What Is the Estimated COVID-19 Reproduction Number and the Proportion of the Population That Needs to Be Immunized to Achieve Herd Immunity in Malaysia? A Mathematical Epidemiology Synthesis

We aimed to determine Malaysia’s COVID-19 reproduction number and herd immunity threshold through a mathematical epidemiology synthesis. Using time-series incidence data, the time-dependent reproduction number (Rt) was yielded over time during the COVID-19 containment measures in Malaysia. The value of Rt at the beginning of the epidemic and prior to any interventions in place was used to determine the proportion of the population that needs to be immunized to achieve herd immunity. Rt was strongly influenced by interventions being put in place. We established that at least 74% of the Malaysian population needs to be vaccinated to achieve herd immunity against COVID-19. This threshold estimate is somewhat influenced by the availability of an efficacious vaccine. A vaccine with 95% efficacy would approximately synthesize a herd immunity threshold of 78%. We conclude that Rt is a valid estimator to determine the effectiveness of control measures and a parameter of use to synthesize herd immunity thresholds in the current COVID-19 pandemic.

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Elementi metodologici per una riflessione sui dati dell’epidemia di sars-cov-2

Giornale di Clinica Nefrologica e Dialisi ◽

10.33393/gcnd.2020.2179 ◽

2020 ◽

Vol 32 (1) ◽

pp. 127-130

Author(s):

Anteo Di Napoli ◽

Francesco Franco ◽

Giuseppe Quintaliani

Keyword(s):

Infectious Disease ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Herd Immunity ◽

Critical Threshold ◽

Primary Case ◽

Containment Measures ◽

Over Time

Findings of the seroprevalence survey conducted by Istat between May 25 and July 15 2020, on a sample of 64,660 people, show that only 2.5% of Italian people developed antibodies to SARS-CoV-2, a prevalence very far from the hypothesis of achieving herd immunity. Starting from the comment on these results, we summarized some of the main indicators used to evaluate the epidemic curves (R, R0, Rt) and the concept of herd immunity. R0, basic reproduction number, represents the average number of secondary cases we expect to observe from a single primary case in a population with no immunity to the disease before prevention and containment measures have been planned. Rt, effective reproduction number, is calculated over time and considers how the outbreak progresses, as a result of the containment measures and of people who might have gained immunity, because they survived from infection or were vaccinated. We presented the issue of herd immunity, or community immunity, a state of protection in a population obtained because the number of people in the population who are immune to infectious disease is above a critical threshold, resulting in a protection even for those who are not immune.

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Modelling the evolution of COVID-19 in high-incidence European countries and regions: estimated number of infections and impact of past and future intervention measures

10.1101/2020.05.09.20096735 ◽

2020 ◽

Author(s):

Juan Fernandez-Recio

Keyword(s):

Reproduction Number ◽

Mechanistic Model ◽

Control Measures ◽

European Countries ◽

Intervention Measures ◽

High Incidence ◽

Long Term Impact ◽

The Impact ◽

Over Time

A previously developed mechanistic model of COVID-19 transmission has been adapted and applied here to study the evolution of the disease and the effect of intervention measures in some European countries and territories where the disease had major impact. A clear impact of the major intervention measures on the reproduction number (Rt) has been found in all studied countries and territories, as already suggested by the drop in the number of deaths over time. Interestingly, the impact of such major intervention measures seems to be the same in most of these countries. The model has also provided realistic estimates of the total number of infections, active cases and future outcome. While the predictive capabilities of the model are much more uncertain before the peak of the outbreak, we could still reliably predict the evolution of the disease after a major intervention by assuming the afterwards reproduction number from current study. More challenging is to foresee the long-term impact of softer intervention measures, but this model can estimate the outcome of different scenarios and help planning changes in the implementation of control measures in a given country or region.

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China’s effective control and other countries’ uncharted challenge against COVID-19: an epidemiological and modelling study

10.21203/rs.3.rs-32370/v1 ◽

2020 ◽

Author(s):

Lingling Zheng ◽

Qin Kang ◽

Xiujuan Chen ◽

Shuai Huang ◽

Dong Liu ◽

...

