeypox outbreaks at a global scale. Our findings provided a preliminary understanding of the transmission potentials of the current situation of monkeypox outbreaks. We highlighted the need for continuous surveillance of monkeypox for transmission risk assessment.

Application of Quantifier Elimination in Epidemiology

Background

An application of a novel method of a quantifier elimination in epidemiology was presented in this paper.

Objective

We investigated the existence of the endemic equilibrium for the SEIRS model by QE method and gave a short review of the epidemic prediction models for covid-19.

Methods

A new method for quantifier elimination for the theory of real closed fields.

Results

Obtained value of a reproduction number and endemic equilibrium for the SEIRS model by QEAnalysis of the SEIR model with the concrete values through the example of Severe Acute Respiratory Syndrome (SARS) (a critical value of a transmission rate is evaluated in the example).

Conclusion

The main result of this paper is the obtained value of the endemic equilibrium for the SEIRS model (similar result is obtained for the SEIR model). Also, we have analysed the SEIR model through the examle of SARS and we reviewed several epidemic prediction models for covid-19.

Reproduction number of monkeypox in the early stage of the 2022 multi-country outbreak

Monkeypox, a fast-spreading viral zoonosis outside of Africa in May 2022, has put scientists on alert. We estimated the reproduction number to be 1.39 (95% CrI: 1.37, 1.42) by aggregating all cases in 70 countries as of 22 July 2022.

Dynamics of a multi-strain malaria model with diffusion in a periodic environment

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers Ri and R^i (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when Ri<1, while if Ri>1>Rj (i≠j,i,j=1,2), then strain i persists and strain j dies out. More interestingly, when R1 and R2 are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are R^1>1 and R^2>1. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.

Dynamics of SARS-CoV-2 Major Genetic Lineages in Moscow in the Context of Vaccine Prophylaxis

Findings collected over two and a half years of the COVID-19 pandemic demonstrated that the level immunity resulting from vaccination and infection is insufficient to stop the circulation of new genetic variants. The short-term decline in morbidity was followed by a steady increase. The early identification of new genetic lineages that will require vaccine adaptation in the future is an important research target. In this study, we summarised data on the variability of genetic line composition throughout the COVID-19 pandemic in Moscow, Russia, and evaluated the virological and epidemiological features of dominant variants in the context of selected vaccine prophylaxes. The prevalence of the Omicron variant highlighted the low effectiveness of the existing immune layer in preventing infection, which points to the necessity of optimising the antigens used in vaccines in Moscow. Logistic growth curves showing the rate at which the new variant displaces the previously dominant variants may serve as early indicators for selecting candidates for updated vaccines, along with estimates of efficacy, reduced viral neutralising activity against the new strains, and viral load in previously vaccinated patients.

Dynamic characteristics of a COVID-19 outbreak in Nanjing, Jiangsu province, China

Objectives

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) lineage B.1.617.2 (also named the Delta variant) was declared as a variant of concern by the World Health Organization (WHO). This study aimed to describe the outbreak that occurred in Nanjing city triggered by the Delta variant through the epidemiological parameters and to understand the evolving epidemiology of the Delta variant.

Methods

We collected the data of all COVID-19 cases during the outbreak from 20 July 2021 to 24 August 2021 and estimated the distribution of serial interval, basic and time-dependent reproduction numbers (R₀ and R_t), and household secondary attack rate (SAR). We also analyzed the cycle threshold (Ct) values of infections.

Results

A total of 235 cases have been confirmed. The mean value of serial interval was estimated to be 4.79 days with the Weibull distribution. The R₀ was 3.73 [95% confidence interval (CI), 2.66-5.15] as estimated by the exponential growth (EG) method. The R_t decreased from 4.36 on 20 July 2021 to below 1 on 1 August 2021 as estimated by the Bayesian approach. We estimated the household SAR as 27.35% (95% CI, 22.04-33.39%), and the median Ct value of open reading frame 1ab (ORF1ab) genes and nucleocapsid protein (N) genes as 25.25 [interquartile range (IQR), 20.53-29.50] and 23.85 (IQR, 18.70-28.70), respectively.

Conclusions

The Delta variant is more aggressive and transmissible than the original virus types, so continuous non-pharmaceutical interventions are still needed.

Late Surges in COVID-19 Cases and Varying Transmission Potential Partially Due to Public Health Policy Changes in 5 Western States, March 10, 2020, to January 10, 2021

OBJECTIVE

This study investigates the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission potential in North Dakota, South Dakota, Montana, Wyoming, and Idaho from March 2020 through January 2021.

