Assessing epidemic curves for evidence of superspreading.

The expected number of secondary infections arising from each index case, referred to as the reproduction or R number, is a vital summary statistic for understanding and managing epidemic diseases. There are many methods for estimating R ; however, few explicitly model heterogeneous disease reproduction, which gives rise to superspreading within the population. We propose a parsimonious discrete-time branching process model for epidemic curves that incorporates heterogeneous individual reproduction numbers. Our Bayesian approach to inference illustrates that this heterogeneity results in less certainty on estimates of the time-varying cohort reproduction number R t . We apply these methods to a COVID-19 epidemic curve for the Republic of Ireland and find support for heterogeneous disease reproduction. Our analysis allows us to estimate the expected proportion of secondary infections attributable to the most infectious proportion of the population. For example, we estimate that the 20% most infectious index cases account for approximately 75%-98% of the expected secondary infections with 95% posterior probability. In addition, we highlight that heterogeneity is a vital consideration when estimating R t .

Estimation of reproduction numbers in real time: Conceptual and statistical challenges.

The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers

Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries. IEEE

Modelling presymptomatic infectiousness in COVID-19

This paper considers SEPIR, an extension of the well-known SEIR continuous simulation compartment model. Both models can be fitted to real data as they include parameters that can be estimated from the data. SEPIR deploys an additional presymptomatic infectious compartment, not modelled in SEIR but known to exist in COVID-19. This stage can also be fitted to data. We focus on how to fit SEPIR to a first wave of COVID. Both SEIR and SEPIR and the existing SEIR models assume a homogeneous mixing population with parameters fixed. Moreover, neither includes dynamically varying control strategies deployed against the virus. If either model is to represent more than just a single wave of the epidemic, then the parameters of the model would have to be time dependent. In view of this, we also show how reproduction numbers can be calculated to investigate the long-term overall outcome of an epidemic. © 2023 The Operational Research Society.

The Prediction of COVID-19 Pandemic Situation in Indonesia Using SVR and SIR Algorithm

The COVID-19 epidemic, which initially surfaced at the end of 2019, has since expanded to every corner of the globe and has profoundly impacted all facets of human existence. This case started to emerge in Indonesia at the end of February 2020, and until this point, there has been a spike in new patients. Researchers have run several models and projections for COVID-19 cases in Indonesia, but the results are not yet entirely reliable. Predictions produced at the national level must take into account these variations in patterns because this is likely related to the distinct patterns in each region. In this study, the prediction process will be conducted for cases of COVID-19 by using the SVR algorithm and mathematical models to predict reproduction numbers. SVR analysis to overcome the problem of nonlinearity of data in model formation. The modeling is done based on the SIR model, whose parameters are estimated based on the data. Testing result by using 3 kernels is different on each test, prediction of data cases and the level of mistake room are by using Kernel ' RBF ' with a value of C = 1E3, and gamma = 0.1 with the value of MAPE and MSE respectively are 4.5% and 4.2. © 2022 IEEE.

Leakage in air handling units, the effects on the transmission of airborne infections

The possibility of unfavorable leakages, especially with infectious diseases, in heat recovery systems in air handling units (AHU) is an essential issue. Typical configurations of AHU are analyzed in this aspect, based on their pressure distribution. It is shown that analyzing only for the design conditions is insufficient and that the changing pressure drops of the air filters due to their nonuniform soiling should be taken into account. The novelty of this paper is in proposed method of considering these leaks in the Wells-Riley model, widely used in the literature for airborne transmission of infectious diseases, including the leakage correction factor fhrleak (outdoor fresh air correction factor) based on EATR (exhaust air transfer ratio). Using the proposed method, for typical rooms, on the example of the SARS-CoV-2 virus and its Delta and Omicron variants, it is shown that considering leaks in heat recovery systems in AHU increases the probability of pathogen transmission. The highest increase in the absolute value of the probability of infection is observed in the single office scenario (4.1%) and in the auditorium with a sick speaker scenario (2.7%). The highest increase in reproduction number is observed in the auditorium with a sick speaker scenario (2.69). Such significant changes in reproduction number, including its change from R < 1.0 to R > 1.0 (auditorium with sick speaker for Delta variant of the virus), are crucial from the point of view of considering event scenarios;they slow down or accelerate the pandemic. © 2023 Elsevier Ltd

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 (COVID-19) with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number (R0) and local stability of the disease-free equilibrium (DFE) in terms of R0 are investigated. Also, the uniqueness and existence of the solution are studied. Numerical simulations are performed by using some real values of parameters. Furthermore, the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also considered. Also, an investigation of the effect of public awareness on transmission dynamics is one of our aim in this work. Finally, a prediction about the evolution of COVID-19 in 1000 days is given. For the qualitative theory of the existence of a solution, we use some tools of nonlinear analysis, including Lipschitz criteria. Also, for the numerical interpretation, we use the Adams-Moulton-Bashforth procedure. All the numerical results are presented graphically. © 2023 Tech Science Press. All rights reserved.