Keyword(s):

Reproduction Number ◽

Case Reports ◽

Effective Control ◽

Second Step ◽

Incidence Data ◽

Step Procedure ◽

Serial Interval ◽

More Care ◽

Interval Distribution ◽

Over Time

Abstract Objective: In this study, we use the time-dependent reproduction number (Rt) to comprise the COVID transmissibility across different countries.Methods: We used data from Jan 20, 2019, to Feb 29, 2020, on the number of newly confirmed cases, obtained from the reports published by the CDC, to infer the incidence of infectious over time. A two-step procedure was used to estimate the Rt. The first step used data on known index-secondary cases pairs, from publicly available case reports, to estimate the serial interval distribution. The second step estimated the Rt jointly from the incidence data and the information data in the first step. Rt was then used to simulate the epidemics across all major cities in China and typical countries worldwide. Results: Based on a total of 126 index-secondary cases pairs from 4 international regions, we estimated that the serial interval for SARS-2-CoV was 4.18 (IQR 1.92 – 6.65) days. Domestically, Rt of China, Hubei province, Wuhan had fallen below 1.0 on 9 Feb, 10 Feb and 13 Feb (Rt were 0.99±0.02, 0.99±0.02 and 0.96±0.02), respectively. Internationally, as of 26 Feb, statistically significant periods of COVID spread (Rt >1) were identified for most regions, except for Singapore (Rt was 0.92±0.17).Conclusions: The epidemic in China has been well controlled, but the worldwide pandemic has not been well controlled. Worldwide preparedness and vulnerability against COVID-19 should be regarded with more care.

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On realized serial and generation intervals given control measures: The COVID-19 pandemic case

PLoS Computational Biology ◽

10.1371/journal.pcbi.1008892 ◽

2021 ◽

Vol 17 (3) ◽

pp. e1008892

Author(s):

Andrea Torneri ◽

Pieter Libin ◽

Gianpaolo Scalia Tomba ◽

Christel Faes ◽

James G. Wood ◽

...

Keyword(s):

Reproduction Number ◽

Transmission Probability ◽

Theoretical Explanation ◽

Control Measures ◽

Strong Impact ◽

Generation Interval ◽

Incidence Data ◽

Intervention Measures ◽

Serial Interval ◽

The Mean

The SARS-CoV-2 pathogen is currently spreading worldwide and its propensity for presymptomatic and asymptomatic transmission makes it difficult to control. The control measures adopted in several countries aim at isolating individuals once diagnosed, limiting their social interactions and consequently their transmission probability. These interventions, which have a strong impact on the disease dynamics, can affect the inference of the epidemiological quantities. We first present a theoretical explanation of the effect caused by non-pharmaceutical intervention measures on the mean serial and generation intervals. Then, in a simulation study, we vary the assumed efficacy of control measures and quantify the effect on the mean and variance of realized generation and serial intervals. The simulation results show that the realized serial and generation intervals both depend on control measures and their values contract according to the efficacy of the intervention strategies. Interestingly, the mean serial interval differs from the mean generation interval. The deviation between these two values depends on two factors. First, the number of undiagnosed infectious individuals. Second, the relationship between infectiousness, symptom onset and timing of isolation. Similarly, the standard deviations of realized serial and generation intervals do not coincide, with the former shorter than the latter on average. The findings of this study are directly relevant to estimates performed for the current COVID-19 pandemic. In particular, the effective reproduction number is often inferred using both daily incidence data and the generation interval. Failing to account for either contraction or mis-specification by using the serial interval could lead to biased estimates of the effective reproduction number. Consequently, this might affect the choices made by decision makers when deciding which control measures to apply based on the value of the quantity thereof.

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Early dynamics of transmission and control of COVID-19: a mathematical modelling study

10.1101/2020.01.31.20019901 ◽

2020 ◽

Cited By ~ 184

Author(s):

Adam J Kucharski ◽

Timothy W Russell ◽

Charlie Diamond ◽

Yang Liu ◽

John Edmunds ◽

...

