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Asymptotic behavior of SIRS models in state-dependent random environments
Nonlinear Analysis: Hybrid Systems ( IF 4.2 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.nahs.2020.100914
Jianhai Bao , Jinghai Shao

The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the random change of the environment. Our contributions consist in (i) giving some sufficient conditions on extinction (persistence) of the infectious individuals even though they are persistent (resp. extinct) in certain fixed environments; (ii) revealing the influence of random switching of incidence functions on extinction for the infectious individuals, which has not been studied before; (iii) establishing a criterion to judge extinction of the infectious individuals for a range of random/stochastic SIRS models with state-dependent switching via a stochastic comparison for functionals of jump processes. Moreover, some examples are set to illustrate the applications of our theory.

中文翻译:

SIRS 模型在状态相关随机环境中的渐近行为

感染个体的灭绝和持续存在与环境的随机变化密切相关。在本文中,我们通过随机/随机 SIRS 模型,定性和定量地分析了环境随机变化造成的影响。我们的贡献在于(i)即使它们在某些固定环境中持续(或灭绝),也为传染性个体的灭绝(持续性)提供了一些充分条件;(ii) 揭示发病函数随机切换对感染个体灭绝的影响,这是以前未研究过的;(iii) 建立一个标准来判断一系列随机/随机 SIRS 模型的感染个体的灭绝,通过对跳跃过程的函数进行随机比较,状态依赖切换。而且,
更新日期:2020-11-01
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