A Sir Model for Viral Growth of Coronavirus: A System Dynamics Approach

In this paper, a system dynamics model depicts the viral growth of COVID-19 at an exponential rate. The outbreak of Corona virus was started from the Feb 26, 2020 when the first case was reported in Pakistan. Local bodies and law enforcing agencies had taken initial preventive measures to restrict the COVID-19 to a particular locality but all in vain. The infected people were increasing every day rising the stocks of recoveries and deaths. Numbers of infected people were alarming and a need was felt to develop the model to calculate the existing reproduction number and transmission rate and highlight its varied values in coming days. People-oriented measures and government-based policies must be explored to fight against this deadly disease. This paper aims the development of epidemic model using the system dynamic framework on simulation software STELLA. The objective of the research is to experiment with the model to replicate the progression of the communicable disease and probe the multiple combinations of the people-based and government-based measures to reduce its spread. The containment measures are of two types;people-based measures and government-based measures and both directly affect the reproduction number and infection growth fraction for mitigating the spread of deadly coronavirus. Combined efforts of public and government can combat this pandemic. Reduced degree of reproduction number and infection growth fraction are the key metrics to judge and evaluate the effectiveness of containment measures. This research points to more holistic combination of public and government-oriented measures that play the vital role to flatten the curve and reduce its spread affecting the reproduction number. Simulation results have been traced to replicate the real-life settings against four combinations of containment measures in tabular form and graphical form. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Modelling the Delta Covid-19 Wave in Mumbai

Using agent based simulator (ABS), we attempt to explain the infectiousness of the delta variant through scenario analysis to best match the observed fatality data in Mumbai, where the variant initially spread. Our somewhat prescient conclusion, based on analysis conducted in March-April 2021 was that the new variant was 2-2.5 times more infectious than the original Wuhan variant. We also observed then that certain performance measures such as timings of peaks and troughs were quite robust to the variations in model parameters and hence can be reliably projected even in presence of model uncertainties. Furthermore, we introduce enhancements to help model variants, vaccinations, basic and effective reproduction number in ABS. Our analysis suggests an interesting observation - although slums have around half of Mumbai population and are much more dense and have higher prevalence, the effective reproduction number between slums and non-slums equalises early on and largely moves together thereafter. © 2022 IEEE.

Predicting COVID-19 Pandemic Endpoint in Some Sub-Saharan African and European Countries

In this study, a novel modified SIR model is presented with two control measures to predict the endpoint of COVID-19, in top three sub-Saharan African countries (South Africa, Ethiopia, and Kenya) including Ghana and top four European countries (France, Germany, UK, and Italy). The reproduction number's sensitivity indices with regard to the model parameters were explicitly derived and then numerically evaluated. Numerical simulations of the suggested optimal control schemes in general showed a continuous result of decline at different anticipated extinction timelines. Another interesting observation was that in the simulation of sub-Saharan African dynamics, it was observed that the use of personal protective equipment was more effective than the use of vaccination, whereas in Europe, the use of vaccination was more effective than personal protective equipment. From the simulations, the conclusion is that COVID-19 will end before the 3rd year in Ghana, before the 6th year in Kenya, and before the 9th year in both Ethiopia and South Africa. © 2023 Saviour Worlanyo Akuamoah et al.

Infectivity of Omicron BA.5 Comparison with Original Strain and Other Mutated Strain of SARS-CoV-2 in Japan

Background: Earlier studies have indicated the BA.5 sublineage of Omicron variant strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) as more infective than BA.2. Object: This study estimated BA.5 infectivity while controlling other factors possibly affecting BA.5 infectivity including vaccine effectiveness, waning effectiveness, other mutated strains, Olympic Games, and countermeasures. Method: The effective reproduction number R(t) was regressed on shares of BA.5 and vaccine coverage, vaccine coverage with some delay, temperature, humid-ity, mobility, shares of other mutated strains, counter-measures including the Go to Travel Campaign, and the Olympic Games and associated countermeasures. The study period was February 2020–July 22, 2022, using data available on August 12, 2022. Results: A 120 day lag was assumed to assess waning. Mobil-ity, some states of emergency, vaccine coverage and those with lag, and the Delta and Omicron BA.2 pro-portions were found to be significant. The omicron BA.1 proportion was significant, but with an unex-pected sign. The estimated coefficient of BA.5 was negative but not significant. The Go to Travel Campaign was significantly negative, indicating reduced infectiv-ity. The Olympic Games were negative but not sig-nificant, indicating that they did not raise infectivity. Discussion: The obtained estimated results show that BA.5 did not have higher infectivity than the original strain. It was lower than either Delta or Omicron BA.2 variant strains. That finding might be inconsis-tent with results obtained from earlier studies. This study controlled several factors potentially affecting R(t), though the earlier studies did not. Therefore, results from this study might be more reliable than those of earlier studies. © Fuji Technology Press Ltd.

