Query: reproduction number

title: Development of the reproduction number from coronavirus SARS CoV 2 case data in Germany and implications for political measures
abstract: SARS CoV 2 has induced a worldwide pandemic and subsequent non pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS CoV 2 pandemic in Germany has led to a consecutive roll out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS CoV 2 that allows daily estimation of a time varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression.  We used a data driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID 19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute.  The time varying reproduction number R t in Germany decreased to <1 in early April 2020, 2 3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in R t until August 2020. Implications of state specific R t on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short term predictions may work for a few weeks, long term projections are complicated by unpredictable structural changes.  The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing quarantine strategy. We show that real time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short term projections for the burden on the healthcare system, and their response to policy changes.

title: Interpretation of the Basic and Effective Reproduction Number
abstract: In epidemiology, the basic reproduction number (R0) is a term that describes the expected number of infections generated by 1 case in a susceptible population. At the beginning of the coronavirus disease 2019 (COVID 19) pandemic, R0 was frequently referenced by the public health community and the wider public. However, this metric is often misused or misinterpreted. Moreover, the complexity of the process of estimating R0 has caused difficulties for a substantial number of researchers. In this article, in order to increase the accessibility of this concept, we address several misconceptions related to the threshold characteristics of R0 and the effective reproduction number (Rt) Moreover, the appropriate interpretation of the metrics is discussed. R0 should be considered as a population averaged value that pools the contact structure according to a stochastic transmission process. Furthermore, it is necessary to understand the unavoidable time lag for Rt due to the incubation period of the disease.

title: Replicating and projecting the path of COVID 19 with a model implied reproduction number
abstract: We demonstrate a methodology for replicating and projecting the path of COVID 19 using a simple epidemiology model. We fit the model to daily data on the number of infected cases in China, Italy, the United States, and Brazil. These four countries can be viewed as representing different stages, from later to earlier, of a COVID 19 epidemic cycle. We solve for a model implied effective reproduction number R t each day so that the model closely replicates the daily number of currently infected cases in each country. For out of sample projections, we fit a behavioral function to the in sample data that allows for the endogenous response of R t to movements in the lagged number of infected cases. We show that declines in measures of population mobility tend to precede declines in the model implied reproduction numbers for each country. This pattern suggests that mandatory and voluntary stay at home behavior and social distancing during the early stages of the epidemic worked to reduce the effective reproduction number and mitigate the spread of COVID 19.

title: The reproduction number of COVID 19 and its correlation with public health interventions
abstract: Throughout the past six months, no number has dominated the public media more persistently than the reproduction number of COVID 19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID 19 pandemic. Here we explore the effectiveness of political interventions using the reproduction number of COVID 19 across Europe. We propose a dynamic SEIR epidemiology model with a time varying reproduction number, which we identify using machine learning. During the early outbreak, the basic reproduction number was 4.22 1.69, with maximum values of 6.33 and 5.88 in Germany and the Netherlands. By May 10, 2020, it dropped to 0.67 0.18, with minimum values of 0.37 and 0.28 in Hungary and Slovakia. We found a strong correlation between passenger air travel, driving, walking, and transit mobility and the effective reproduction number with a time delay of 17.24 2.00 days. Our new dynamic SEIR model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health.

title: Estimation of exponential growth rate and basic reproduction number of the coronavirus disease 2019 (COVID 19) in Africa
abstract: Since the first case of coronavirus disease 2019 (COVID 19) in Africa was detected on February 14, 2020, the cumulative confirmations reached 15 207 including 831 deaths by April 13, 2020. Africa has been described as one of the most vulnerable region with the COVID 19 infection during the initial phase of the outbreak, due to the fact that Africa is a great commercial partner of China and some other EU and American countries. Which result in large volume of travels by traders to the region more frequently and causing African countries face even bigger health threat during the COVID 19 pandemic. Furthermore, the fact that the control and management of COVID 19 pandemic rely heavily on a country's health care system, and on average Africa has poor health care system which make it more vulnerable indicating a need for timely intervention to curtail the spread. In this paper, we estimate the exponential growth rate and basic reproduction number R 0 of COVID 19 in Africa to show the potential of the virus to spread, and reveal the importance of sustaining stringent health measures to control the disease in Africa.  We analyzed the initial phase of the epidemic of COVID 19 in Africa between 1 March and 13 April 2020, by using the simple exponential growth model. We examined the publicly available materials published by the WHO situation report to show the potential of COVID 19 to spread without sustaining strict health measures. The Poisson likelihood framework is adopted for data fitting and parameter estimation. We modelled the distribution of COVID 19 generation interval (GI) as Gamma distributions with a mean of 4.7 days and standard deviation of 2.9 days estimated from previous work, and compute the basic reproduction number.  We estimated the exponential growth rate as 0.22 per day (95% CI 0.20 0.24) and the basic reproduction number, R 0 as 2.37 (95% CI 2.22 2.51) based on the assumption that the exponential growth starting from 1 March 2020. With an R 0 at 2.37, we quantified the instantaneous transmissibility of the outbreak by the time varying effective reproductive number to show the potential of COVID 19 to spread across African region.  The initial growth of COVID 19 cases in Africa was rapid and showed large variations across countries. Our estimates should be useful in preparedness planning against further spread of the COVID 19 epidemic in Africa.