METHODS

Time-varying reproduction numbers, R _t , of a 7-d-sliding-window and of non-overlapping-windows between policy changes were estimated using the instantaneous reproduction number method. Linear regression was performed to evaluate if per-capita cumulative case-count varied across counties with different population size or density.

RESULTS

The median 7-d-sliding-window R _t estimates across the studied region varied between 1 and 1.25 during September through November 2020. Between November 13 and 18, R _t was reduced by 14.71% (95% credible interval, CrI, [14.41%, 14.99%]) in North Dakota following a mask mandate; Idaho saw a 1.93% (95% CrI [1.87%, 1.99%]) reduction and Montana saw a 9.63% (95% CrI [9.26%, 9.98%]) reduction following the tightening of restrictions. High-population and high-density counties had higher per-capita cumulative case-count in North Dakota on June 30, August 31, October 31, and December 31, 2020. In Idaho, North Dakota, South Dakota, and Wyoming, there were positive correlations between population size and per-capita weekly incident case-count, adjusted for calendar time and social vulnerability index variables.

CONCLUSIONS

R _t decreased after mask mandate during the region's case-count spike suggested reduction in SARS-CoV-2 transmission.

Forecasting COVID-19 cases by assessing control-intervention effects in Republic of Korea: A statistical modeling approach

The Coronavirus disease of 2019 (COVID-19) is an ongoing public health concern worldwide. COVID-19 infections continue to occur and thus, it is important to assess the effects of various public health measures. This study aims to forecast COVID-19 cases by geographical area in Korea, based on the effects of different control-intervention intensities (CII). Methods involved estimating the effective reproduction number (Rt) by Korean geographical area using the SEIHR model, and the instantaneous reproduction number using statistical model, comparing the epidemic curves and high-, intermediate-, and low-intensity control interventions. Here, short-term four-week forecasts by geographical area were conducted. The mean of delayed instantaneous reproduction number was estimated at 1.36, 1.03, and 0.93 for the low-, intermediate-, and high-intensity control interventions, respectively, in the capital area of Korea from July 16, 2020, to March 4, 2021. The COVID-19 cases were forecasted with an accuracy rate of 11.28%, 13.62%, and 20.19% MAPE in Korea, including both the capital and non-capital areas. High-intensity control measures significantly reduced the reproduction number to be less than one. The proposed model forecasted COVID-19 transmission dynamics with good accuracy and interpretability. High-intensity control intervention, active case detection, and isolation efforts should be maintained to control the pandemic.

Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm

Well parameterized epidemiological models including accurate representation of contacts are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here, we fit age-stratified models, including re-estimation of relative contact rates between age classes, to public data describing the 2020-2021 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing approximate Bayesian computation (ABC) methodology with model-based proposals (MBPs) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalization rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrization of dynamic transmission models that can inform data-driven public health policy and interventions. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The impact of COVID-19 on a Malaria dominated region: A mathematical analysis and simulations

One of society’s major concerns that have continued for a long time is infectious diseases. It has been demonstrated that certain disease infections, in particular multiple disease infections, make it more challenging to identify and treat infected individuals, thus deteriorating human health. As a result, a COVID-19-malaria co-infection model is developed and analyzed to study the effects of threshold quantities and co-infection transmission rate on the two diseases’ synergistic relationship. This allowed us to better understand the co-dynamics of the two diseases in the population. The existence and stability of the disease-free equilibrium of each single infection were first investigated by using their respective reproduction number. The COVID-19 and malaria-free equilibrium are locally asymptotically stable when the individual threshold quantities RC and RM are below unity. Additionally, the occurrence of the malaria prevalent equilibrium is examined, and the requirements for the backward bifurcation’s existence are provided. Sensitivity analysis reveals that the two main parameters that influence the spread of COVID-19 infection are the disease transmission rate (βc) and the fraction of the exposed individuals becoming symptomatic (ψ), while malaria transmission is influenced by the abundance of vector population, which is driven by recruitment rate (πv) with an increase in the effective biting rate (b), probability of malaria transmission per mosquito bite (βm), and probability of malaria transmission from infected humans to vectors (βv). The findings from the numerical simulation of the model show that COVID-19 will predominate in the populace and drives malaria to extinction when RM<1<RC, whereas malaria will dominate in the population and drives COVID-19 into extinction when RC<1<RM. At the disease’s endemic equilibrium, the two diseases will coexist with the one with the highest reproduction number predominating but not eradicating the other. It was demonstrated in particular that COVID-19 will invade a population where malaria is endemic if the invasion reproduction number exceeds unity. The findings also demonstrate that when the two diseases are at endemic equilibrium, the prevalence of co-infection increases COVID-19’s burden on the population while decreasing malaria incidence.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Early Estimates of Monkeypox Incubation Period, Generation Time, and Reproduction Number, Italy, May-June 2022

We analyzed the first 255 PCR-confirmed cases of monkeypox in Italy in 2022. Preliminary estimates indicate mean incubation period of 9.1 (95% CI 6.5-10.9) days, mean generation time of 12.5 (95% CI 7.5-17.3) days, and reproduction number among men who have sex with men of 2.43 (95% CI 1.82-3.26).