A mathematical model reveals the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant.

An SVEIR SARS-CoV-2 Omicron variant model is proposed to provide some insights to coordinate non-pharmaceutical interventions (NPIs) and vaccination. Mathematically, we define the basic reproduction number R 0 and the effective reproduction number R e to measure the infection potential of Omicron variant and formulate an optimal disease control strategy. Our inversion results imply that the sick period of Omicron variant in the United States is longer than that of Delta variant in India. The decrease in the infectious period of the infection with infectiousness implies that the risk of hospitalization is reduced; but the increasing period of the infection with non-infectiousness signifies that Omicron variant lengthens the period of nucleic acid test being negative. Optimistically, Omicron's death rate is only a quarter of Delta's. Moreover, we forecast that the cumulative cases will exceed 100 million in the United States on February 28, 2022, and the daily confirmed cases will reach a peak on February 2, 2022. The results of parameters sensitivity analysis imply that NPIs are helpful to reduce the number of confirmed cases. In particular, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relationships of the effective reproduction number R e , the vaccination rate and the efficacy of vaccine, we find that it is impossible to achieve the herd immunity without NPIs while the efficiency of vaccine is lower than 88.7 % . Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficacy of vaccine. Finally, we present that the disease-induced mortality rate demonstrates the periodic oscillation and an almost periodic function is deduced to match the curve. A discussion completes the paper.

Impact of COVID-19 asymptomatic individuals on effective regenerative math by multi-agent simulation based on the SEAIR model

Various simulations are currently being conducted in response to the spread of the novel coronavirus infection. However, few multi-agent simulations have been conducted using a model that considers asymptomatic persons, who are one of the factors contributing to the spread of infection. In this study, we extended the SEAIR model, which considers asymptomatic persons, to multi-agent simulations to investigate the effect of the proportion of asymptomatic persons on the effective number of reproductions. The results indicate that asymptomatic persons may influence the number of positive groups at the peak of the spread of infection and the convergence period. © 2022 IEEE.

Spatiotemporal heterogeneities of the associations between human mobility and close contacts with COVID-19 infections in the United States

It has been well-established that human mobility has an inseparable relationship with COVID-19 infections. As the COVID-19 pandemic progresses, our knowledge on how human behaviors including mobility and close contact associates with the pandemic also need to stay updated. In this paper, we examine the relationship of the effective reproduction number (Rt) of COVID-19 daily cases with the two indices that provide mobility insights: Mobility Index (CMI) and Contact Index (CCI). Both relationships are evaluated through Maximal Information Coefficient (MIC). Using the Bayesian Change Point Detection and the KShape clustering algorithms, we found significant temporal and spatial heterogeneities among the relationship between two indices and the daily confirmed COVID-19 cases. Although CMI has demonstrated high correlation with COVID-19 cases in 2020, CCI became much more correlated with COVID-19 cases than CMI in 2021. During the first wave in 2020, it is also shown that mobility has a high impact on states outside of Farwest and Southeast than those states within that region. © 2022 ACM.

Does COVID-19 Behave as Lightning Strike?

Early stages of an epidemic are characterized by exponential growth in the number of infected cases, corresponding to the effective reproduction number greater than 1. After deliberate interventions in the disease transmission are introduced, the effective reproduction number should drop below 1. The number of active infections should follow the downward trend conditioned by the stringency of the measures and drop exponentially. The growth phase is in general of shorter duration than the decay phase. This asymmetry imposes itself as an aggravating factor onto common mathematical models used to capture the epidemic dynamics. To overcome aforementioned issue, in this paper, we compare the functional form of the epidemic dynamics with the analytical expression often found in the lightning research and standardization. Computational examples are given for different countries that kept track of the number of daily positive cases, recovered cases and deaths during the period of the first outbreak of Coronavirus disease 2019 (COVID-19). © 2022 University of Split, FESB.

