Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways

Song, Haifeng; Zhang, Yuxiang

doi:10.14232/ejqtde.2019.1.86

Cited by 4 publications

(8 citation statements)

References 35 publications

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“…of which the discussion is the same as that in Song and Zhang [29,Proposition 1.1]. We now define the spreading speed by the theory in [11,19,21,45], and it is denoted by C * .…”

Section: Consider the Nonlinear Systemmentioning

confidence: 99%

“…Besides the SIR-B models, mathematical models involving both direct and indirect infective ways have been established and studied, see very recent works [3,12,22,29,31,32,35] and references cited therein. In particular, Song and Zhang [29] considered the following diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates…”

Section: Introductionmentioning

confidence: 99%

“…Incidence functions F 1 and F 2 reflect the rate of direct and indirect transmissions, respectively, and F 3 determines the intake rate of the pathogen in the environment due to bacterial shedding from infected hosts. In [29], these general incidence functions are set to be…”

Section: Introductionmentioning

confidence: 99%

“…Traveling wave solutions of epidemic models have been widely studied, which has been proven to be useful in understanding the extinction or persistence of the disease, spatial expansion speed of the disease [6,7,23,25,38,39]. To formulate the disease spreading phenomena in model (1.1), Song and Zhang [29] studied the traveling wave solutions of ( By constructing upper and lower solutions and passing to a limit process, they showed the existence of traveling wave solutions and obtained the minimal wave speed of traveling wave solutions.…”

Section: Introductionmentioning

confidence: 99%

“…One typical example is the SIR-B epidemic model formulating the transmission and spread of cholera (see, e.g., [2,4,24,31,40,41] and the references therein), in which the dynamical evolution of the bacteria is introduced. Besides the SIR-B models, mathematical models involving both direct and indirect infective ways have been established and studied, see very recent works [3,12,22,29,31,32,35] and references cited therein. In particular, Song and Zhang [29] considered the following diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Asymptotic Spreading of a Cholera Epidemic Model in a Periodic Environment

Lin

Pan

2022

Preprint

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This paper is devoted to the spreading property of a cholera epidemic model, which is built upon a time-periodic reaction-diffusion system that is not necessarily monotonic. When the initial distribution of infected hosts and bacteria appears on a compact domain, we derive a rough expansion speed of the infection over space. In the case where the model parameters are constants, we obtain some analytic properties for the speed, which allows us to understand the factors that affect the spatial spreading ability of cholera. In particular, the spreading speed of cholera is the minimal wave speed of traveling wave solutions in earlier works by taking constant parameters and special incidence functions. AMS Subject Classification (2010): 35K57; 92D30

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“…of which the discussion is the same as that in Song and Zhang [29,Proposition 1.1]. We now define the spreading speed by the theory in [11,19,21,45], and it is denoted by C * .…”

Section: Consider the Nonlinear Systemmentioning

confidence: 99%