Estimating effective reproduction number revisited

Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks.In this study,we improve the estimation of the effective reproduction number through two main approaches.First,we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework.We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme.By doing so,we enhance the accuracy of approximating the underlying epidemic process compared to previous methods,even when the counting period is similar to the mean generation time of an infectious disease.Second,we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion.Specifically,given that observed incidence counts follow a negative binomial distribution,the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution.With this formulation,we establish posterior uncertainty bounds for the effective reproduction number.Finally,we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.

Mathematical Modelling of the COVID-19 Epidemic in Northern Ireland in 2020

In this study, we investigate the dynamics of the COVID-19 epidemic in Northern Ireland from 1st March 2020 up to 25th December 2020, using several copies of a Susceptible-Exposed-Infectious-Recovered (SEIR) compartmental model, and compare it to a detailed publicly available dataset. We split the data into 10 time intervals and fit the models on the consecutive intervals to the cumulative number of confirmed positive cases on each interval. Using the fitted parameter estimates, we also provide estimates of the reproduction number. We also discuss the limitations and possible extensions of the employed model.

Estimating the Level of Asymptomatic COVID-19 Infections in Northern Ireland in 2020

The identification and understanding of COVID-19 potential routes of transmission are fundamental to informing policies and strategies to successfully control the outbreak. Various studies highlighted asymptomatic infections as one of the silent drivers of the epidemic. An accurate estimation of the asymptomatic cases and the understanding of their contribution to the spread of the disease could enhance the effectiveness of current control strategies, mainly based on the symptom onset, to curb transmission. We investigate the dynamics of the COVID-19 epidemic in Northern Ireland during the period 1st March 25th to December 2020 to estimate the proportion of the asymptomatic infections in the country. We extended our previous model to include the stage of the asymptomatic infection, and we implement the corresponding deterministic model using a publicly available dataset. We partition the data into 11 sets over the period of study and fit the model parameters on the consecutive intervals using the cumulative number of confirmed positive cases for each interval. Moreover, we assess numerically the impacts of uncertainty in testing and we provide estimates of the reproduction numbers using the fitted parameters. We found that the proportion of asymptomatically infectious subpopulations, in Northern Ireland during the period of study, ranged between 5% and 25% of exposed individuals. Also, the estimate of the basic reproduction number, R0, is 3.3089. The lower and upper estimates for herd immunity are (0.6181, 0.7243) suggesting that around 70% of the population of Northern Ireland should acquire immunity via infection or vaccination, which is in line with estimates reported in other studies.

The Method for Optimum Estimation of COVID-19 Variant Type Virus Infection Status Analysis by the Multivariate Analysis Considering the Environmental Variability Impact in Japan

Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. Since ERN in the Sequential SIR model fluctuates in multiple dimensions due to changes in the surrounding environment, it is difficult to set the appropriate accuracy of the uncertainty region of the estimated data. The challenge in this study is to build a mathematical model of infectious disease according to the characteristics and data characteristics of the infectious disease and select an appropriate estimation method. Highly accurate quantitative research that analyzes the validity of “how infectious diseases prevail” from an academic point of view is the key to prediction and estimation in appropriate infection situation analysis. In this study, we adopted a statistical multivariate analysis method (T method) that enables evaluation and prediction of important factors related to ERN estimation and analysis of phenomena that change in real time (time series analysis). It was clarified that it is possible to estimate with higher accuracy by applying the T method to the estimated value of ERN by the current SIR mathematical model.

Estimating the instantaneous reproduction number(R_(t))by using particle filter

Background:Monitoring the transmission of coronavirus disease 2019(COVID-19)requires accurate estimation of the effective reproduction number(Rt).However,existing methods for calculating Rt may yield biased estimates if important real-world factors,such as delays in confirmation,pre-symptomatic transmissions,or imperfect data observation,are not considered.Method:To include real-world factors,we expanded the susceptible-exposed-infectiousrecovered(SEIR)model by incorporating pre-symptomatic(P)and asymptomatic(A)states,creating the SEPIAR model.By utilizing both stochastic and deterministic versions of the model,and incorporating predetermined time series of Rt,we generated simulated datasets that simulate real-world challenges in estimating Rt.We then compared the performance of our proposed particle filtering method for estimating Rt with the existing EpiEstim approach based on renewal equations.Results:The particle filtering method accurately estimated Rt even in the presence of data with delays,pre-symptomatic transmission,and imperfect observation.When evaluating via the root mean square error(RMSE)metric,the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided,and substantially better when Rt exhibited short-term fluctuations and the data was right truncated.Conclusions:The SEPIAR model,in conjunction with the particle filtering method,offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies.This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.