title: Bidirectional impact of imperfect mask use on reproduction number of COVID 19: A next generation matrix approach
abstract: The use of masks as a means of reducing transmission of COVID 19 outside healthcare settings has proved controversial. Masks are thought to have two modes of effect: they prevent infection with COVID 19 in wearers; and prevent transmission by individuals with subclinical infection. We used a simple next generation matrix approach to estimate the conditions under which masks would reduce the reproduction number of COVID 19 under a threshold of 1. Our model takes into account the possibility of assortative mixing, where mask users interact preferentially with other mask users. We make 3 key observations: 1. Masks, even with suboptimal efficacy in both prevention of acquisition and transmission of infection, could substantially decrease the reproduction number for COVID 19 if widely used. 2. Widespread masking may be sufficient to suppress epidemics where R has been brought close to 1 via other measures (e.g. distancing) 3. "Assortment" within populations (the tendency for interactions between masked individuals to be more likely than interactions between masked and unmasked individuals) would rapidly erode the impact of masks. As such, mask uptake needs to be fairly universal to have an effect. This simple model suggests that widespread uptake of masking could be determinative in suppressing COVID 19 epidemics in regions with R(t) at or near 1.

title: Association of Social Distancing, Population Density, and Temperature With the Instantaneous Reproduction Number of SARS CoV 2 in Counties Across the United States
abstract: Question How is the instantaneous reproduction number of severe acute respiratory syndrome coronavirus 2 (SARS CoV 2) associated with social distancing, wet bulb temperature, and population density in counties across the United States?  In this cohort study of 211 counties in 46 states, social distancing, temperate weather, and lower population density were associated with a decrease in the instantaneous reproduction number of SARS CoV 2. Of these county specific factors, social distancing appeared to have the most substantial association with a reduction in SARS CoV 2 transmission. Meaning In this study, the instantaneous reproduction number of SARS CoV 2 varied substantially among counties; the associations between the reproduction number and county specific factors could inform policies to reduce SARS CoV 2 transmission in selective and heterogeneous communities.

title: Modelling of reproduction number for COVID 19 in India and high incidence states
abstract: Since the onset of the COVID 19 in China, forecasting and projections of the epidemic based on epidemiological models have been in the centre stage. Researchers have used various models to predict the maximum extent of the number of cases and the time of peak. This yielded varying numbers. This paper aims to estimate the effective reproduction number (R) for COVID 19 over time using incident number of cases that are reported by the government.  Exponential Growth method to estimate reproduction rate R0, and Time dependent method to calculate the effective reproduction number (dynamic) were used. "R0" package in R software was used to estimate these statistics.  The basic reproduction number (R0) for India was estimated at 1.379 (95% CI: 1.375, 1.384) This was 1.450 (1.441, 1.460) for Maharashtra, 1.444 (1.430, 1.460) for Gujarat, 1.297 (1.284, 1.310) for Delhi and 1.405 (1.389, 1.421) for Tamil Nadu. In India, the R at the first week from March 2 8, 2020 was 3.2. It remained around 2 units for three weeks, from March 9 29, 2020. After March 2020, it started declining and reached around 1.3 in the following week suggesting a stabilisation of the transmissibility rate.  The study estimated a baseline R0 of 1.379 for India. It also showed that the R was getting stabilised from first week of April (R 1.1) despite the increase in March. This suggested that in due course there will be a reversal of epidemic. However, these analyses should be revised periodically.

title: Incubation Period and Reproduction Number for novel coronavirus (COVID 19) infections in India
abstract: Novel coronavirus (COVID 19) rapidly spread from China to other parts of the world. Knowledge of incubation period and reproduction number is important in controlling any epidemic. The distribution of these parameters helps estimate the epidemic size and transmission potential of the disease. We estimated incubation period and reproduction number of COVID 19 for India utilizing data reported by Ministry of Health and Family Welfare (MoHFW) Government of India (GOI) and data in public domain. The mean incubation period seems to be larger at 6.93 (SD=5.87, 95% CI: 6.11, 7.75) and 95th percentile estimate for best fit normal distribution is 17.8 days. Weibull distribution, the best fit for the reproduction number estimated pre lockdown reproduction number as 2.6 (95% CI=2.34, 2.86) and post lockdown reduced to 1.57 (95% CI=1.3 1.84) implying effectiveness of the epidemic response strategies. The herd immunity is estimated between 36 to 61% for R0 of 1.57 and 2.6 respectively.

title: Serial interval and time varying reproduction number estimation for COVID 19 in western Iran
abstract: There is no report on the serial interval (SI) of coronavirus disease 2019 (COVID 19) in Iran, the present report aims to estimate the SI and time varying R of COVID 19 in western Iran. In this study, there were 1477 confirmed, probable and suspected cases of severe acute respiratory syndrome coronavirus 2 for Kermanshah from 22 February to 9 April. The close contacts of the confirmed cases were identified using telephone follow up of patients and their contacts. The SI distribution was used as an alternative. We fitted different models using the clinical onset dates of patients with their close contact (infector infectee) Also, we applied a 'serial interval from sample' approach as a Bayesian methodology for estimating reproduction number. From 22 February to 29 March, 247 COVID 19 cases were confirmed by RT PCR. Close contact between 21 patients (21 infector infectee pairs) including 12 primary cases and 21 secondary cases, was confirmed. The mean and standard deviation of the SI were estimated as 5.71 and 3.89 days. The R varied from 0.79 to 1.88 for a 7 day time lapse and ranged from 0.92 to 1.64 for a 14 day time lapse on raw data. Also, the R varied from 0.83 to 1.84 for 7 day time lapse and from 0.95 to 1.54 for a 14 day time lapse using moving average data, respectively. It can be concluded that the low reproduction number for COVID 19 in Kermanshah province is an indication of the effectiveness of preventive and interventive programmes such as quarantine and isolation. Consequently, continuing these preventive measures is highly recommended.