2021
DOI: 10.3934/dcdsb.2020335
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Persistence and extinction of a stochastic SIS epidemic model with regime switching and Lévy jumps

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Cited by 6 publications
(3 citation statements)
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“…It is worth mentioning that although we have analyzed the influences of environmental heterogeneity and population movement on disease transmission, there are still other factors worth considering, such as stochastic perturbation [27,28,29], the periodic incidence rate, saturated treatment rate, advection [5,6,46], nonlocal dispersal [10], and boundary conditions [13,15,44]. We leave these as future research.…”
Section: Discussionmentioning
confidence: 99%
“…It is worth mentioning that although we have analyzed the influences of environmental heterogeneity and population movement on disease transmission, there are still other factors worth considering, such as stochastic perturbation [27,28,29], the periodic incidence rate, saturated treatment rate, advection [5,6,46], nonlocal dispersal [10], and boundary conditions [13,15,44]. We leave these as future research.…”
Section: Discussionmentioning
confidence: 99%
“…Consequently, we should employ the stochastic differential equation with significant discontinuities, so-called jumps [65] . Based on some nice properties: (i) stationary and independent increments (ii) sample paths which are almost surely right continuous with left limits, Lévy processes can be applied to many concrete and real situations [54] , [66] , [67] , [68] , [69] , [70] . To depict this randomness, Zhang and Wang in [57] proposed the following SIC epidemic model with Lévy perturbation: where …”
Section: Introductionmentioning
confidence: 99%
“…Other works have used two types of noise in their models. For example, Li and Guo [15] presented a stochastic SIS epidemic model in which they mixed three types of noise, namely, white noise, colored noise, and Lévy noise. In the works [16,17], the authors proposed models with delay and Markovian switching for ecological populations.…”
Section: Introductionmentioning
confidence: 99%