The extinction and persistence of a stochastic SIR model

Ji, Chunyan; Jiang, Daqing

doi:10.1186/s13662-016-1068-z

Cited by 15 publications

(9 citation statements)

References 12 publications

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“…It is well known that environmental fluctuation plays an important role in the study of ecosystems. Therefore, many authors have introduced stochastic white noise into deterministic models to describe the effect of random noise [15][16][17][18][19][20][21][22][23][24][25][26][27]. For example, Han et al [16] obtained two systems admitting a unique random attractor under some conditions.…”

Section: 2)mentioning

confidence: 99%

Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model

2019

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Environmental fluctuations and toxin-producing phytoplankton are crucial factors affecting marine ecosystems. In this paper, we propose a stochastic phytoplankton-toxin phytoplankton-zooplankton model to study the effect of environmental fluctuations on extinction and persistence of the population. The results show that large environmental fluctuations may lead to the extinction of the population, and small environmental fluctuation can keep population weakly persistent in the mean. We also find that the noise-induced extinction of one phytoplankton population may lead to the density increase of the other phytoplankton population in two competitive phytoplankton populations. By constructing appropriate Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution of the model. Finally, numerical simulations are carried out to support our main results.

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Section: 2)mentioning

confidence: 99%

Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model

2019

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“…The amount of literature studying the properties of solutions of such models is huge, see e.g. Brauer and Castillo-Chávez, 2012 , Ji and Jiang, 2017 , Jiao et al, 2020 , Kuniya and Nakata, 2012 , Li and Muldowney, 1995 , Zhang and Teng, 2007 , Zhao et al, 2017 and the references therein among many others. In the present, much effort is taken in order to estimate the evolution of the COVID-19 pandemic, see e.g.…”

Section: Introductionmentioning

confidence: 99%

COVID-19 and other viruses: Holding back its spreading by massive testing

Sainz-Pardo

Valero

2021

Expert Systems with Applications

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The experience of Singapore and South Korea makes it clear that under certain circumstances massive testing is an effective way for containing the advance of the COVID-19. In this paper, we propose a modified SEIR model which takes into account tracing and massive testing, proving theoretically that more tracing and testing implies a reduction of the total number of infected people in the long run. We apply this model to the spreading of the first wave of the disease in Spain, obtaining numerical results. After that, we introduce a heuristic approach in order to minimize the COVID-19 spreading by planning effective test distributions among the populations of a region over a period of time. As an application, the impact of distributing tests among the counties of New York according to this method is computed in terms of the number of saved infected individuals.

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“…Quarantine can greatly reduce the probability of contact between infective and susceptible individuals. In recent years, a large number of epidemic models have been used in the study of disease prevention and control strategies [3][4][5][6][7][8][9][10][11][12][13][14]. The influence of quarantine measures on the second epidemic of plague in Europe was studied in literature [15].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior and threshold of a stochastic SIQS epidemic model with vertical transmission and Beddington–DeAngelis incidence

Chen

Zhao

2020

Adv Differ Equ

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This paper investigates a deterministic and stochastic SIQS epidemic model with vertical transmission and Beddington-DeAngelis incidence. Firstly, for the corresponding deterministic system, the global asymptotic stability of disease-free equilibrium and the endemic equilibrium is proved through the stability theory. Secondly, for the stochastic system, the threshold conditions which decide the extinction or permanence of the disease are derived. By constructing suitable Lyapunov functions, we investigate the oscillation behavior of the stochastic system solution near the endemic equilibrium. The results of this paper show that there exists a great difference between the deterministic and stochastic systems, which implies that the large stochastic noise contributes to inhibiting the spread of disease. Finally, in order to validate the theoretical results, a series of numerical simulations are presented.

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The extinction and persistence of a stochastic SIR model

Cited by 15 publications

References 12 publications

Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model

Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model

COVID-19 and other viruses: Holding back its spreading by massive testing

Asymptotic behavior and threshold of a stochastic SIQS epidemic model with vertical transmission and Beddington–DeAngelis incidence

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