Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

2020 ◽  
pp. 2050085
Author(s):  
Luyao Xin ◽  
Yingxin Guo ◽  
Quanxin Zhu
Keyword(s):  
Mathematical Model ◽  
White Noise ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Deterministic Case ◽  
Epidemic Dynamics ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Permanence In Mean ◽  
Theoretical Results

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

scholarly journals A stochastic mathematical model of two different infectious epidemic under vertical transmission

2021 ◽  
Vol 19 (3) ◽  
pp. 2179-2192
Author(s):  
Xunyang Wang ◽  
◽  
Canyun Huang ◽  
Yixin Hao ◽  
Qihong Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Vertical Transmission ◽  
Biological Significance ◽  
Sufficient Conditions ◽  
Discussion Section ◽  
Stochastic Permanence ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Well Posed ◽  
Theoretical Results

<abstract><p>In this study, considering the effect of environment perturbation which is usually embodied by the alteration of contact infection rate, we formulate a stochastic epidemic mathematical model in which two different kinds of infectious diseases that spread simultaneously through both horizontal and vertical transmission are described. To indicate our model is well-posed and of biological significance, we prove the existence and uniqueness of positive solution at the beginning. By constructing suitable $ Lyapunov $ functions (which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation) and applying $ It\hat{o} $'s formula as well as $ Chebyshev $'s inequality, we also establish the sufficient conditions for stochastic ultimate boundedness. Furthermore, when some main parameters and all the stochastically perturbed intensities satisfy a certain relationship, we finally prove the stochastic permanence. Our results show that the perturbed intensities should be no greater than a certain positive number which is up-bounded by some parameters in the system, otherwise, the system will be surely extinct. The reliability of theoretical results are further illustrated by numerical simulations. Finally, in the discussion section, we put forward two important and interesting questions left for further investigation.</p></abstract>

scholarly journals Dynamical Analysis of a Stochastic Multispecies Turbidostat Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Mu ◽  
Zuxiong Li ◽  
Huili Xiang ◽  
Hailing Wang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Dilution Rate ◽  
Stochastic Analysis ◽  
Competitive Exclusion ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Stochastic Disturbance ◽  
Dynamical Behaviors ◽  
Theoretical Results

A stochastic turbidostat system in which the dilution rate is subject to white noise is investigated in this paper. First of all, sufficient conditions of the competitive exclusion among microorganisms are obtained by employing the techniques of stochastic analysis. Furthermore, the results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms. Finally, the theoretical results obtained in this contribution are illustrated by numerical simulations.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals A Stochastic Switched Epidemic Model with Two Epidemic Diseases

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Amine El Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Analytical Results ◽  
Stochastic Epidemic ◽  
Telegraph Noise ◽  
Stochastic Epidemic Model ◽  
Epidemic Diseases

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results.

scholarly journals Correlated Stochastic Epidemic Model for the Dynamics of SARS-CoV-2 with Vaccination

2021 ◽  
Author(s):  
Tahir Khan ◽  
Roman Ullah ◽  
Gul Zaman ◽  
Youssef Khatib
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Human Population ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Virus Spreading ◽  
Theoretical Results

Abstract We formulate a mathematical model has been proposed to describe the stochastic influence of SARS-CoV-2 virus with various sources of randomness and vaccination. We assume the various sources of ran-domness in each population groups by different Brownian motion. We develop the correlated stochastic model by taking into account the various sources of randomness by different Brownian motions and distributed the total human population in three groups of susceptible, infected and recovered with reservoir class. Because reservoir play a significant role in the transmission of SARS-CoV-2 virus spreading. Moreover, the vaccination of susceptible are also accorded. Once we formulate the correlated stochastic model, the existence and uniqueness of positive solution will be discussed to show the problem feasibility. The SARS-CoV-2 extinction as well as persistency will be also discussed and we will obtain the sufficient conditions for it. At the last all the theoretical results will be supported via numerical/graphical findings.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

scholarly journals A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

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