Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

We constructed a simple Susceptible−Exposed–Infectious–Removed model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, β, and exclusion rate, γ. The rates depend on nontherapeutic interventions and determine the basic reproduction number, R0 = β/γ, and, together with τ, the daily multiplication coefficient in the early exponential phase, θ. Initial R0 determines the reduction of β required to contain the spread of the epidemic. We demonstrate that introduction of a cascade of multiple exposed states enables the model to reproduce the distributions of the incubation period and the serial interval reported by epidemiologists. Using the model, we consider a hypothetical scenario in which β is modulated solely by anticipated changes of social behaviours: first, β decreases in response to a surge of daily new cases, pressuring people to self-isolate, and then, over longer time scale, β increases as people gradually accept the risk. In this scenario, initial abrupt epidemic spread is followed by a plateau and slow regression, which, although economically and socially devastating, grants time to develop and deploy vaccine or at least limit daily cases to a manageable number.

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Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

10.1101/2020.03.13.20035485 ◽

2020 ◽

Cited By ~ 3

Author(s):

Marek Kochańczyk ◽

Frederic Grabowski ◽

Tomasz Lipniacki

Keyword(s):

Reproduction Number ◽

Exponential Phase ◽

Time Dependent ◽

Therapeutic Interventions ◽

Contact Rate ◽

Epidemic Spread ◽

Early Exponential Phase ◽

Contact Rates ◽

Multiplication Coefficient

We constructed a simple Susceptible–Infected–Infectious–Excluded model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, rC, and exclusion rate, rE. The rates can be manipulated by non-therapeutic interventions and determine the basic reproduction number, R = rC/rE, and, together with τ, the daily multiplication coefficient at the early exponential phase, β. Initial β determines the reduction of rC required to contain epidemic spread. In the long-term, we consider a scenario based on typical social behaviours, in which rC first decreases in response to a surge of daily new cases, forcing people to self-isolate, and then slowly increases when people gradually accept higher risk. Consequently, initial abrupt epidemic spread is followed by a plateau and slow regression. This scenario, although economically and socially devastating, will grant time to develop, produce, and distribute a vaccine, or at least limit daily cases to a manageable number.

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Meta-analysis of the SARS-CoV-2 serial interval and the impact of parameter uncertainty on the COVID-19 reproduction number

10.1101/2020.11.17.20231548 ◽

2020 ◽

Author(s):

Robert Challen ◽

Ellen Brooks-Pollock ◽

Krasimira Tsaneva-Atanasova ◽

Leon Danon

Keyword(s):

Incubation Period ◽

Time Delays ◽

Hospital Admissions ◽

Reproduction Number ◽

Meta Analysis ◽

Model Parameters ◽

Small Data ◽

Generation Interval ◽

Serial Interval ◽

The Impact

AbstractThe serial interval of an infectious disease, commonly interpreted as the time between onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections) and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early COVID-19 data. In this paper we estimate these key quantities in the context of COVID-19 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean 5.6 (95% CrI 5.1–6.2) and SD 4.2 (95% CrI 3.9–4.6) days (empirical distribution), the generation interval with a mean 4.8 (95% CrI 4.3–5.41) and SD 1.7 (95% CrI 1.0–2.6) days (fitted gamma distribution), and the incubation period with a mean 5.5 (95% CrI 5.1–5.8) and SD 4.9 (95% CrI 4.5–5.3) days (fitted log normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modelling COVID-19 transmission.

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Transmission interval estimates suggest pre-symptomatic spread of COVID-19

10.1101/2020.03.03.20029983 ◽

2020 ◽

Cited By ~ 76

Author(s):

Lauren C. Tindale ◽

Michelle Coombe ◽

Jessica E. Stockdale ◽

Emma S. Garlock ◽

Wing Yin Venus Lau ◽

...