Keyword(s):

Reproduction Number ◽

Control Measures ◽

Transmission Model ◽

The Novel ◽

Transmission Potential ◽

Travel Restrictions ◽

Gates Foundation ◽

Novel Coronavirus ◽

And Control ◽

Over Time

AbstractBackgroundAn outbreak of the novel coronavirus SARS-CoV-2 has led to 46,997 confirmed cases as of 13th February 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.MethodsWe combined a stochastic transmission model with data on cases of novel coronavirus disease (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January and February 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas.FindingsWe estimated that the median daily reproduction number, Rt, declined from 2.35 (95% CI: 1.15-4.77) one week before travel restrictions were introduced on 23rd January to 1.05 (95% CI: 0.413-2.39) one week after. Based on our estimates of Rt,we calculated that in locations with similar transmission potential as Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.InterpretationOur results show that COVID-19 transmission likely declined in Wuhan during late January 2020, coinciding with the introduction of control measures. As more cases arrive in international locations with similar transmission potential to Wuhan pre-control, it is likely many chains of transmission will fail to establish initially, but may still cause new outbreaks eventually.FundingWellcome Trust (206250/Z/17/Z, 210758/Z/18/Z), HDR UK (MR/S003975/1), Gates Foundation (INV-003174), NIHR (16/137/109)

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Dynamics of Transmission and Control of COVID-19: A Real-time Estimation Using the Kalman Filter

10.1101/2020.04.19.20071886 ◽

2020 ◽

Cited By ~ 1

Author(s):

Francisco Arroyo Marioli ◽

Francisco Bullano ◽

Carlos Rondón-Moreno

Keyword(s):

Kalman Filter ◽

South Korea ◽

Real Time ◽

Reproduction Number ◽

Time Estimation ◽

Control Measures ◽

Significant Heterogeneity ◽

Real Time Estimation ◽

And Control ◽

Over Time

AbstractThe COVID-19 pandemic has become the center of attention for both researchers and authorities. In this paper, we propose and test a methodology to estimate the daily effective reproduction number (ℛt) through the lens of the Kalman Filter and Bayesian estimation. Moreover, we apply our method to data from the current COVID-19 pandemic in China, Italy, Japan, and South Korea. We correlate our findings with the implementation of control measures in each of these countries. Our results show that China, Italy, and South Korea have been able to reduce ℛt over time. We find significant heterogeneity in the way ℛt decreases across countries. For instance, China reduced ℛt from its peak to below one in 19 days, while South Korea achieved the same reduction in 12 days. In contrast, it has taken Italy almost a month to reach similar levels. We hypothesize this is related to how strict, enforceable, and comprehensive are the implemented policies.

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The Estimated Time-Varying Reproduction Numbers during the Ongoing Epidemic of the Coronavirus Disease 2019 (COVID-19) in China

10.1101/2020.04.11.20061838 ◽

2020 ◽

Cited By ~ 1

Author(s):

Fu-Chang Hu ◽

Fang-Yu Wen

Keyword(s):

Infectious Disease ◽

Reproduction Number ◽

Control Measures ◽

Time Varying ◽

Epidemic Curve ◽

Health Authorities ◽

Reproduction Numbers ◽

Public Health Authorities ◽

Control And Prevention ◽

Over Time

AbstractBackgroundHow could we anticipate the progression of the ongoing epidemic of the coronavirus disease 2019 (COVID-19) in China? As a measure of transmissibility, the value of basic reproduction number varies over time during an epidemic of infectious disease. Hence, this study aimed to estimate concurrently the time-varying reproduction number over time during the COVID-19 epidemic in China.MethodsWe extracted the epidemic data from the “Tracking the Epidemic” website of the Chinese Center for Disease Control and Prevention for the duration of January 19, 2020 and March 14, 2020. Then, we applied the novel method implemented in the incidence and EpiEstim packages to the data of daily new confirmed cases for robustly estimating the time-varying reproduction number in the R software.ResultsThe epidemic curve of daily new confirmed cases in China peaked around February 4−6, 2020, and then declined gradually, except the very high peak on February 12, 2020 owing to the added clinically diagnosed cases (Hubei Province only). Under two specified plausible scenarios for the distribution of serial interval, both curves of the estimated time-varying reproduction numbers fell below 1.0 around February 17−18, 2020. Finally, the COVID-19 epidemic in China abated around March 7−8, 2020, indicating that the prompt and aggressive control measures of China were effective.ConclusionSeeing the estimated time-varying reproduction number going downhill was more informative than looking for the drops in the daily number of new confirmed cases during an ongoing epidemic of infectious disease. We urged public health authorities and scientists to estimate time-varying reproduction numbers routinely during epidemics of infectious diseases and to report them daily to the public until the end of the COVID-19 epidemic.