Estimating Effective Reproduction Number for SIR Compartmental Model: A Stochastic Evolutionary Approach

Compartmental pandemic models have become a significant tool in the battle against disease outbreaks. Despite this, pandemic models sometimes require extensive modification to accurately reflect the actual epidemic condition. The Susceptible-Infectious-Removed (SIR) model, in particular, contains two primary parameters: the infectious rate parameter ß and the removal rate parameter y, in addition to additional unknowns such as the initial infectious population. Adding to the complexity, there is an obvious challenge to track the evolution of these parameters, especially ß and y, over time which leads to the estimation of the reproduction number for the particular time window, RT. This reproduction number may provide better understanding on the effectiveness of isolation or control measures. The changing RT values (evolving over time window) will lead to even more possible parameter scenarios. Given the present Coronavirus Disease 2019 (COVID-19) pandemic, a stochastic optimization strategy is proposed to fit the model on the basis of parameter changes over time. Solutions are encoded to reflect the changing parameters of ßT and γt, allowing the changing RT to be estimated. In our approach, an Adaptive Differential Evolution (ADE) and Particle Swarm Optimization (PSO) are used to fit the curves into previously recorded data. ADE eliminates the need to tune the parameters of the Differential Evolution (DE) to balance the exploitation and exploration in the solution space. Results show that the proposed optimized model can generally fit the curves well albeit high variance in the solutions. © 2020 Tsinghua University Press.

Teaching undergraduate physical chemistry lab with kinetic analysis of COVID-19 in the United States.

A physical chemistry lab for undergraduate students described in this report is about applying kinetic models to analyze the spread of COVID-19 in the United States and obtain the reproduction numbers. The susceptible-infectious-recovery (SIR) model and the SIR-vaccinated (SIRV) model are explained to the students and are used to analyze the COVID-19 spread data from U.S. Centers for Disease Control and Prevention (CDC). The basic reproduction number R 0 and the real-time reproduction number R t of COVID-19 are extracted by fitting the data with the models, which explains the spreading kinetics and provides a prediction of the spreading trend in a given state. The procedure outlined here shows the differences between the SIR model and the SIRV model. The SIRV model considers the effect of vaccination which helps explain the later stages of the ongoing pandemic. The predictive power of the models is also shown giving the students some certainty in the predictions they made for the following months.

Estimation of Reproduction Number for Covid-19 with Statistical Correction of Notifications Delay

The pandemic of Covid-19 began in Brazil in February 2020. To evaluate the evolution of pandemics some metrics can be estimated, such as the reproduction number, Rt, and the basic reproduction number, R0. Due to the delay in the notifications, these estimates may present a bias. Taking the reported data, besides a sample of individuals who reported the day of symptoms onset, it is possible to estimate delay probabilities and to perform a deconvolution to correct the notifications' delay. In this work, it was performed a corrected estimate of Rt. This estimate is done based on the curve of notifications corrected through deconvolution. The approach is applied in three country cities and in the capital of Minas Gerais state. The behavior of Rt concerning the Minas Consciente program was evaluated. It was observed that the corrected Rt was more suitable to measure the effect of the program when compared to the raw Rt. When it was determined a more rigid mobility and activities regime by the program, it was observed a decrease in the median of the variation of the Rt of the cities studied. © 2003-2012 IEEE.

The minimal COVID-19 vaccination coverage and efficacy to compensate for a potential increase of transmission contacts, and increased transmission probability of the emerging strains.

BACKGROUND: Mass immunization is a potentially effective approach to finally control the local outbreak and global spread of the COVID-19 pandemic. However, it can also lead to undesirable outcomes if mass vaccination results in increased transmission of effective contacts and relaxation of other public health interventions due to the perceived immunity from the vaccine. METHODS: We designed a mathematical model of COVID-19 transmission dynamics that takes into consideration the epidemiological status, public health intervention status (quarantined/isolated), immunity status of the population, and strain variations. Comparing the control reproduction numbers and the final epidemic sizes (attack rate) in the cases with and without vaccination, we quantified some key factors determining when vaccination in the population is beneficial for preventing and controlling future outbreaks. RESULTS: Our analyses predicted that there is a critical (minimal) vaccine efficacy rate (or a critical quarantine rate) below which the control reproduction number with vaccination is higher than that without vaccination, and the final attack rate in the population is also higher with the vaccination. We also predicted the worst case scenario occurs when a high vaccine coverage rate is achieved for a vaccine with a lower efficacy rate and when the vaccines increase the transmission efficient contacts. CONCLUSIONS: The analyses show that an immunization program with a vaccine efficacy rate below the predicted critical values will not be as effective as simply investing in the contact tracing/quarantine/isolation implementation. We reached similar conclusions by considering the final epidemic size (or attack rates). This research then highlights the importance of monitoring the impact on transmissibility and vaccine efficacy of emerging strains.

Matching theory and evidence on Covid-19 using a stochastic network SIR model.

This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate the identification and estimation of the transmission rates. The paper then proposes a method that jointly estimates the transmission rate and the magnitude of under-reporting of infected cases. Empirical evidence on six European countries matches the simulated outcomes once the under-reporting of infected cases is addressed. It is estimated that the number of actual cases could be between 4 to 10 times higher than the reported numbers in October 2020 and declined to 2 to 3 times in April 2021. The calibrated models are used in the counterfactual analyses of the impact of social distancing and vaccination on the epidemic evolution and the timing of early interventions in the United Kingdom and Germany.