scholarly journals Elementary time-delay dynamics of COVID-19 disease

2020 ◽  
Author(s):  
José Menéndez
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
South Korea ◽  
Ordinary Differential Equations ◽  
Delay Differential Equations ◽  
Survival Function ◽  
Elementary Model ◽  
Infected People ◽  
Delay Differential ◽  
Good Agreement

An elementary model of COVID-19 dynamics—based on time-delay differential equations with a step-like survival function—is shown to be in good agreement with data from China and South Korea. The time-delal approach overcomes the major limitation of standard Susceptible-Exposed-Infected-Recovered (SEIR) models based on ordinary differential equations, namely their inability to predict the observed curve of infected individuals as a function of time. The model is also applied to countries where the epidemic is in earlier stages, such as Italy and Spain, to obtain estimates of the total number of cases and peak number of infected people that might be observed.

scholarly journals The Sturm Separation Theorem for Impulsive Delay Differential Equations

2018 ◽  
Vol 71 (1) ◽  
pp. 65-70
Author(s):  
Alexander Domoshnitsky ◽  
Vladimir Raichik
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Delay Differential Equations ◽  
Independent Solution ◽  
Delay Equations ◽  
Separation Theorem ◽  
Linearly Independent ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential

Abstract Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour of solutions of delay equations. For instance, non-vanishing Wronskian ensures validity of the Sturm separation theorem (between two adjacent zeros of any solution there is one and only one zero of every other nontrivial linearly independent solution) for delay equations. We propose the Sturm separation theorem in the case of impulsive delay differential equations and obtain assertions about its validity.

scholarly journals Time delay identification in chaotic cryptosystems ruled by delay-differential equations

2005 ◽  
Vol 72 (5) ◽  
pp. 373 ◽  
Author(s):  
V. S. Udaltsov ◽  
L. Larger ◽  
J. P. Goedgebuer ◽  
A. Locquet ◽  
D. S. Citrin
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Delay Differential

scholarly journals Tumour Oscillation Analysis in Angiogenesis Models

2006 ◽  
Vol 1 ◽  
pp. 330
Author(s):  
P. Daugulis
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Oscillation Analysis ◽  
Point Analysis ◽  
Delay Differential

In this paper we describe Hopf point analysis for several systems of ordinary and time delay differential equations which encode the most important assumptions concerning anguigenesis processes induced by tumours It is shown that in most cases Hopf points exist only if time delays are nonzero and for most nonzero time delays there are Hopf points in these families of models.

scholarly journals Distribution of incubation periods of COVID-19 in the Canadian context

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Subhendu Paul ◽  
Emmanuel Lorin
Keyword(s):  
Computational Complexity ◽  
Confidence Interval ◽  
Differential Equations ◽  
Incubation Period ◽  
Delay Differential Equations ◽  
Canadian Context ◽  
Incubation Periods ◽  
Delay Differential ◽  
Novel Model ◽  
Good Agreement

AbstractWe propose a novel model based on a set of coupled delay differential equations with fourteen delays in order to accurately estimate the incubation period of COVID-19, employing publicly available data of confirmed corona cases. In this goal, we separate the total cases into fourteen groups for the corresponding fourteen incubation periods. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval(CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), corresponding to a good agreement with statistical supported studies. This model provides an almost zero-cost computational complexity to estimate the incubation period.

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