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Assessing Changes in the Reproduction Number of COVID-19 in Cameroon

Asian Journal of Research in Infectious Diseases ◽

10.9734/ajrid/2021/v8i230234 ◽

2021 ◽

pp. 30-40

Author(s):

Solange Whegang Youdom ◽

Djam Chefor Alain ◽

Charles Kouanfack

Keyword(s):

Reproduction Number ◽

Moving Average ◽

Model Parameters ◽

Time Varying ◽

Autoregressive Integrated Moving Average ◽

Social Distancing ◽

Vaccine Introduction ◽

Incidence Data ◽

A Value ◽

Containment Measures

Aim: The purpose of this work is to assess changes that occur on COVID-19 infection in Cameroon since the start of the epidemic. Study Design: We use a data-based analysis on longitudinal data of reported COVID-19 cases in Cameroon. Place and Duration: The data for the study were obtained from the reports of confirmed COVID-19 cases from an official website between March 7, 2020 to September 29, 2021. Methodology: A modified Susceptible-Infected-Recovered-Deceased (SIRD) model for the contagion was used to describe the cumulated cases of COVID-19 during different phases of the epidemic that correlated with highest spikes. The approach features several aspects: one is that model parameters can be time-varying, allowing us to capture possible changes of the epidemic behaviour, due for example to containment measures enforced by authorities or modifications of the epidemic characteristics, country events, and COVID-19 vaccine introduction; the second aspect is that the model accounts for a social distancing parameter. The time-varying parameters was handled using a phase-to-phase modelling in which initial parameters were the number of susceptible individuals at the end of each phase. In addition, daily incidence data were used to estimate daily reproduction number. Secondly, we used an Autoregressive Integrated Moving Average (ARIMA) approach to analyse the dynamic of the effective reproduction number R and forecast the new number of infected contacts. Results: There was less than 54% compliance of social distancing during all phases. The reproduction number was above 1 during each phase of the analysis. As of September 2021, it was 2.43 suggesting a constant increase of infection. Time-series of the reproduction number was unseasonal and stationary. Forecasting of R gave a value of more than 2, suggesting a continued rise in the number of infected cases in the Country in the next coming months. Conclusion: It is uncertain when the pandemic will last in the country. While social distancing is in decrease, prevention through vaccination is an option to reach more people and stop the propagation of the disease.

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The 2020 SARS-CoV-2 epidemic in England: key epidemiological drivers and impact of interventions

10.1101/2021.01.11.21249564 ◽

2021 ◽

Author(s):

Edward S. Knock ◽

Lilith K. Whittles ◽

John A. Lees ◽

Pablo N. Perez-Guzman ◽

Robert Verity ◽

...

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Clinical Care ◽

Herd Immunity ◽

The Elderly ◽

Surveillance Data ◽

Control Measures ◽

Care Homes ◽

The Impact ◽

Regional Surveillance

AbstractWe fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Among control measures implemented, only national lockdown brought the reproduction number below 1 consistently; introduced one week earlier it could have reduced first wave deaths from 36,700 to 15,700 (95%CrI: 8,900–26,800). Improved clinical care reduced the infection fatality ratio from 1.25% (95%CrI: 1.18%–1.33%) to 0.77% (95%CrI: 0.71%–0.84%). The infection fatality ratio was higher in the elderly residing in care homes (35.9%, 95%CrI: 29.1%–43.4%) than those residing in the community (10.4%, 95%CrI: 9.1%–11.5%). England is still far from herd immunity, with regional cumulative infection incidence to 1st December 2020 between 4.8% (95%CrI: 4.4%–5.1%) and 15.4% (95%CrI: 14.9%–15.9%) of the population.One-sentence summaryWe fit a mathematical model of SARS-CoV-2 transmission to surveillance data from England, to estimate transmissibility, severity, and the impact of interventions