Preventive control strategy on second wave of Covid-19 pandemic model incorporating lock-down effect

This study presents an optimal control strategy through a mathematical model of the Covid-19 outbreak without lock-down. The pandemic model analyses the lock-down effect without control strategy based on the current scenario of second wave data to control the rapid spread of the virus. The pandemic model has been discussed with respect to the basic reproduction number and stability analysis of disease-free and endemic equilibrium. A new optimal control problem with treatment is framed to minimize the vulnerable situation of the second wave. This system is applied to study the effects of vaccines and treatment controls. Numerical solutions and the graphical presentation of the results predict the fate of India’s second wave situation on account of the control strategy. Lastly, a comparative study with control and without control has been analysed for the exposed phase, infective phase, and recovery phase to understand the effectiveness of the controls. This model is used to estimate the total number of infected and active cases, deaths, and recoveries in order to control the disease using this system and studying the effects of vaccines and treatment controls.

The Role of Staff in Transmission of SARS-CoV-2 in Long-term Care Facilities

BACKGROUND

US long-term care facilities (LTCFs) have experienced a disproportionate burden of COVID-19 morbidity and mortality.

METHODS

We examined SARS-CoV-2 transmission among residents and staff in 60 LTCFs in Fulton County, Georgia, from March 2020 to September 2021. Using the Wallinga-Teunis method to estimate the time-varying reproduction number, R(t), and linear-mixed regression models, we examined associations between case characteristics and R(t).

RESULTS

Case counts, outbreak size and duration, and R(t) declined rapidly and remained low after vaccines were first distributed to LTCFs in December 2020, despite increases in community incidence in summer 2021. Staff cases were more infectious than resident cases (average individual reproduction number, R i = 0.6 [95% confidence intervals [CI] = 0.4, 0.7] and 0.1 [95% CI = 0.1, 0.2], respectively). Unvaccinated resident cases were more infectious than vaccinated resident cases (R i = 0.5 [95% CI = 0.4, 0.6] and 0.2 [95% CI = 0.0, 0.8], respectively), but estimates were imprecise.

CONCLUSIONS

COVID-19 vaccines slowed transmission and contributed to reduced caseload in LTCFs. However, due to data limitations, we were unable to determine whether breakthrough vaccinated cases were less infectious than unvaccinated cases. Staff cases were six times more infectious than resident cases, consistent with the hypothesis that staff were the primary drivers of SARS-CoV-2 transmission in LTCFs.

Fitting to the UK COVID-19 outbreak, short-term forecasts and estimating the reproductive number

The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provide a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the effective reproduction number, [Formula: see text], has taken on special significance in terms of the general understanding of whether the epidemic is under control ([Formula: see text]). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, focusing on the dynamics of the first wave (March-June 2020), we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the time course of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence.

SARS-CoV-2 Transmission Potential and Policy Changes in South Carolina, February 2020 - January 2021

INTRODUCTION

We aimed to examine how public health policies influenced the dynamics of coronavirus disease 2019 (COVID-19) time-varying reproductive number (R _t ) in South Carolina from February 26, 2020, to January 1, 2021.

METHODS

COVID-19 case series (March 6, 2020, to January 10, 2021) were shifted by 9 d to approximate the infection date. We analyzed the effects of state and county policies on R _t using EpiEstim. We performed linear regression to evaluate if per-capita cumulative case count varies across counties with different population size.

RESULTS

R _t shifted from 2-3 in March to <1 during April and May. R _t rose over the summer and stayed between 1.4 and 0.7. The introduction of statewide mask mandates was associated with a decline in R _t (-15.3%; 95% CrI, -13.6%, -16.8%), and school re-opening, an increase by 12.3% (95% CrI, 10.1%, 14.4%). Less densely populated counties had higher attack rates (P < 0.0001).

CONCLUSIONS

The R _t dynamics over time indicated that public health interventions substantially slowed COVID-19 transmission in South Carolina, while their relaxation may have promoted further transmission. Policies encouraging people to stay home, such as closing nonessential businesses, were associated with R _t reduction, while policies that encouraged more movement, such as re-opening schools, were associated with R _t increase.