Keyword(s):

Incubation Period ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Interval Estimates ◽

Secondary Infections ◽

Serial Interval ◽

Incubation Periods ◽

Key Variables ◽

The Mean ◽

Interval Distribution

AbstractBackgroundAs the COVID-19 epidemic is spreading, incoming data allows us to quantify values of key variables that determine the transmission and the effort required to control the epidemic. We determine the incubation period and serial interval distribution for transmission clusters in Singapore and in Tianjin. We infer the basic reproduction number and identify the extent of pre-symptomatic transmission.MethodsWe collected outbreak information from Singapore and Tianjin, China, reported from Jan.19-Feb.26 and Jan.21-Feb.27, respectively. We estimated incubation periods and serial intervals in both populations.ResultsThe mean incubation period was 7.1 (6.13, 8.25) days for Singapore and 9 (7.92, 10.2) days for Tianjin. Both datasets had shorter incubation periods for earlier-occurring cases. The mean serial interval was 4.56 (2.69, 6.42) days for Singapore and 4.22 (3.43, 5.01) for Tianjin. We inferred that early in the outbreaks, infection was transmitted on average 2.55 and 2.89 days before symptom onset (Singapore, Tianjin). The estimated basic reproduction number for Singapore was 1.97 (1.45, 2.48) secondary cases per infective; for Tianjin it was 1.87 (1.65, 2.09) secondary cases per infective.ConclusionsEstimated serial intervals are shorter than incubation periods in both Singapore and Tianjin, suggesting that pre-symptomatic transmission is occurring. Shorter serial intervals lead to lower estimates of R0, which suggest that half of all secondary infections should be prevented to control spread.

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Epidemiologic Characteristics of COVID-19 in Guizhou Province, China

The Journal of Infection in Developing Countries ◽

10.3855/jidc.12818 ◽

2021 ◽

Vol 15 (03) ◽

pp. 389-397

Author(s):

Kaike Ping ◽

Mingyu Lei ◽

Yun Gou ◽

Zhongfa Tao ◽

Guanghai Yao ◽

...

Keyword(s):

Incubation Period ◽

Reproduction Number ◽

Asymptomatic Carrier ◽

Control Measures ◽

Guizhou Province ◽

Serial Interval ◽

Two Peaks ◽

Epidemiologic Characteristics ◽

Close Contacts

Introduction: At the end of 2019, the COVID-19 broke out, and spread to Guizhou province in January of 2020. Methodology: To acquire the epidemiologic characteristics of COVID-19 in Guizhou province, we collected data from 169 laboratory-confirmed COVID-19 related cases. We described the demographic characteristics of the cases and estimated the incubation period, serial interval and the effective reproduction number. We also presented two representative case studies in Guizhou province: Case Study 1 was an example of the asymptomatic carrier; while Case Study 2 was an example of a large and complex infection chain that involved four different regions, spanning three provinces and eight families. Results: Two peaks in the incidence distribution associated with COVID-19 in Guizhou province were related to the 6.04 days (95% CI: 5.00 – 7.10) of incubation period and 6.14±2.21 days of serial interval. We also discussed the effectiveness of the control measures based on the instantaneous effective reproduction number that was a constantly declining curve. Conclusions: As of February 2, 2020, the estimated effective reproduction number was below 1, and no new cases were reported since February 26. These showed that Guizhou Province had achieved significant progress in preventing the spread of the epidemic. The medical isolation of close contacts was consequential. Meanwhile, the asymptomatic carriers and the super-spreaders must be isolated in time, who would cause a widespread infection.