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Transmission dynamics of the COVID-19 epidemic in India and modelling optimal lockdown exit strategies

10.1101/2020.05.13.20096826 ◽

2020 ◽

Cited By ~ 7

Author(s):

Mohak Gupta ◽

Saptarshi Soham Mohanta ◽

Aditi Rao ◽

Giridara Gopal Parameswaran ◽

Mudit Agarwal ◽

...

Keyword(s):

Symptom Onset ◽

Reproduction Number ◽

Control Strategies ◽

Tertiary Care ◽

Time Lag ◽

Control Measures ◽

Surveillance Systems ◽

Care Hospital ◽

Incidence Data ◽

Second Wave

Background: The coronavirus disease 2019 (COVID-19) has caused over 3 200 000 cases and 230 000 deaths as on 2 May 2020, and has quickly become an unprecedented global health threat. India, with its unique challenges in fighting this pandemic, imposed one of the worlds strictest and largest population-wide lockdown on 25 March 2020. Here, we estimated key epidemiological parameters and evaluated the effect of control measures on the COVID-19 epidemic in India. Through a modelling approach, we explored various strategies to exit the lockdown. Methods: We obtained data from 140 confirmed COVID-19 patients at a tertiary care hospital in India to estimate the delay from symptom onset to confirmation and the proportion of cases without symptoms. We estimated the basic reproduction number (R0) and time-varying effective reproduction number (Rt) after adjusting for imported cases and reporting lag, using incidence data from 4 March to 25 April 2020 for India. We built upon the SEIR model to account for underreporting, reporting delays, and varying asymptomatic proportion and infectivity. Using this model, we simulated lockdown relaxation under various scenarios to evaluate its effect on the second wave, and also modelled increased detection through testing. We hypothesised that increased testing after lockdown relaxation will decrease the epidemic growth enough to allow for a greater resumption of normal social mixing thus minimising the social and economic fallout. Findings: The median delay from symptom onset to confirmation (reporting lag) was estimated to be 2·68 days (95% CI 2·00−3·00) with an IQR of 2·03 days (95% CI 1·00−3·00). 60·7% of confirmed COVID-19 cases (n=140) were found to be asymptomatic. The R0 for India was estimated to be 2·083 (95% CI 2·044−2·122 ; R2 = 0·972), while the Rt gradually down trended from 1·665 (95%CI 1·539−1·789) on 30 March to 1·159 (95% CI 1·128−1·189) on 22 April. In the modelling, we observed that the time lag from date of lockdown relaxation to start of second wave increases as lockdown is extended farther after the first wave peak. This benefit was greater for a gradual relaxation as compared to a sudden lifting of lockdown. We found that increased detection through testing decreases the number of total infections and symptomatic cases, and the benefit of detecting each extra case was higher when prevailing transmission rates were higher (as when restrictions are relaxed). Lower levels of social restrictions when coupled with increased testing, could achieve similar outcomes as an aggressive social distancing regime where testing was not increased. Interpretation: The aggressive control measures in India since 25 March have produced measurable reductions in transmission, although suppression needs to be maintained to achieve sub-threshold Rt. Additional benefits for mitigating the second wave can be achieved if lockdown can be feasibly extended farther after the peak of active cases has passed. Aggressive measures like lockdowns may inherently be enough to suppress the epidemic, however other measures need to be scaled up as lockdowns are relaxed. Expanded testing is expected to play a pivotal role in the lockdown exit strategy and will determine the degree of return to normalcy that will be possible. Increased testing coverage will also ensure rapid feedback from surveillance systems regarding any resurgence in cases, so that geo-temporally targeted measures can be instituted at the earliest. Considering that asymptomatics play an undeniable role in transmission of COVID-19, it may be prudent to reduce the dependence on presence of symptoms for implementing control strategies, behavioral changes and testing.

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