scholarly journals Fractal kinetics of COVID-19 pandemic (with update 3/1/20)

2020 ◽  
Author(s):  
Anna L. Ziff ◽  
Robert M. Ziff
Keyword(s):  
Power Law ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Small World ◽  
Rate Equations ◽  
The Novel ◽  
Daily Rate ◽  
Exponential Decline ◽  
Power Law Kinetics ◽  
Novel Coronavirus

AbstractWe give an update to the original paper posted on 2/17/20 – now (as of 3/1/20) the China deaths are rapidly decreasing, and we find an exponential decline to the power law similar to the that predicted by the network model of Vazquez [2006]. At the same time, we see non-China deaths increasing rapidly, and similar to the early behavior of the China statistics. Thus, we see three stages of the spread of the disease in terms of number of deaths: exponential growth, power-law behavior, and then exponential decline in the daily rate.(Original abstract) The novel coronavirus (COVID-19) continues to grow rapidly in China and is spreading in other parts of the world. The classic epidemiological approach in studying this growth is to quantify a reproduction number and infection time, and this is the approach followed by many studies on the epidemiology of this disease. However, this assumption leads to exponential growth, and while the growth rate is high, it is not following exponential behavior. One approach that is being used is to simply keep adjusting the reproduction number to match the dynamics. Other approaches use rate equations such as the SEIR and logistical models. Here we show that the current growth closely follows power-law kinetics, indicative of an underlying fractal or small-world network of connections between susceptible and infected individuals. Positive deviations from this growth law might indicate either a failure of the current containment efforts while negative deviations might indicate the beginnings of the end of the pandemic. We cannot predict the ultimate extent of the pandemic but can get an estimate of the growth of the disease.

scholarly journals Preliminary estimating the reproduction number of the coronavirus disease (COVID-19) outbreak in Republic of Korea from 31 January to 1 March 2020

2020 ◽  
Author(s):  
Zian Zhuang ◽  
Shi Zhao ◽  
Qianying Lin ◽  
Peihua Cao ◽  
Yijun Lou ◽  
...  
Keyword(s):  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Republic Of Korea ◽  
The Novel ◽  
Transmission Process ◽  
Novel Coronavirus ◽  
Dispersion Term ◽  
The Basic Reproduction Number

AbstractThe novel coronavirus disease 2019 (COVID-19) outbreak in Republic of Korea has caused 3736 cases and 18 deaths by 1 March 2020. We modeled the transmission process in Republic of Korea with a stochastic model and estimated the basic reproduction number R0 as 2.6 (95%CI: 2.3-2.9) and 3.2 (95%CI: 2.9-3.5), under the assumption that the exponential growth starting 31 January and 5 February, 2020, respectively. Estimates of dispersion term (k) were larger than 10 significantly, which implies few super-spreading events..

scholarly journals Early epidemiological assessment of the transmission potential and virulence of coronavirus disease 2019 (COVID-19) in Wuhan City: China, January-February, 2020

2020 ◽  
Author(s):  
Kenji Mizumoto ◽  
Katsushi Kagaya ◽  
Gerardo Chowell
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Public Health Intervention ◽  
Ecological Modelling ◽  
The Novel ◽  
Wuhan City ◽  
Transmission Potential ◽  
The World ◽  
Novel Coronavirus ◽  
Epidemiological Parameters

AbstractBackgroundSince the first cluster of cases was identified in Wuhan City, China, in December, 2019, coronavirus disease 2019 (COVID-19) rapidly spread around the world. Despite the scarcity of publicly available data, scientists around the world have made strides in estimating the magnitude of the epidemic, the basic reproduction number, and transmission patterns. Accumulating evidence suggests that a substantial fraction of the infected individuals with the novel coronavirus show little if any symptoms, which highlights the need to reassess the transmission potential of this emerging disease. In this study, we derive estimates of the transmissibility and virulence of COVID-19 in Wuhan City, China, by reconstructing the underlying transmission dynamics using multiple data sources.MethodsWe employ statistical methods and publicly available epidemiological datasets to jointly derive estimates of transmissibility and severity associated with the novel coronavirus. For this purpose, the daily series of laboratory–confirmed COVID-19 cases and deaths in Wuhan City together with epidemiological data of Japanese repatriated from Wuhan City on board government–chartered flights were integrated into our analysis.ResultsOur posterior estimates of basic reproduction number (R) in Wuhan City, China in 2019–2020 reached values at 3.49 (95%CrI: 3.39–3.62) with a mean serial interval of 6.0 days, and the enhanced public health intervention after January 23rd in 2020 was associated with a significantly reduced R at 0.84 (95%CrI: 0.81–0.88), with the total number of infections (i.e. cumulative infections) estimated at 1906634 (95%CrI: 1373500–2651124) in Wuhan City, elevating the overall proportion of infected individuals to 19.1% (95%CrI: 13.5–26.6%). We also estimated the most recent crude infection fatality ratio (IFR) and time–delay adjusted IFR at 0.04% (95% CrI: 0.03%–0.06%) and 0.12% (95%CrI: 0.08–0.17%), respectively, estimates that are several orders of magnitude smaller than the crude CFR estimated at 4.06%ConclusionsWe have estimated key epidemiological parameters of the transmissibility and virulence of COVID-19 in Wuhan, China during January-February, 2020 using an ecological modelling approach. The power of this approach lies in the ability to infer epidemiological parameters with quantified uncertainty from partial observations collected by surveillance systems.