Mathematical Analysis of a COVID-19 Epidemic Model by Using Data Driven Epidemiological Parameters of Diseases Spread in India

This paper attempts to describe the outbreak of Severe Acute Respiratory Syndrome Coronavirus 2 (COVID-19) via an epidemic model. This virus has dissimilar effects in different countries. The number of new active coronavirus cases is increasing gradually across the globe. India is now in the second stage of COVID-19 spreading, it will be an epidemic very quickly if proper protection is not undertaken based on the database of the transmission of the disease. This paper is using the current data of COVID-19 for the mathematical modeling and its dynamical analysis. We bring in a new representation to appraise and manage the outbreak of infectious disease COVID-19 through SEQIR pandemic model, which is based on the supposition that the infected but undetected by testing individuals are send to quarantine during the incubation period. During the incubation period if any individual be infected by COVID-19, then that confirmed infected individuals are isolated and the necessary treatments are arranged so that they cannot taint the other residents in the community. Dynamics of the SEQIR model is presented by basic reproduction number R ₀ and the comprehensive stability analysis. Numerical results are depicted through apt graphical appearances using the data of five states and India.

Mathematical Analysis of a COVID-19 Epidemic Model by Using Data Driven Epidemiological Parameters of Diseases Spread in India

This paper attempts to describe the outbreak of Severe Acute Respiratory Syndrome Coronavirus 2 (COVID-19) via an epidemic model. This virus has dissimilar effects in different countries. The number of new active coronavirus cases is increasing gradually across the globe. India is now in the second stage of COVID-19 spreading, it will be an epidemic very quickly if proper protection is not undertaken based on the database of the transmission of the disease. This paper is using the current data of COVID-19 for the mathematical modeling and its dynamical analysis. We bring in a new representation to appraise and manage the outbreak of infectious disease COVID-19 through SEQIR pandemic model, which is based on the supposition that the infected but undetected by testing individuals are send to quarantine during the incubation period. During the incubation period if any individual be infected by COVID-19, then that confirmed infected individuals are isolated and the necessary treatments are arranged so that they cannot taint the other residents in the community. Dynamics of the SEQIR model is presented by basic reproduction number R 0 and the comprehensive stability analysis. Numerical results are depicted through apt graphical appearances using the data of five states and India.

Extending the susceptible-exposed-infected-removed (SEIR) model to handle the false negative rate and symptom-based administration of COVID-19 diagnostic tests: SEIR-fansy

False negative rates of severe acute respiratory coronavirus 2 diagnostic tests, together with selection bias due to prioritized testing can result in inaccurate modeling of COVID-19 transmission dynamics based on reported "case" counts. We propose an extension of the widely used Susceptible-Exposed-Infected-Removed (SEIR) model that accounts for misclassification error and selection bias, and derive an analytic expression for the basic reproduction number R 0 as a function of false negative rates of the diagnostic tests and selection probabilities for getting tested. Analyzing data from the first two waves of the pandemic in India, we show that correcting for misclassification and selection leads to more accurate prediction in a test sample. We provide estimates of undetected infections and deaths between April 1, 2020 and August 31, 2021. At the end of the first wave in India, the estimated under-reporting factor for cases was at 11.1 (95% CI: 10.7,11.5) and for deaths at 3.58 (95% CI: 3.5,3.66) as of February 1, 2021, while they change to 19.2 (95% CI: 17.9, 19.9) and 4.55 (95% CI: 4.32, 4.68) as of July 1, 2021. Equivalently, 9.0% (95% CI: 8.7%, 9.3%) and 5.2% (95% CI: 5.0%, 5.6%) of total estimated infections were reported on these two dates, while 27.9% (95% CI: 27.3%, 28.6%) and 22% (95% CI: 21.4%, 23.1%) of estimated total deaths were reported. Extensive simulation studies demonstrate the effect of misclassification and selection on estimation of R 0 and prediction of future infections. A R-package SEIRfansy is developed for broader dissemination.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

Modelling preventive measures and their effect on generation times in emerging epidemics

We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.

Are epidemic growth rates more informative than reproduction numbers?

statistics, often derived from simplified models of epidemic spread, inform public health policy in real time. The instantaneous reproduction number,R t , is predominant among these statistics, measuring the average ability of an infection to multiply. However,R t encodes no temporal information and is sensitive to modelling assumptions. Consequently, some have proposed the epidemic growth rate,r t , that is, the rate of change of the log-transformed case incidence, as a more temporally meaningful and model-agnostic policy guide. We examine this assertion, identifying if and when estimates ofr t are more informative than those ofR t . We assess their relative strengths both for learning about pathogen transmission mechanisms and for guiding public health interventions in real time.

