scholarly journals Estimating the last day for COVID-19 outbreak in mainland China

2020 ◽  
Author(s):  
Quentin Griette ◽  
Zhihua Liu ◽  
Pierre Magal
Keyword(s):  
Probability Distribution ◽  
Mainland China ◽  
Stochastic Simulations ◽  
Absolute Difference ◽  
Cumulative Probability ◽  
List Type ◽  
Deterministic Approach ◽  
Cumulative Probability Distribution ◽  
The Individual ◽  
Reported Data

1AbstractOur main aim is to estimate the last day for COVID-19 outbreak in mainland China. We developed mathematical models to predict reasonable bounds on the date of end of the COVID-19 epidemics in mainland China with strong quarantine and testing measures for a sufficiently long time. We used reported data in China from January 20, 2020 to April 9, 2020. We firstly used a deterministic approach to obtain a formula to compute the probability distribution of the extinction date by combining the models and continuous-time Markov processes. Then we present the individual based model (IMB) simulations to compare the result by deterministic approach and show the absolute difference between the estimated cumulative probability distribution computed by simulations and formula. We provide the predictions of the last day of epidemic for different fractions f of asymptomatic infectious that become reported symptomatic infectious.2Key pointsWe conducted a study of the last day for COVID-19 outbreak in mainland China. By using a deterministic approach, we obtain a formula to compute the probability distribution of the extinction date.We estimated the probability distribution of the extinction date by individual-based stochastic simulations and compared the results from two methods (simulations and formula).Stochastic simulations were used to precisely estimate the cumulative probability distribution of the date of end of the epidemic.We predict the last day of epidemic for different fractions f of asymptomatic infectious that become reported symptomatic infectious.

Branching design of the bronchial tree based on a diameter-flow relationship

1997 ◽  
Vol 82 (3) ◽  
pp. 968-976 ◽  
Author(s):  
Hiroko Kitaoka ◽  
Béla Suki
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Design Method ◽  
Random Variable ◽  
Bronchial Tree ◽  
Cumulative Probability ◽  
Cumulative Probability Distribution ◽  
Tree Models ◽  
Flow Division

Kitaoka, Hiroko, and Béla Suki. Branching design of the bronchial tree based on a diameter-flow relationship. J. Appl. Physiol. 82(3): 968–976, 1997.—We propose a method for designing the bronchial tree where the branching process is stochastic and the diameter ( d) of a branch is determined by its flow rate (Q). We use two principles: the continuum equation for flow division and a power-law relationship between d and Q, given by Q ∼ d n, where n is the diameter exponent. The value of n has been suggested to be ∼3. We assume that flow is divided iteratively with a random variable for the flow-division ratio, defined as the ratio of flow in the branch to that in its parent branch. We show that the cumulative probability distribution function of Q, P(>Q) is proportional to Q−1. We analyzed prior morphometric airway data (O. G. Raabe, H. C. Yeh, H. M. Schum, and R. F. Phalen, Report No. LF-53, 1976) and found that the cumulative probability distribution function of diameters, P(> d), is proportional to d −n, which supports the validity of Q ∼ d n since P(>Q) ∼ Q−1. This allowed us to assign diameters to the segments of the flow-branching pattern. We modeled the bronchial trees of four mammals and found that their statistical features were in good accordance with the morphometric data. We conclude that our design method is appropriate for robust generation of bronchial tree models.

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