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Epidemiologic Characteristics of COVID-19 in Guizhou, China

10.1101/2020.03.01.20028944 ◽

2020 ◽

Cited By ~ 4

Author(s):

Kaike Ping ◽

Mingyu Lei ◽

Yun Gou ◽

Ying Tao ◽

Yan Huang

Keyword(s):

Incubation Period ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Demographic Characteristics ◽

Guizhou Province ◽

Serial Interval ◽

Epidemiologic Characteristics

AbstractAt the end of 2019, a coronavirus disease 2019 (COVID-19) outbroke in Wuhan, China, and spread to Guizhou province on January of 2020. To acquire the epidemiologic characteristics of COVID-19 in Guizhou, China, we collected data on 162 laboratory-confirmed cases related to COVID-19. We described the demographic characteristics of the cases and estimated the incubation period, serial interval and basic reproduction number. With an estimation of 8 days incubation period and 6 days serial interval, our results indicate that there may exist infectiousness during the incubation period for 2019-nCoV. This increases the difficulty of screening or identifying cases related to COVID-19.

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Nine-month Trend of Time-Varying Reproduction Numbers of COVID-19 in West of Iran

Journal of Research in Health Sciences ◽

10.34172/jrhs.2021.54 ◽

2021 ◽

Vol 21 (2) ◽

pp. e00517-e00517

Author(s):

Ebrahim Rahimi ◽

Seyed Saeed Hashemi Nazari ◽

Yaser Mokhayeri ◽

Asaad Sharhani ◽

Rasool Mohammadi

Keyword(s):

Reproduction Number ◽

Infectious Period ◽

Time Varying ◽

Cross Sectional ◽

Disease Epidemiology ◽

Infectious Disease Epidemiology ◽

Contact Rates ◽

Reproduction Numbers ◽

Serial Interval ◽

Log Normal

Background: The basic reproduction number (R0) is an important concept in infectious disease epidemiology and the most important parameter to determine the transmissibility of a pathogen. This study aimed to estimate the nine-month trend of time-varying R of COVID-19 epidemic using the serial interval (SI) and Markov Chain Monte Carlo in Lorestan, west of Iran. Study design: Descriptive study. Methods: This study was conducted based on a cross-sectional method. The SI distribution was extracted from data and log-normal, Weibull, and Gamma models were fitted. The estimation of time-varying R0, a likelihood-based model was applied, which uses pairs of cases to estimate relative likelihood. Results: In this study, Rt was estimated for SI 7-day and 14-day time-lapses from 27 February-14 November 2020. To check the robustness of the R0 estimations, sensitivity analysis was performed using different SI distributions to estimate the reproduction number in 7-day and 14-day time-lapses. The R0 ranged from 0.56 to 4.97 and 0.76 to 2.47 for 7-day and 14-day time-lapses. The doubling time was estimated to be 75.51 days (95% CI: 70.41, 81.41). Conclusions: Low R0 of COVID-19 in some periods in Lorestan, west of Iran, could be an indication of preventive interventions, namely quarantine and isolation. To control the spread of the disease, the reproduction number should be reduced by decreasing the transmission and contact rates and shortening the infectious period.

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Early reports of epidemiological parameters of the COVID-19 pandemic

Western Pacific Surveillance and Response ◽

10.5365/wpsar.2020.11.4.001 ◽

2021 ◽

Vol 12 (2) ◽

pp. 65-81

Author(s):

Keeley Allen ◽

Ame Elizabeth Parry ◽

Kathryn Glass

Keyword(s):