scholarly journals Slow domain reconfiguration causes power-law kinetics in a two-state enzyme

2018 ◽  
Vol 115 (3) ◽  
pp. 513-518 ◽  
Author(s):  
Iris Grossman-Haham ◽  
Gabriel Rosenblum ◽  
Trishool Namani ◽  
Hagen Hofmann
Keyword(s):  
Free Energy ◽  
Single Molecule ◽  
Power Law ◽  
Energy Landscape ◽  
Rate Equations ◽  
Free Energy Landscape ◽  
Closed Domain ◽  
Single Molecule Fret ◽  
Power Law Kinetics ◽  
Interdomain Interactions

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.

scholarly journals The basic reproduction number and prediction of the epidemic size of the novel coronavirus (COVID-19) in Shahroud, Iran

2020 ◽  
Vol 148 ◽  
Author(s):  
A. Khosravi ◽  
R. Chaman ◽  
M. Rohani-Rasaf ◽  
F. Zare ◽  
S. Mehravaran ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Early Stage ◽  
Screening Tests ◽  
The Novel ◽  
Epidemic Size ◽  
Serial Interval ◽  
Novel Coronavirus ◽  
Interval Distribution ◽  
The Basic Reproduction Number

Abstract The aim of this study was to estimate the basic reproduction number (R0) of COVID-19 in the early stage of the epidemic and predict the expected number of new cases in Shahroud in Northeastern Iran. The R0 of COVID-19 was estimated using the serial interval distribution and the number of incidence cases. The 30-day probable incidence and cumulative incidence were predicted using the assumption that daily incidence follows a Poisson distribution determined by daily infectiousness. Data analysis was done using ‘earlyR’ and ‘projections’ packages in R software. The maximum-likelihood value of R0 was 2.7 (95% confidence interval (CI): 2.1−3.4) for the COVID-19 epidemic in the early 14 days and decreased to 1.13 (95% CI 1.03–1.25) by the end of day 42. The expected average number of new cases in Shahroud was 9.0 ± 3.8 cases/day, which means an estimated total of 271 (95% CI: 178–383) new cases for the period between 02 April to 03 May 2020. By day 67 (27 April), the effective reproduction number (Rt), which had a descending trend and was around 1, reduced to 0.70. Based on the Rt for the last 21 days (days 46–67 of the epidemic), the prediction for 27 April to 26 May is a mean daily cases of 2.9 ± 2.0 with 87 (48–136) new cases. In order to maintain R below 1, we strongly recommend enforcing and continuing the current preventive measures, restricting travel and providing screening tests for a larger proportion of the population.

scholarly journals Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 290
Author(s):  
Anwarud Din ◽  
Amir Khan ◽  
Anwar Zeb ◽  
Moulay Rchid Sidi Ammi ◽  
Mouhcine Tilioua ◽  
...  
Keyword(s):  
Hybrid Method ◽  
Reproduction Number ◽  
Real Data ◽  
The Novel ◽  
Order Analysis ◽  
The Laplace Transform ◽  
Case Application ◽  
Novel Coronavirus ◽  
Available Information ◽  
Fractional Orders

In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel type operator known as the Atangana-Baleanu-Caputo (ABC) derivative. We parametrize the model adopting available information of the disease from Pakistan in the period 9 April to 2 June 2020. We obtain the required solution with the help of a hybrid method, which is a combination of the decomposition method and the Laplace transform. Furthermore, a sensitivity analysis is carried out to evaluate the parameters that are more sensitive to the basic reproduction number of the model. Our results are compared with the real data of Pakistan and numerical plots are presented at various fractional orders.

scholarly journals Early Phylogenetic Estimate Of The Effective Reproduction Number Of 2019-nCoV

