Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

Li, Fēi; Zhang, Shengqiang; Meng, Xinzhu

doi:10.1007/s40314-019-0857-x

Cited by 37 publications

(15 citation statements)

References 35 publications

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“…In order to make this model more reasonable, we can also investigate delay stochastic differential equation models, control stochastic differential equation models, and impulsive stochastic differential equation models of system (2) for further work. The approaches are shown in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Discussionmentioning

confidence: 99%

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Liu

Meng

2020

Symmetry

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In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

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Section: Discussionmentioning

confidence: 99%

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Liu

Meng

2020

Symmetry

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“…Theorem 1. For any given initial condition (6), model (5) has a unique global positive solution (x 1 (t), x 2 (t), u(t)), and the solution will remain in R 3 + with probability one.…”

Section: Existence and Uniqueness Of Globalmentioning

confidence: 99%

“…Theorem 3. For any given initial condition (6), if assumptions (A 1 ) and (A 2 ) hold at the same time, the solution (x 1 (t), x 2 (t), u(t)) of system (5) is persistent that…”

Section: Persistencementioning

confidence: 99%

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Dynamic Analysis of Stochastic Lotka–Volterra Predator‐Prey Model with Discrete Delays and Feedback Control

Liu

Zhao

2019

Complexity

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In this paper, a stochastic Lotka–Volterra predator-prey model with discrete delays and feedback control is studied. Firstly, the existence and uniqueness of global positive solution are proved. Further, we investigate the asymptotic property of stochastic system at the positive equilibrium point of the corresponding deterministic model and establish sufficient conditions for the persistence and extinction of the model. Finally, the correctness of the theoretical derivation is verified by numerical simulations.

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“…Indeed, stochastic models could be more appropriate way of modeling in comparison with their deterministic counterparts, since they can provide some additional degree of realism. By introducing (stochastic) environmental noise, many investigators have studied stochastic epidemic models [14][15][16][17][18][19][20][21][22][23] and stochastic population models [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. ey focus on the e ect of environmental uctuations on the dynamic behavior of these models.…”

Section: Introductionmentioning

confidence: 99%

Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

Wei

2020

Complexity

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In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations.

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Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function

Cited by 37 publications

References 35 publications

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Dynamic Analysis of Stochastic Lotka–Volterra Predator‐Prey Model with Discrete Delays and Feedback Control

Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

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