Incubation Period ◽

Reproduction Number ◽

Rapid Assessment ◽

Control Measures ◽

Inclusion Criteria ◽

Early Analysis ◽

Outbreak Response ◽

Median Length ◽

Serial Interval ◽

The Mean

Background: The emergence of a new pathogen requires a rapid assessment of its transmissibility, to inform appropriate public health interventions. Methods: The peer-reviewed literature published between 1 January and 30 April 2020 on COVID-19 in PubMed was searched. Estimates of the incubation period, serial interval and reproduction number for COVID-19 were obtained and compared. Results: A total of 86 studies met the inclusion criteria. Of these, 33 estimated the mean incubation period (4–7 days) and 15 included estimates of the serial interval (mean 4–8 days; median length 4–5 days). Fifty-two studies estimated the reproduction number. Although reproduction number estimates ranged from 0.3 to 14.8, in 33 studies (63%), they fell between 2 and 3. Discussion: Studies calculating the incubation period and effective reproduction number were published from the beginning of the pandemic until the end of the study period (30 April 2020); however, most of the studies calculating the serial interval were published in April 2020. The calculated incubation period was similar over the study period and in different settings, whereas estimates of the serial interval and effective reproduction number were setting-specific. Estimates of the serial interval were shorter at the end of the study period as increasing evidence of pre-symptomatic transmission was documented and as jurisdictions enacted outbreak control measures. Estimates of the effective reproduction number varied with the setting and the underlying model assumptions. Early analysis of epidemic parameters provides vital information to inform the outbreak response.

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An improved method to estimate the effective reproduction number of the COVID-19 pandemic: lessons from its application in Greece

10.1101/2020.09.19.20198028 ◽

2020 ◽

Author(s):

Theodore Lytras ◽

Vana Sypsa ◽

Demosthenes Panagiotakos ◽

Sotirios Tsiodras

Keyword(s):

Incubation Period ◽

Reproduction Number ◽

Surveillance Data ◽

Control Measures ◽

Population Mobility ◽

Improved Method ◽

Mobility Patterns ◽

Routine Surveillance ◽

Serial Interval ◽

Tourism Activity

Introduction: Monitoring the time-varying effective reproduction number Rt is crucial for assessing the evolution of the COVID-19 pandemic. We present an improved method to estimate Rt and its application to routine surveillance data from Greece. Methods: Our method extends that of Cori et al (2013), adding Bayesian imputation of missing symptom onset dates, imputation of infection times using an external estimate of the incubation period, and an adjustment for reporting delay. To facilitate its use, we provide an R software package named "bayEStim". We applied the method to COVID-19 surveillance data from Greece, and examined the resulting Rt estimates in relation to control measures applied, in order to assess their effectiveness. We also associated Rt, as a measure of transmissibility, to population mobility as recorded in Google data and to ambient temperature. We used a serial interval between 4 and 7.5 days, and a median incubation period of 5.1 days. Results: In Greece Rt fell rapidly as the first control measures were introduced, dropping below 1 at least a week before a full lockdown came into effect. In mid-July Rt started increasing again, as increased mobility associated with tourism activity was observed. Each 10% of increase in relative mobility increased Rt by 8.1% (95% CrI 6.1-10.2%), whereas each unit celsius of temperature increase decreased Rt by 4.6% (95% CrI 5.4-13.7%). Conclusions: Mobility patterns significantly affect Rt. Most of the reduction in COVID-19 transmissibility in Greece occurred already before the lockdown, likely as a result of decreased population mobility. Lower viral transmissibility in summer does not appear sufficient to counterbalance the increased mobility due to tourism. Monitoring Rt is an essential component of COVID-19 surveillance, and it is crucial for correctly assessing the effect of control measures.

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Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number

Statistical Methods in Medical Research ◽

10.1177/09622802211065159 ◽

2021 ◽

pp. 096228022110651

Author(s):

Robert Challen ◽

Ellen Brooks-Pollock ◽

Krasimira Tsaneva-Atanasova ◽

Leon Danon

Keyword(s):

Incubation Period ◽

Time Delays ◽

Hospital Admissions ◽

Reproduction Number ◽

Meta Analysis ◽

Model Parameters ◽

Small Data ◽

Generation Interval ◽

Serial Interval ◽

The Impact

The serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission.

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Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽

10.3390/j4020008 ◽

2021 ◽

Vol 4 (2) ◽

pp. 86-100

Author(s):

Nita H. Shah ◽

Ankush H. Suthar ◽

Ekta N. Jayswal ◽

Ankit Sikarwar

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Transmission Rate ◽

Sir Model ◽

Time Dependent ◽

Contact Rate ◽

Distribution Maps ◽

Fundamental Parameters ◽

Different Order ◽

The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

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