A reaction–diffusion SIS epidemic model in an almost periodic environment

Wang, Bin-Guo; Li, Wan–Tong; Wang, Zhicheng

doi:10.1007/s00033-015-0585-z

Cited by 27 publications

(12 citation statements)

References 32 publications

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“…Zhang et al [67] proposed a timeperiodic reaction-diffusion epidemic model which incorporates simple demographic structure and a fixed latent period of the infectious disease, introduced the basic reproduction number R 0 via a next generation operator, and investigated the threshold dynamics of the epidemic model in terms of R 0 . Some other studies on the dynamics of time heterogeneous epidemic models can be found in [33,54,55,65,68] and the references therein. However, for such non-autonomous (even autonomous) diffusion-reaction epidemic models with distributed delays, much less is done.…”

Section: Lin Zhao Zhi-cheng Wang and Liang Zhangmentioning

confidence: 99%

Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

Zhao

Wang

Zhang

2017

MBE

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In this paper, a time periodic and two--group reaction--diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number R0 for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of R0, that is, the disease is uniformly persistent if R0>1, while the disease goes to extinction if R0< 1. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio--temporal variables.

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Section: Lin Zhao Zhi-cheng Wang and Liang Zhangmentioning

confidence: 99%

Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

Zhao

Wang

Zhang

2017

MBE

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“…Along this line, there have been some works studying the transmission dynamics for almost periodic epidemic models (see, e.g., [9,34]). Recently, Wang et al [33] studied the threshold dynamics of an almost periodic reaction-diffusion epidemic model. For the almost periodic reaction-diffusion epidemic model with incubation period, the global dynamics does not have an adequate characterisation.…”

Section: Introductionmentioning

confidence: 99%

A reaction–diffusion epidemic model with incubation period in almost periodic environments

Qiang¹,

Wang²,

Wang³

2020

Eur. J. Appl. Math

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In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent $${\lambda ^*}$$ for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of $${\lambda ^*}$$ . It is shown that the disease-free almost periodic solution is globally attractive if $${\lambda ^*} < 0$$ , while the disease is persistent if $${\lambda ^*} < 0$$ . By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

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“…In recent years, a great deal of mathematical models has been developed to study the impact of seasonal periodicity and environmental heterogeneity on the dynamics of infectious diseases [7] [8] [9]. On the other hand, the periodicity of environmental factors is realistic and highly important for the dynamics of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Periodicity in the Fecally-Orally Epidemic Model in a Heterogeneous Environment

Tarboush¹,

Zhang²

2019

JAMP

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To understand the influence of seasonal periodicity and environmental heterogeneity on the transmission dynamics of an infectious disease, we consider asymptotic periodicity in the fecally-orally epidemic model in a heterogeneous environment. By using the next generation operator and the related eigenvalue problems, the basic reproduction number is introduced and shows that it plays an important role in the existence and non-existence of a positive T-periodic solution. The sufficient conditions for the existence and non-existence of a positive T-periodic solution are provided by applying upper and lower solutions method. Our results showed that the fecally-orally epidemic model in a heterogeneous environment admits at least one positive T-periodic solution if the basic reproduction number is greater than one, while no T-periodic solution exists if the basic reproduction number is less than or equal to one. By means of monotone iterative schemes, we construct the true positive solutions. The asymptotic behavior of periodic solutions is presented. To illustrate our theoretical results, some numerical simulations are given. The paper ends with some conclusions and future considerations.

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A reaction–diffusion SIS epidemic model in an almost periodic environment

Cited by 27 publications

References 32 publications

Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

A reaction–diffusion epidemic model with incubation period in almost periodic environments

Asymptotic Periodicity in the Fecally-Orally Epidemic Model in a Heterogeneous Environment

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