Periodic solution of a stochastic SIRS epidemic model with seasonal variation

Jin, Manli; Lin, Yuguo

doi:10.1080/17513758.2017.1396369

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…The effects of seasonal variation on disease dynamics have been studied in ODE models, e.g., (Bacaër and Guernaoui 2006 ; Bacaër 2007 ; Gao et al. 2014 ; Jin and Lin 2018 ; McLennan-Smith and Mercer 2014 ; Mitchell and Kribs 2017 ; Posny and Wang 2014 ; Schwartz and Smith 1983 ; Suparit et al. 2018 ; Vaidya and Wahl 2015 ; Wang et al.…”

Section: Introductionmentioning

confidence: 99%

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Disease Emergence in Multi-Patch Stochastic Epidemic Models with Demographic and Seasonal Variability

Nipa

Allen

2020

Bull Math Biol

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Factors such as seasonality and spatial connectivity affect the spread of an infectious disease. Accounting for these factors in infectious disease models provides useful information on the times and locations of greatest risk for disease outbreaks. In this investigation, stochastic multi-patch epidemic models are formulated with seasonal and demographic variability. The stochastic models are used to investigate the probability of a disease outbreak when infected individuals are introduced into one or more of the patches. Seasonal variation is included through periodic transmission and dispersal rates. Multi-type branching process approximation and application of the backward Kolmogorov differential equation lead to an estimate for the probability of a disease outbreak. This estimate is also periodic and depends on the time, the location, and the number of initial infected individuals introduced into the patch system as well as the magnitude of the transmission and dispersal rates and the connectivity between patches. Examples are given for seasonal transmission and dispersal in two and three patches.

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Section: Introductionmentioning

confidence: 99%

“… 2006 ) and in stochastic models, e.g., (Bacaër and Ait Dads 2014 ; Billings and Forgoston 2018 ; Breban et al. 2009 ; Jin and Lin 2018 ; Keeling et al. 2001 ; Lin et al.…”

Section: Introductionmentioning

confidence: 99%

Disease Emergence in Multi-Patch Stochastic Epidemic Models with Demographic and Seasonal Variability

Nipa

Allen

2020

Bull Math Biol

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“…Recently, many authors have studied epidemic models with the effect of seasonal variation and stochastically. Jin et al [13] considered an SIRS epidemic model with general seasonal variation in the constant rate. Bai et al considered a nonautonomous SIR model with periodic transmission rate and a constant removal rate in [3].…”

Section: Introductionmentioning

confidence: 99%

Dynamics for a stochastic delayed SIRS epidemic model

Shi

Cao

Zhou

2020

NAMC

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In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained.

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