Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching

Stationary distribution, extinction, density function and periodicity of an n-species competition system with infinite distributed delays and nonlinear perturbations

“…This implies that the existence of the distribution ℓ(•) cannot be directly verified due to the finite number of iterations of the computer simulation. If (A 1 )-(A 2 ) hold, by a similar argument in [79], one obtains from Theorem 5.3 that for any finite time interval [0, T ], system (6) will have a transient distribution function ℓ(•, T ) that relies on the variable T , and the function ℓ(•, T ) can reflect most of the dynamical properties of ℓ(•). Also, for some sufficiently large T , ℓ(•, T ) will undulate around ℓ(•) and satisfies lim sup T →∞ || ℓ(z, T ) − ℓ(z)|| = 0 for any z ∈ R n 2 + .…”

“…In [39], Lv et al considered an impulsive chemostat model with nonlinear perturbation and studied the impact of impulsive toxicant input on the survival of microorganisms. Zhou et al [79] established a weak criterion for the existence of an ergodic stationary distribution of a hybrid SEQIHR epidemic model with continuous-time Markov chain, nonlinear perturbations and media coverage. Inspired by the above, in this paper, all the growth rates b k and intraspecific competition coefficients a kk (k = 1, 2, ..., n) of system (3) should be regarded as random variables b k and a kk , respectively, and are perturbed by…”

The Power of Delay on a Stochastic Epidemic Model in a Switching Environment

“…us, the system frequently transitions from one regime to another. Many scholars studied the effect of telegraphic noise on the transmission of an epidemic (see, for example, [18][19][20][21][22][23]).…”

A multi‐group SEIRI epidemic model with logistic population growth under discrete Markov switching: Extinction, persistence, and positive recurrence

“…Zhang et al 21 constructed a stochastic eco‐epidemiological model with disease in predators, and analyzed the fundamental properties of their model. Furthermore, it has been shown that modeling the behavior of dynamical systems by stochastic differential equations with colored noises has more advantages than deterministic modeling 22–33 . Gray et al 25 first put forward and studied a piecewise deterministic SIS epidemic model with Markovian switching.…”

“…Gray et al 25 first put forward and studied a piecewise deterministic SIS epidemic model with Markovian switching. Zhou et al 29 studied a hybrid stochastic SEQIHR epidemic model with media coverage and obtained the sufficient conditions for disease extinction and the existence of an ergodic stationary distribution of stochastic model. Tuong et al 33 investigated a stochastic SIRS model perturbed by both white noise and colored noise, and they obtained the threshold which is used to classify the extinction and permanence of the disease.…”