Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

doi:10.1016/j.cnsns.2017.11.028

Cited by 102 publications

(44 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By the literature [34], system (26) has a unique solution Proof To prove Theorem 4.2, we just have to verify that conditions (i), (ii) and (iii) in Lemma 2.3 be satisfied. First, assumption q ij > 0 for i = j in Sect.…”

Section: Extinction Of the Disease And The Ergodic Stationary Distribmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

View full text Add to dashboard Cite

In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtained firstly. Then we show that the stochastic system has at least one nontrivial positive T-periodic solution under some conditions. For the model that are both disturbed by the white noise and telephone noise, we construct a suitable Lyapunov functions to verify the existence of a unique ergodic stationary distribution. Meanwhile, the sufficient condition for the extinction of the disease is also established. Finally, examples are introduced to illustrate the theoretical analysis. MSC: 60H10; 65C30; 91B70

show abstract

Section: Extinction Of the Disease And The Ergodic Stationary Distribmentioning

confidence: 99%

“…In the real world, besides white noise, the system may be disturbed by many other noises. For example, telephone noise often causes the system to switch from one state to another [34,35]. Recently, a large number of researchers have widely concerned the stochastic models with regime switching (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Since stationary distribution of stochastic system means that all the individuals can be coexistent and persistent in the long term, many authors proved the existence of a unique ergodic stationary distribution (see [28,29,46,50,51] and the references cited therein). It is worthy to note that in those literatures the proofs depend heavily on the uniform ellipticity condition.…”

Section: Theorem 21 For Any Given Initial Value Smentioning

confidence: 99%

“…However, the white noise cannot describe the phenomena that the population may suffer sudden catastrophic shocks or alien species invasion in nature [40] . The telegraph noise (namely, color noise) can be illustrated as a switching between two or more regimes of environment, which differ by factors such as nutrition or as rain falls [41] .…”

Section: Introductionmentioning

confidence: 99%

“…The telegraph noise (namely, color noise) can be illustrated as a switching between two or more regimes of environment, which differ by factors such as nutrition or as rain falls [41] . Frequently, the switching among different environments is memoryless and the waiting time for the next switch is exponentially distributed [42,[44][45][46][47][48][49][50][51][52][53] . Thus we can model the regime switching by a continuous-time Markov chain with values in a finite state space, which drives the changes of the main parameters of epidemic models with state switchings of the Markov chain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

Lan

Lin

Wei

et al. 2019

Journal of the Franklin Institute

View full text Add to dashboard Cite

In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number R s 0 is established: the disease can be eradicated almost surely if R s 0 < 1 and under mild extra conditions, whereas if R s 0 > 1 , the densities of the distributions of the solution can converge in L 1 to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.

show abstract