Reproduction Number of the Omicron Variant Triples That of the Delta Variant

COVID-19 remains a persistent threat, especially with the predominant Omicron variant emerging in early 2022, presenting with high transmissibility, immune escape, and waning. There is a need to rapidly ramp up global vaccine coverage while enhancing public health and social measures. Timely and reliable estimation of the reproduction number throughout a pandemic is critical for assessing the impact of mitigation efforts and the potential need to adjust for control measures. We conducted a systematic review on the reproduction numbers of the Omicron variant and gave the pooled estimates. We identified six studies by searching PubMed, Embase, Web of Science, and Google Scholar for articles published between 1 January 2020 and 6 March 2022. We estimate that the effective reproduction number ranges from 2.43 to 5.11, with a pooled estimate of 4.20 (95% CI: 2.05, 6.35). The Omicron variant has an effective reproduction number which is triple (2.71 (95% CI: 1.86, 3.56)) that of the Delta variant.

Time-discrete SIR model for COVID-19 in Fiji

Using the data provided by Fiji's ministry of health and medical services, we apply an implicit time-discrete SIR (susceptible people–infectious people–removed people) model that tracks the transmission and recovering rate at time, t to predict the trend of the coronavirus disease 2019 (COVID-19) pandemic in Fiji. The model implied time-varying transmission and recovery rates were calculated from 4 May 2021 to 9 October 2021. The estimator functions for these rates were determined, and a short-term (30 days) forecast was done. The model was validated with observed values of the active and recovered cases from 11 October 2021 to 9 December 2021. Statistical results reveal a good fit of profiles between model simulated and the reported COVID-19 data. The gradual decrease of the time-varying basic reproduction number with values below one towards the end of the study period suggest the government's success in controlling the epidemic. The mean reproduction number for the second wave of COVID-19 in Fiji was estimated as 2.7818. The results from this study can be used by researchers, the Fijian government, and the relevant health policy makers in making informed decisions should a third COVID-19 wave occur.

The required size of cluster randomized trials of nonpharmaceutical interventions in epidemic settings

To control the SARS‐CoV‐2 pandemic and future pathogen outbreaks requires an understanding of which nonpharmaceutical interventions are effective at reducing transmission. Observational studies, however, are subject to biases that could erroneously suggest an impact on transmission, even when there is no true effect. Cluster randomized trials permit valid hypothesis tests of the effect of interventions on community transmission. While such trials could be completed in a relatively short period of time, they might require large sample sizes to achieve adequate power. However, the sample sizes required for such tests in outbreak settings are largely undeveloped, leaving unanswered the question of whether these designs are practical. We develop approximate sample size formulae and simulation‐based sample size methods for cluster randomized trials in infectious disease outbreaks. We highlight key relationships between characteristics of transmission and the enrolled communities and the required sample sizes, describe settings where trials powered to detect a meaningful true effect size may be feasible, and provide recommendations for investigators in planning such trials. The approximate formulae and simulation banks may be used by investigators to quickly assess the feasibility of a trial, followed by more detailed methods to more precisely size the trial. For example, we show that community‐scale trials requiring 220 clusters with 100 tested individuals per cluster are powered to identify interventions that reduce transmission by 40% in one generation interval, using parameters identified for SARS‐CoV‐2 transmission. For more modest treatment effects, or when transmission is extremely overdispersed, however, much larger sample sizes are required.

Estimation of Serial Interval and Reproduction Number to Quantify the Transmissibility of SARS-CoV-2 Omicron Variant in South Korea

The omicron variant (B.1.1.529) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was the predominant variant in South Korea from late January 2022. In this study, we aimed to report the early estimates of the serial interval distribution and reproduction number to quantify the transmissibility of the omicron variant in South Korea between 25 November 2021 and 31 December 2021. We analyzed 427 local omicron cases and reconstructed 73 transmission pairs. We used a maximum likelihood estimation to assess serial interval distribution from transmission pair data and reproduction numbers from 74 local cases in the first local outbreak. We estimated that the mean serial interval was 3.78 (standard deviation, 0.76) days, which was significantly shorter in child infectors (3.0 days) compared to adult infectors (5.0 days) (p < 0.01). We estimated the mean reproduction number was 1.72 (95% CrI, 1.60−1.85) for the omicron variant during the first local outbreak. Strict adherence to public health measures, particularly in children, should be in place to reduce the transmission risk of the highly transmissible omicron variant in the community.