scholarly journals 2019-nCoV Transmission in Hubei Province, China: Stochastic and Deterministic Analyses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zhiming Li ◽  
Zhidong Teng ◽  
Changxing Ma
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Optimal Strategies ◽  
Hubei Province ◽  
Transmission Mechanism ◽  
Control Input ◽  
Deterministic Models ◽  
Novel Coronavirus ◽  
And Diffusion ◽  
Quasi Stationary Distribution

Currently, a novel coronavirus (2019-nCoV) causes an outbreak of viral pneumonia in Hubei province, China. In this paper, stochastic and deterministic models are proposed to investigate the transmission mechanism of 2019-nCoV from 15 January to 5 February 2020 in Hubei province. For the deterministic model, basic reproduction number R0 is defined and endemic equilibrium is given. Under R0>1, quasi-stationary distribution of the stochastic process is approximated by Gaussian diffusion. Residual, sensitivity, dynamical, and diffusion analyses of the models are conducted. Further, control variables are introduced to the deterministic model and optimal strategies are provided. Based on empirical results, we suggest that the first and most important thing is to control input, screening, treatment, and isolation.

scholarly journals Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanan Zhao ◽  
Daqing Jiang
Keyword(s):  
Epidemic Model ◽  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Standard Technique ◽  
Deterministic Models ◽  
Sis Epidemic Model ◽  
Disease Free ◽  
Sis Epidemic

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction numberR0is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value ofR0. IfR0≤1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, ifR0>1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

scholarly journals Analysis of the stochastic model for predicting the novel coronavirus disease

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ndolane Sene
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
The Novel ◽  
Stochastic Perturbations ◽  
Numerical Investigations ◽  
Rapid Spread ◽  
The World ◽  
Novel Coronavirus

Abstract In this paper, we propose a mathematical model to predict the novel coronavirus. Due to the rapid spread of the novel coronavirus disease in the world, we add to the deterministic model of the coronavirus the terms of the stochastic perturbations. In other words, we consider in this paper a stochastic model to predict the novel coronavirus. The equilibrium points of the deterministic model have been determined, and the reproduction number of our deterministic model has been implemented. The asymptotic behaviors of the solutions of the stochastic model around the equilibrium points have been studied. The numerical investigations and the graphical representations obtained with the novel stochastic model are made using the classical stochastic numerical scheme.

scholarly journals Dynamics of cholera epidemic models in fluctuating environments

2020 ◽  
Vol 21 (02) ◽  
pp. 2150011
Author(s):  
Tuan Anh Phan ◽  
Jianjun Paul Tian ◽  
Bixiang Wang
Keyword(s):  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Deterministic Models ◽  
Dynamical Behaviors ◽  
All Solutions ◽  
Number Formula ◽  
Asymptotical Analysis ◽  
The Basic Reproduction Number

Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value [Formula: see text] is defined in terms of the basic reproduction number [Formula: see text] for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When [Formula: see text], the cholera infection will extinct within finite periods of time almost surely. When [Formula: see text], the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number [Formula: see text] for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that [Formula: see text], the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.

scholarly journals A deterministic epidemic model for the emergence of COVID-19 in China

2020 ◽  
Author(s):  
Meng Wang ◽  
Jingtao Qi
Keyword(s):  
Prevention And Control ◽  
Reproduction Number ◽  
Chinese Mainland ◽  
Hubei Province ◽  
Control Measures ◽  
The Novel ◽  
Health Authorities ◽  
Prevention And Control Measures ◽  
Novel Coronavirus ◽  
And Control

AbstractCoronavirus disease (COVID-19) broke out in Wuhan, Hubei province, China, in December 2019 and soon after Chinese health authorities took unprecedented prevention and control measures to curb the spreading of the novel coronavirus-related pneumonia. We develop a mathematical model based on daily updates of reported cases to study the evolution of the epidemic. With the model, on 95% confidence level, we estimate the basic reproduction number, R0 = 2.82 ± 0.11, time between March 19 and March 21 when the effective reproduction number becoming less than one, the epidemic ending after April 2 and the total number of confirmed cases approaching 14408 ± 429 on the Chinese mainland excluding Hubei province.

Current updates on COVID-19 - A review

2020 ◽  
Vol 10 (1) ◽  
pp. 1-8
Author(s):  
Ghotekar D S ◽  
Vishal N Kushare ◽  
Sagar V Ghotekar
Keyword(s):  
World Health Organization ◽  
Common Cold ◽  
Respiratory Diseases ◽  
Gastrointestinal Diseases ◽  
Hubei Province ◽  
World Health ◽  
The World ◽  
The Common ◽  
Novel Coronavirus ◽  
Health Organization

Coronaviruses are a family of viruses that cause illness such as respiratory diseases or gastrointestinal diseases. Respiratory diseases can range from the common cold to more severe diseases. A novel coronavirus outbreak was first documented in Wuhan, Hubei Province, China in December 2019. The World Health Organization (WHO) has declared the coronavirus disease 2019 (COVID-19) a pandemic. A global coordinated effort is needed to stop the further spread of the virus. A novel coronavirus (nCoV) is a new strain that has not been identified in humans previously. Once scientists determine exactly what coronavirus it is, they give it a name (as in the case of COVID-19, the virus causing it is SARS-CoV-2).

The Risk of Death in 2019 Novel Coronavirus Disease (COVID-19) in Hubei Province

2020 ◽  
Author(s):  
Vincent Yi Fong Su ◽  
Yao-Hsu Yang ◽  
Kuang-Yao Yang ◽  
Kun-Ta Chou ◽  
Wei-Juin Su ◽  
...  
Keyword(s):  
Hubei Province ◽  
Risk Of Death ◽  
Novel Coronavirus

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Determinism

2021 ◽  
Vol 20 (5) ◽  
pp. 1-34
Author(s):  
Edward A. Lee
Keyword(s):  
Quantum Physics ◽  
Deterministic Model ◽  
Physical World ◽  
Deterministic Models ◽  
Newtonian Physics ◽  
Physical Systems ◽  
Newton’S Laws ◽  
And Behavior

This article is about deterministic models, what they are, why they are useful, and what their limitations are. First, the article emphasizes that determinism is a property of models, not of physical systems. Whether a model is deterministic or not depends on how one defines the inputs and behavior of the model. To define behavior, one has to define an observer. The article compares and contrasts two classes of ways to define an observer, one based on the notion of “state” and another that more flexibly defines the observables. The notion of “state” is shown to be problematic and lead to nondeterminism that is avoided when the observables are defined differently. The article examines determinism in models of the physical world. In what may surprise many readers, it shows that Newtonian physics admits nondeterminism and that quantum physics may be interpreted as a deterministic model. Moreover, it shows that both relativity and quantum physics undermine the notion of “state” and therefore require more flexible ways of defining observables. Finally, the article reviews results showing that sufficiently rich sets of deterministic models are incomplete. Specifically, nondeterminism is inescapable in any system of models rich enough to encompass Newton’s laws.

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