scholarly journals The reproductive number R0 of COVID-19 based on estimate of a statistical time delay dynamical system

2020 ◽  
Author(s):  
Nian Shao ◽  
Jin Cheng ◽  
Wenbin Chen
Keyword(s):  
Dynamical System ◽  
Growth Rate ◽  
Time Delay ◽  
Dynamic System ◽  
Reproductive Number ◽  
Generation Interval ◽  
Delay Dynamical System ◽  
Simulation Results ◽  
Statistical Time

AbstractIn this paper, we estimate the reproductive number R0 of COVID-19 based on Wallinga and Lipsitch framework [11] and a novel statistical time delay dynamic system. We use the observed data reported in CCDC’s paper to estimate distribution of the generation interval of the infection and apply the simulation results from the time delay dynamic system as well as released data from CCDC to fit the growth rate. The conclusion is: Based our Fudan-CCDC model, the growth rate r of COVID-19 is almost in [0.30, 0.32] which is larger than the growth rate 0.1 estimated by CCDC [9], and the reproductive number R0 of COVID-19 is estimated by 3.25 ≤ R0 ≤ 3.4 if we simply use R = 1 + r ∗ Tc with Tc = 7.5, which is bigger than that of SARS. Some evolutions and predictions are listed.

scholarly journals Dynamical system of the growth of COVID-19 with controller

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dania Altulea ◽  
Rafida M. Elobaid
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Growth Rate ◽  
Dynamic System ◽  
Unique Solution ◽  
Population Dynamic ◽  
Integral Control ◽  
The Social ◽  
Social Separation ◽  
Strong Control

AbstractRecently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.

TWO-SCROLL ATTRACTOR IN A DELAY DYNAMICAL SYSTEM

2007 ◽  
Vol 17 (10) ◽  
pp. 3455-3460 ◽  
Author(s):  
ARŪNAS TAMAŠEVIČIUS ◽  
TATJANA PYRAGIENĖ ◽  
MANTAS MEŠKAUSKAS
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Nonlinear Function ◽  
Delay System ◽  
The Novel ◽  
Type Function ◽  
Delay Dynamical System ◽  
Glass Type ◽  
Electronic Oscillator

Nonvanishing 𐑍-shaped nonlinear function has been introduced in delay dynamical system instead of commonly used Mackey–Glass type function. Depending on time delay the system exhibits not only mono-scroll, but also more complex two-scroll hyperchaotic attractors. Delay system with the novel nonlinear function can be implemented as an analogue electronic oscillator.

scholarly journals How generation intervals shape the relationship between growth rates and reproductive numbers

2006 ◽  
Vol 274 (1609) ◽  
pp. 599-604 ◽  
Author(s):  
J Wallinga ◽  
M Lipsitch
Keyword(s):  
Growth Rate ◽  
Infectious Diseases ◽  
Emerging Infectious Diseases ◽  
Reproductive Number ◽  
Empirical Estimate ◽  
Management Tools ◽  
Generation Interval ◽  
The Mean ◽  
The Relationship ◽  
Interval Distribution

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R . For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r . Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

Determination and modelling of the formative and statistical time delay in neon

2007 ◽  
Vol 38 (1) ◽  
pp. 73-78 ◽  
Author(s):  
V. Lj. Marković ◽  
S. N. Stamenković ◽  
S. R. Gocić ◽  
S. M. Durić
Keyword(s):  
Time Delay ◽  
Statistical Time

scholarly journals A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Parameter Identification ◽  
Typical Feature ◽  
The Novel ◽  
Isolation Rate ◽  
High Isolation ◽  
The Government ◽  
System With Time Delay ◽  
Official Data

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

Comprehensive Analysis for Influence of Controllable Damper Time Delay on Semi-Active Suspension Control Strategies

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Yechen Qin ◽  
Feng Zhao ◽  
Zhenfeng Wang ◽  
Liang Gu ◽  
Mingming Dong
Keyword(s):  
Time Delay ◽  
Dynamic Characteristics ◽  
Ride Comfort ◽  
Hybrid Control ◽  
Sliding Mode ◽  
Control Strategies ◽  
Active Suspension ◽  
Test System ◽  
Suspension Control ◽  
Simulation Results

This paper presents a comprehensive comparison and analysis for the effect of time delay on the five most representative semi-active suspension control strategies, and refers to four unsolved problems related to semi-active suspension performance and delay mechanism that existed. Dynamic characteristics of a commercially available continuous damping control (CDC) damper were first studied, and a material test system (MTS) load frame was used to depict the velocity-force map for a CDC damper. Both inverse and boundary models were developed to determine dynamic characteristics of the damper. In addition, in order for an improper damper delay of the form t+τ to be corrected, a delay mechanism of controllable damper was discussed in detail. Numerical simulation for five control strategies, i.e., modified skyhook control SC, hybrid control (HC), COC, model reference sliding mode control (MRSMC), and integrated error neuro control (IENC), with three different time delays: 5 ms, 10 ms, and 15 ms was performed. Simulation results displayed that by changing control weights/variables, performance of all five control strategies varied from being ride comfort oriented to being road handling oriented. Furthermore, increase in delay time resulted in deterioration of both ride comfort and road handling. Specifically, ride comfort was affected more than road handling. The answers to all four questions were finally provided according to simulation results.

scholarly journals Precise regulation of the relative rates of surface area and volume synthesis in bacterial cells growing in dynamic environments

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Handuo Shi ◽  
Yan Hu ◽  
Pascal D. Odermatt ◽  
Carlos G. Gonzalez ◽  
Lichao Zhang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Time Delay ◽  
Surface Area ◽  
Environmental Changes ◽  
Volume Ratio ◽  
Dynamic Environments ◽  
Bacterial Cells ◽  
Bacterial Growth Rate ◽  
State Size ◽  
Insight Into

AbstractThe steady-state size of bacterial cells correlates with nutrient-determined growth rate. Here, we explore how rod-shaped bacterial cells regulate their morphology during rapid environmental changes. We quantify cellular dimensions throughout passage cycles of stationary-phase cells diluted into fresh medium and grown back to saturation. We find that cells exhibit characteristic dynamics in surface area to volume ratio (SA/V), which are conserved across genetic and chemical perturbations as well as across species and growth temperatures. A mathematical model with a single fitting parameter (the time delay between surface and volume synthesis) is quantitatively consistent with our SA/V experimental observations. The model supports that this time delay is due to differential expression of volume and surface-related genes, and that the first division after dilution occurs at a tightly controlled SA/V. Our minimal model thus provides insight into the connections between bacterial growth rate and cell shape in dynamic environments.

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