scholarly journals Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiaoqin Gao ◽  
Zhijiang Luo ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Lyapunov Method ◽  
Markovian Switching ◽  
Dynamics Analysis ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Global Positive Solution ◽  
Theoretical Results

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.

scholarly journals The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yanan Jiang ◽  
Liangjian Hu ◽  
Jianqiu Lu
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Markovian Switching ◽  
Theoretical Results

AbstractIn this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals Stability of a Nonlinear Stochastic Epidemic Model with Transfer from Infectious to Susceptible

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yanmei Wang ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Method ◽  
Deterministic Model ◽  
Vital Role ◽  
Nonlinear Incidence Rate ◽  
Sirs Model ◽  
Stochastic Epidemic ◽  
Almost Surely Exponential Stability ◽  
Theoretical Results ◽  
Disease Free

We investigate a stochastic SIRS model with transfer from infectious to susceptible and nonlinear incidence rate. First, using stochastic stability theory, we discuss stochastic asymptotic stability of disease-free equilibrium of this model. Moreover, if the transfer rate from infectious to susceptible is sufficiently large, disease goes extinct. Then, we obtain almost surely exponential stability of disease-free equilibrium, which implies that noises can lead to extinction of disease. By the Lyapunov method, we give conditions to ensure that the solution of this model fluctuates around endemic equilibrium of the corresponding deterministic model in average time. Furthermore, numerical simulations show that the fluctuation increases with increase in noise intensity. Finally, these theoretical results are verified by numerical simulations. Hence, noises play a vital role in epidemic transmission. Our results improve and extend previous related results.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

scholarly journals Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity

2021 ◽  
Vol 6 (11) ◽  
pp. 12359-12378
Author(s):  
Yuhuai Zhang ◽  
◽  
Xinsheng Ma ◽  
Anwarud Din ◽  
◽  
...  
Keyword(s):  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Noise Intensity ◽  
Epidemic Spreading ◽  
General Incidence Rate ◽  
Global Positive Solution ◽  
Simulation Results ◽  
Theoretical Results ◽  
Temporary Immunity

<abstract><p>In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.</p></abstract>

scholarly journals On stability of stochastic delay model for tumor-immune interaction

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1273-1283
Author(s):  
Marija Krstic
Keyword(s):  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Interaction Model ◽  
Reliable Data ◽  
Lyapunov Functionals ◽  
Resting Cells ◽  
Random Perturbations ◽  
Delay Model ◽  
Stochastic Delay ◽  
Global Positive Solution

In this paper we study a stochastic model for tumor-immune interaction with delay. More precisely, we extend the deterministic delay tumor-immune interaction model by introducing random perturbations and obtain stochastic model. For this model, we first prove existence and uniqueness of the global positive solution, and then, by using suitable Lyapunov functionals, we obtain stability conditions for the equilibrium state when tumor cells and resting cells approach their carrying capacities. We also carry numerical simulation with reliable data to illustrate our theoretical findings.

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 Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Permanence and Extinction of a Stochastic Delay Logistic Model with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun Lu ◽  
Xiaohua Ding
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Population Model ◽  
Logistic Model ◽  
Necessary Conditions ◽  
Biological Significance ◽  
Jump Process ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Sufficient And Necessary Conditions

This paper is concerned with a stochastic delay logistic model with jumps. Sufficient and necessary conditions for extinction are obtained as well as stochastic permanence. Numerical simulations are introduced to support the theoretical analysis results. The results show that the jump process can affect the properties of the population model significantly, which conforms to biological significance.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

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