The Acceleration Index as a Test-Controlled Reproduction Number: Application to COVID-19 in France*

We show that the acceleration index, a novel indicator that measures acceleration and deceleration of viral spread (Baunez et al. 2020a,b), is essentially a test-controlled version of the reproduction number. As such it is a more accurate indicator to track the dynamics of an infectious disease outbreak in real time. We indicate a discrepancy between the acceleration index and the reproduction number, based on the infectivity and test rates and we provide a formal decomposition of this difference. When applied to French data for the ongoing COVID-19 pandemic, our decomposition shows that the reproduction number consistenly underestimates the resurgence of the pandemic since the summer of 2020, compared to the acceleration index which accounts for the time-varying volume of tests. From the comparison that we present here follows that the acceleration index is a sufficient statistic to track the pandemic’s propagation, as it captures in real time the sizeable time variation featured by viral circulation.JEL Classification NumbersI18; H12

Changing transmission dynamics of COVID-19 in China: a nationwide population-based piecewise mathematical modelling study

BackgroundThe first case of COVID-19 atypical pneumonia was reported in Wuhan, China on December 1, 2019. Since then, at least 33 other countries have been affected and there is a possibility of a global outbreak. A tremendous amount of effort has been made to understand its transmission dynamics; however, the temporal and spatial transmission heterogeneity and changing epidemiology have been mostly ignored. The epidemic mechanism of COVID-19 remains largely unclear.MethodsEpidemiological data on COVID-19 in China and daily population movement data from Wuhan to other cities were obtained and analyzed. To describe the transmission dynamics of COVID-19 at different spatio-temporal scales, we used a three-stage continuous-time Susceptible-Exposed-Infectious-Recovered (SEIR) meta-population model based on the characteristics and transmission dynamics of each stage: 1) local epidemic from December 1, 2019 to January 9, 2020; 2) long-distance spread due to the Spring Festival travel rush from January 10 to 22, 2020; and 3) intra-provincial transmission from January 23, 2020 when travel restrictions were imposed. Together with the basic reproduction number (R0) for mathematical modelling, we also considered the variation in infectivity and introduced the controlled reproduction number (Rc) by assuming that exposed individuals to be infectious; we then simulated the future spread of COVID across Wuhan and all the provinces in mainland China. In addition, we built a novel source tracing algorithm to infer the initial exposed number of individuals in Wuhan on January 10, 2020, to estimate the number of infections early during this epidemic.FindingsThe spatial patterns of disease spread were heterogeneous. The estimated controlled reproduction number (Rc) in the neighboring provinces of Hubei province were relatively large, and the nationwide reproduction number ‐ except for Hubei ‐ ranged from 0.98 to 2.74 with an average of 1.79 (95% CI 1.77‐1.80). Infectivity was significantly greater for exposed than infectious individuals, and exposed individuals were predicted to have become the major source of infection after January 23. For the epidemic process, most provinces reached their epidemic peak before February 10, 2020. It is expected that the maximum number of infections will be approached by the end of March. The final infectious size is estimated to be about 58,000 for Wuhan, 20,800 for the rest of Hubei province, and 17,000 for the other provinces in mainland China. Moreover, the estimated number of the exposed individuals is much greater than the officially reported number of infectious individuals in Wuhan on January 10, 2020.InterpretationThe transmission dynamics of COVID-19 have been changing over time and were heterogeneous across regions. There was a substantial underestimation of the number of exposed individuals in Wuhan early in the epidemic, and the Spring Festival travel rush played an important role in enhancing and accelerating the spread of COVID-19. However, China’s unprecedented large-scale travel restrictions quickly reduced Rc. The next challenge for the control of COVID-19 will be the second great population movement brought by removing these travel restrictions.

Estimation of the Time-Varying Reproduction Number of COVID-19 Outbreak in China

BackgroundThe 2019-nCoV outbreak in Wuhan, China has attracted world-wide attention. As of February 11, 2020, a total of 44730 cases of novel coronavirus-infected pneumonia associated with COVID-19 were confirmed by the National Health Commission of China.MethodsThree approaches, namely Poisson likelihood-based method (ML), exponential growth rate-based method (EGR) and stochastic Susceptible-Infected-Removed dynamic model-based method (SIR), were implemented to estimate the basic and controlled reproduction numbers.ResultsA total of 71 chains of transmission together with dates of symptoms onset and 67 dates of infections were identified among 5405 confirmed cases outside Hubei as reported by February 2, 2020. Based on this information, we find the serial interval having an average of 4.41 days with a standard deviation of 3.17 days and the infectious period having an average of 10.91 days with a standard deviation of 3.95 days.ConclusionsThe controlled reproduction number is declining. It is lower than one in most regions of China, but is still larger than one in Hubei Province. Sustained efforts are needed to further reduce the Rc to below one in order to end the current epidemic.

Activation of sperm in the female reproductive tract in mammals

The formation of a new diploidal organism is preceded by a series of mutual interactions of haploidal gametes. This process is very complicated and requires the prior activation of reproductive cells. Male gametes eventually mature in the female reproductive tract, acquiring mobility and fertilization. This process takes place in two stages. Sperms are first capacitated. This phenomenon is reversible and leads to structural, cytophysiological and biochemical changes in the sperm plasma membrane as well as to the sperm hyperactivation. Then, due to the contact with the zona pellucida of the oocyte, the irreversible acrosome reaction occurs. This process involves the fusion of the sperm plasma membrane with the outer membrane of the acrosome, the release of enzymes and exposure of the inner acrosome membrane. This enables sperm to penetrate towards the perivitelline space and oolemma. Contact with the oocyte initiates a series of interactions leading to egg activation and the fusion of gametes. Each of these stages involves many different factors that result in the recognition, attraction and adhesion of reproductive cells. Knowledge about the activation mechanisms can improve the effectiveness of supported and controlled reproduction techniques.