Wastewater Surveillance Provides Spatiotemporal SARS-CoV-2 Infection Dynamics

Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine months daily WWS for severe acute respiratory syndrome coronavirus 2(SARSCoV-2)from 12 wastewater treatment plants(WWTPs),covering approximately 80%of the population,to monitor infection dynamics in Hong Kong,China.We found that the SARS-CoV-2 virus concentration in wastewater was correlated with the daily number of reported cases and reached two pandemic peaks three days earlier during the study period.In addition,two different methods were established to estimate the prevalence/incidence rates from wastewater measurements.The estimated results from wastewater were consistent with findings from two independent citywide clinical surveillance programmes(rapid antigen test(RAT)surveillance and serology surveillance),but higher than the cases number reported by the Centre for Health Protection(CHP)of Hong Kong,China.Moreover,the effective reproductive number(R_(t))was estimated from wastewater measurements to reflect both citywide and regional transmission dynamics.Our findings demonstrate that large-scale intensive WWS from WWTPs provides cost-effective and timely public health information,especially when the clinical surveillance is inadequate and costly.This approach also provides insights into pandemic dynamics at higher spatiotemporal resolutions,facilitating the formulation of effective control policies and targeted resource allocation.

Analysis of intervention effectiveness using early outbreak transmission dynamics to guide future pandemic management and decision-making in Kuwait

Severe Acute Respiratory Syndrome Coronavirus 2(SARS-CoV-2)is a World Health Organization designated pandemic that can result in severe symptoms and death that disproportionately affects older patients or those with comorbidities.Kuwait reported its first imported cases of COVID-19 on February 24,2020.Analysis of data from the first three months of community transmission of the COVID-19 outbreak in Kuwait can provide important guidance for decision-making when dealing with future SARS-CoV-2 epidemic wave management.The analysis of intervention scenarios can help to evaluate the possible impacts of various outbreak control measures going forward which aim to reduce the effective reproduction number during the initial outbreak wave.Herein we use a modified susceptible-exposed-asymptomatic-infectious-removed(SEAIR)transmission model to estimate the outbreak dynamics of SARS-CoV-2 transmission in Kuwait.We fit case data from the first 96 days in the model to estimate the effective reproduction number and used Google mobility data to refine community contact matrices.The SEAIR modelled scenarios allow for the analysis of various interventions to determine their effectiveness.The model can help inform future pandemic wave management,not only in Kuwait but for other countries as well.

Mathematical modeling of COVID-19 infection dynamics in Ghana: Impact evaluation of integrated government and individual level interventions

The raging COVID-19 pandemic is arguably the most important threat to global health presently.Although there is currently a vaccine,preventive measures have been proposed to reduce the spread of infection but the efficacy of these interventions,and their likely impact on the number of COVID-19 infections is unknown.In this study,we proposed the SEIQHRS model(susceptible-exposed-infectious-quarantine-hospitalized-recovered-susceptible)model that predicts the trajectory of the epidemic to help plan an effective control strategy for COVID-19 in Ghana.We provided a short-term forecast of the early phase of the epidemic trajectory in Ghana using the generalized growth model.We estimated the effective basic Reproductive number Re in real-time using three different estimation procedures and simulated worse case epidemic scenarios and the impact of integrated individual and government interventions on the epidemic in the long term using compartmental models.The maximum likelihood estimates of Re and the corresponding 95%confidence interval was 2.04[95%CI:1.82e2.27;12th March-7th April 2020].The Re estimate using the exponential growth method was 2.11[95%CI:2.00e2.24]within the same period.The Re estimate using time-dependent(TD)method showed a gradual decline of the Effective Reproductive Number since March 12,2020 when the first 2 index cases were recorded but the rate of transmission remains high(TD:Re=2.52;95%CI:[1.87e3.49]).The current estimate of Re based on the TD method is 1.74[95%CI:1.41 e2.10;(13th May 2020)]but with comprehensive integrated government and individual level interventions,the Re could reduce to 0.5 which is an indication of the epidemic dying out in the general population.Our results showed that enhanced government and individual-level interventions and the intensity of media coverage could have a substantial effect on suppressing transmission of new COVID-19 cases and reduced death rates in Ghana until such a time that a potent vaccine or drug is discovered.

