Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

Guo, Yingjia

doi:10.1186/s13662-017-1424-7

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…For example, one may construct some more realistic but complex models, such as considering the effects of delay, complex network, pulse vaccination and Lévy noise. Some scholars have already done a great deal of work (see [34][35][36][37][38][39][40]). We leave these investigations for future work.…”

Section: Resultsmentioning

confidence: 99%

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

Wang

2020

Adv Differ Equ

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In this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

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Section: Resultsmentioning

confidence: 99%

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

Wang

2020

Adv Differ Equ

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“…For practical and realistic reasons, we consider that at the initial state, each compartment of our model is not empty. As in similar work done in [6] and [7] our study is organized as follows. In Section 2, we prove that the equation (13) has a unique global and positive solution.…”

Section: X(t-)mentioning

confidence: 99%

A Stochastic Model with Jumps for Smoking

COULIBALY¹,

N'zi²

2019

JAMCS

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Some stochastic epidemiological models are less significant. They do not take into account some sudden events that could disrupt the behavior of the studied phenomenon. In this work, we introduce a white noise and jumps in a deterministic SIRS model for smoking to take into account of the effects of randomly fluctuation and such sudden factors respectively. First of all we prove that the solution of the stochastic differential equation with jumps of the new modelis positive. Then we study the asymptotic behavior around the smoking-free equilibrium state and the smoking-present equilibrium state of the original deterministic model. Under certain conditions, we show that the solution oscillate respectively around these equilibrium states. We prove that the intensity of these oscillations depends on the magnitude of noise and the jump diffusion coefficient of our stochastic differential equation with jumps. To support our theoretical results, we realise numerical simulations. The observations confirm our conclusions.

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Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine

Gamboa

Lopez-Herrero

2020

Acta Biotheor

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An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number R 0 , which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, R 0 overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to R 0 are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.

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Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

Cited by 7 publications

References 21 publications

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

A Stochastic Model with Jumps for Smoking

Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine

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