2020 ◽  
Author(s):  
Alessia Lai ◽  
Annalisa Bergna ◽  
Carla Acciarri ◽  
Massimo Galli ◽  
Gianguglielmo Zehender
Keyword(s):  
Exponential Growth ◽  
Doubling Time ◽  
Evolutionary Dynamics ◽  
Evolutionary Rate ◽  
Reproduction Number ◽  
R Value ◽  
Phylogenetic Estimate ◽  
Novel Coronavirus ◽  
Birth Death

ABSTRACTTo reconstruct the evolutionary dynamics of the 2019 novel coronavirus, 52 2019-nCOV genomes available on 04 February 2020 at GISAID were analysed.The two models used to estimate the reproduction number (coalescent-based exponential growth and a birth-death skyline method) indicated an estimated mean evolutionary rate of 7.8 × 10−4 subs/site/year (range 1.1×10−4–15×10−4).The estimated R value was 2.6 (range 2.1-5.1), and increased from 0.8 to 2.4 in December 2019. The estimated mean doubling time of the epidemic was between 3.6 and 4.1 days.This study proves the usefulness of phylogeny in supporting the surveillance of emerging new infections even as the epidemic is growing.

scholarly journals Transmission potential of the novel coronavirus (COVID-19) onboard the Diamond Princess Cruises Ship, 2020

2020 ◽  
Author(s):  
Kenji Mizumoto ◽  
Gerardo Chowell
Keyword(s):  
Mathematical Modeling ◽  
Time Series ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
The Novel ◽  
Epidemic Threshold ◽  
Transmission Potential ◽  
Incidence Data ◽  
The Mean ◽  
Novel Coronavirus

AbstractAn outbreak of COVID-19 developed aboard the Princess Cruises Ship during January-February 2020. Using mathematical modeling and time-series incidence data describing the trajectory of the outbreak among passengers and crew members, we characterize how the transmission potential varied over the course of the outbreak. Our estimate of the mean reproduction number in the confined setting reached values as high as ∼11, which is higher than mean estimates reported from community-level transmission dynamics in China and Singapore (approximate range: 1.1-7). Our findings suggest that Rt decreased substantially compared to values during the early phase after the Japanese government implemented an enhanced quarantine control. Most recent estimates of Rt reached values largely below the epidemic threshold, indicating that a secondary outbreak of the novel coronavirus was unlikely to occur aboard the Diamond Princess Ship.

scholarly journals Modelling daily infections with Covid-19 in Germany, France, and Sweden with a trend line based on day-to-day reproduction rates

2020 ◽  
Author(s):  
Dieter Mergel
Keyword(s):  
Steady State ◽  
Power Law ◽  
Exponential Growth ◽  
Initial Phase ◽  
Private Life ◽  
Reproduction Rate ◽  
Infection Rates ◽  
Public And Private ◽  
Trend Line ◽  
Exponential Decline

AbstractThe number of persons daily infected with Covid-19 as a function of time is fitted with a trend line based on an iterative power law (n = ¼) with a day-to-day reproduction rate modelled with a polyline. From the trend line, an effective reproduction rate Reff of Covid-19 is calculated. In all three states, Reff decreases in the initial phase to one indicating that there is no exponential growth. In Sweden, a steady state with Reff around 1 and a high daily infection rates. In Germany, Reff = 1 is reached before public and private life is restricted. With these restrictions, Reff is reduced further to 0.87 (CI95 [0.83.; 0.91]) after 40 days so that, speculatively estimated, 9500 premature fatalities within two months may have been avoided. In France, it seems that only strongly restricting private life sends Reff down to 1 and further down to about 0.7 (CI95 [0.3; 1.1]) after 45 days. With Reff permanently below 1, an exponential decline of the number of daily infections is observed in Germany and France.

scholarly journals Purely data-driven exploration of COVID-19 pandemic after three months of the outbreak

2020 ◽  
Author(s):  
Shirali Kadyrov ◽  
Hayot Berk Saydaliev
Keyword(s):  
Reproduction Number ◽  
Statistical Tests ◽  
Disease Outbreak ◽  
Data Driven ◽  
The Novel ◽  
Epidemic Modeling ◽  
Death Rates ◽  
Sir Epidemic ◽  
Novel Coronavirus ◽  
Epidemiological Characteristics

AbstractIt has been three months since the novel coronavirus (COVID-19) pandemic outbreak. Many research studies were carried to understand its epidemiological characteristics in the early phase of the disease outbreak. The current study is yet another contribution to better understand the disease properties by parameter estimation of mathematical SIR epidemic modeling. The authors use Johns Hopkins University’s dataset to estimate the basic reproduction number of COVID-19 for representative countries (Japan, Germany, Italy, France, and Netherlands) selected using cluster analysis. As a by-product, the authors estimate transmission, recovery, and death rates for each selected country and carry statistical tests to see if there are any significant differences.

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