Infer HIV transmission dynamics from gene sequences among young men who have sex with men in China

To investigate the transmission dynamics and temporal and spatial migration characteristics of HIV spread among men who have sex with men(MSM)in China,a total of 1012 HIV-1 partial pol sequences,including five subtypes,were studied.Bayesian analysis were applied for each subtype to infer its dynamic characters including the effective reproductive number(R_(e))and migration process.The mean curve of each R_(e) was almost always greater than 1(even the 95%highest posterior density(HPD)lower value)along with time,which supports the necessity for a comprehensive study about risk behaviors among young MSM group in China.We also should reappraise the free treatment strategy,especially the therapeutic effect during the free treatment policy.

Control measures during the COVID-19 outbreak reduced the transmission of hand,foot,and mouth disease

Control measures during the coronavirus disease 2019(COVID-19)outbreak may have limited the spread of infectious diseases.This study aimed to analyze the impact of COVID-19 on the spread of hand,foot,and mouth disease(HFMD)in China.A mathematical model was established to fit the reported data of HFMD in six selected cities in China's Mainland from 2015 to 2020.The absolute difference(AD)and relative difference(RD)between the reported incidence in 2020,and simulated maximum,minimum,or median incidence of HFMD in 2015-2019 were calculated.The incidence and R effof HFMD have decreased in six selected cities since the outbreak of COVID-19,and in the second half of 2020,the incidence and R effof HFMD have rebounded.The results show that the total attack rate(TAR)in 2020 was lower than the maximum,minimum,and median TAR fitted in previous years in six selected cities(except Changsha City).For the maximum,median,minimum fitted TAR,the range of RD(%)is 42·20-99·20%,36·35-98·41%48·35-96·23%(except Changsha City)respectively.The preventive and control measures of COVID-19 have significantly contributed to the containment of HFMD transmission.

Coronavirus disease 2019 epidemic prediction in Shanghai under the “dynamic zero-COVID policy”using time-dependent SEAIQR model

It’s urgently needed to assess the COVID-19 epidemic under the“dynamic zero-COVID policy”in China,which provides a scientific basis for evaluating the effectiveness of this strategy in COVID-19 control.Here,we developed a time-dependent susceptible-exposed-asymptomatic-infected-quarantined-remov ed(SEAIQR)model with stage-specific interventions based on recent Shanghai epidemic data,considering a large number of asymptomatic infectious,the changing parameters,and control procedures.The data collected from March 1st,2022 to April 15th,2022 were used to fit the model,and the data of subsequent 7 days and 14 days were used to evaluate the model performance of forecasting.We then calculated the effective regeneration number(Rt)and analyzed the sensitivity of different measures scenarios.Asymptomatic infectious accounts for the vast majority of the outbreaks in Shanghai,and Pudong is the district with the most positive cases.The peak of newly confirmed cases and newly asymptomatic infectious predicted by the SEAIQR model would appear on April 13th,2022,with 1963 and 28,502 cases,respectively,and zero community transmission may be achieved in early to mid-May.The prediction errors for newly confirmed cases were considered to be reasonable,and newly asymptomatic infectious were considered to be good between April 16th to 22nd and reasonable between April 16th to 29th.The final ranges of cumulative confirmed cases and cumulative asymptomatic infectious predicted in this round of the epidemic were 26,477~47,749 and 402,254~730,176,respectively.At the beginning of the outbreak,Rt was 6.69.Since the implementation of comprehensive control,Rt showed a gradual downward trend,dropping to below 1.0 on April 15th,2022.With the early implementation of control measures and the improvement of quarantine rate,recovery rate,and immunity threshold,the peak number of infections will continue to decrease,whereas the earlier the control is implemented,the earlier the turning point of the epidemic will arrive.The proposed time-dependent SEAIQR dynamic model fits and forecasts the epidemic well,which can provide a reference for decision making of the“dynamic zero-COVID policy”.

Analysis of the outbreak of COVID-19 in Japan by SIQR model

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable.It is assumed that the society consists of four compartments;susceptible individuals(S),infected individuals at large(I),quarantined patients(Q)and recovered individuals(R),and the time evolution of the pandemic is described by a set of ordinary differential equations.It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases,from which the number of infected individuals can be estimated.The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government.The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR(Polymerase Chain Reaction)testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population.An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.

QUALITATIVE STUDY FOR A MULTI-DRUG RESISTANT TB MODEL WITH EXOGENOUS REINFECTION AND RELAPSE

One tuberculosis transmission model is formulated by incorporating exogenous reinfec- tion, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.

A COVID-19 mathematical model of at-risk populations with non-pharmaceutical preventive measures:The case of Brazil and South Africa

This work examines a mathematical model of COVID-19 among two subgroups:low-risk and high-risk populations with two preventive measures;non-pharmaceutical interventions including wearing masks,maintaining social distance,and washing hands regularly by the low-risk group.In addition to the interventions mentioned above,highrisk individuals must take extra precaution measures,including telework,avoiding social gathering or public places,etc.to reduce the transmission.Those with underlying chronic diseases and the elderly(ages 60 and above)were classified as high-risk individuals and the rest as low-risk individuals.The parameter values used in this study were estimated using the available data from the Johns Hopkins University on COVID-19 for Brazil and South Africa.We evaluated the effective reproduction number for the two countries and observed how the various parameters affected the effective reproduction number.We also performed numerical simulations and analysis of the model.Susceptible and infectious populations for both low-risk and high-risk individuals were studied in detail.Results were displayed in both graphical and table forms to show the dynamics of each country being studied.We observed that non-pharmaceutical interventions by highrisk individuals significantly reduce infections among only high-risk individuals.In contrast,non-pharmaceutical interventions by low-risk individuals have a significant reduction in infections in both subgroups.Therefore,low-risk individuals’preventive actions have a considerable effect on reducing infections,even among high-risk individuals.

Mathematical modeling of contact tracing and stability analysis to inform its impact on disease outbreaks;an application to COVID-19

We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases.We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing.The model is fitted to data reported for the early spread of COVID-19 in South Korea,Brazil,and Venezuela.The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries.Using the fitted values,we estimate the effective reproduction number R_(e)and investigate its responses to varied control scenarios of contact tracing.Alongside the positivity of solutions,and a stability analysis of the disease-free equilibrium are provided.

Inferring community transmission of SARS-CoV-2 in the United Kingdom using the ONS COVID-19 Infection Survey

Key epidemiological parameters,including the effective reproduction number,,and the instantaneous growth rate,,generated from an ensemble of models,have been informing public health policy throughout the COVID-19 pandemic in the four nations of the United Kingdom of Great Britain and Northern Ireland(UK).However,estimation of these quantities became challenging with the scaling down of surveillance systems as part of the transition from the“emergency”to“endemic”phase of the pandemic.The Office for National Statistics(ONS)COVID-19 Infection Survey(CIS)provided an opportunity to continue estimating these parameters in the absence of other data streams.We used a penalised spline model fitted to the publicly-available ONS CIS test positivity estimates to produce a smoothed estimate of the prevalence of SARS-CoV-2 positivity over time.The resulting fitted curve was used to estimate the“ONS-based”and across the four nations of the UK.Estimates produced under this model are compared to government-published estimates with particular consideration given to the contribution that this single data stream can offer in the estimation of these parameters.Depending on the nation and parameter,we found that up to 77%of the variance in the government-published estimates can be explained by the ONS-based estimates,demonstrating the value of this singular data stream to track the epidemic in each of the four nations.We additionally find that the ONS-based estimates uncover epidemic trends earlier than the corresponding government-published estimates.Our work shows that the ONS CIS can be used to generate key COVID-19 epidemiological parameters across the four UK nations,further underlining the enormous value of such population-level studies of infection.This is not intended as an alternative to ensemble modelling,rather it is intended as a potential solution to the aforementioned challenge faced by public health officials in the UK in early 2022.