On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

Magal, Pierre; Webb, Glenn; Wu, Yixiang

doi:10.1137/18m1182243

Cited by 87 publications

(39 citation statements)

References 33 publications

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“…In recent years there have been many studies on SIS and other types of disease transmission models in spatially and/or temporally varying environments; see [31,32,33,34,48,49,50,51,95,96,120,133,134,135,136,154]. For instance, to study the effect of the movement of exposed individuals on disease outbreaks, the following SEIRS (susceptible-exposed-infected-recovered-susceptible) epidemic reaction-diffusion model was considered in [143]: Here we divide the individuals into four different compartments: susceptible (S), exposed (E), infectious (I), recovered (immune by vaccination, R).…”

Section: Spatial Dynamics Of Epidemic Diseasesmentioning

confidence: 99%

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

2020

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We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction–diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplanktongrowth, and spatial spread of epidemic disease. Open problems and conjectures are presented.P arts of this survey are adopted from the materials in [89,108,109], and some very recent progress are also included.

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Section: Spatial Dynamics Of Epidemic Diseasesmentioning

confidence: 99%

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

2020

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“…The basic reproduction number is far different for different infectious diseases, for example, Zika: 1.4-6.6 [4], H1N1: 1.4-3.1 [5], dengue: 1.52-3.90 [6], Ebola: 1.3-2.7 [7], SARS: 2.2-3.7 [8], MERS: 2.0-6.7 [9], smallpox: 3.5-6.0 [10], measles: 12-18 [11], pertussis: 12-17 [12], etc. Usually, it is difficult to directly measure the value of R 0 since R 0 is affected by numerous biological, sociobehavioral, and environmental factors [13], and thus statistical models are widely applied to estimate R 0 [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Evaluating the effect of Chinese control measures on COVID-19 via temporal reproduction number estimation

Chen

Zhou

2021

PLoS ONE

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Control measures are necessary to contain the spread of serious infectious diseases such as COVID-19, especially in its early stage. We propose to use temporal reproduction number an extension of effective reproduction number, to evaluate the efficacy of control measures, and establish a Monte-Carlo method to estimate the temporal reproduction number without complete information about symptom onsets. The province-level analysis indicates that the effective reproduction numbers of the majority of provinces in mainland China got down to < 1 just by one week from the setting of control measures, and the temporal reproduction number of the week [15 Feb, 21 Feb] is only about 0.18. It is therefore likely that Chinese control measures on COVID-19 are effective and efficient, though more research needs to be performed.

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“…(v) The proof of the case where D E > 0, D I → 0 is similar to that of Theorem 4.9 in [32], thus the details are omitted here. This completes the proof.…”

Section: Introduction Since Kemack and Mckendrickmentioning

confidence: 99%

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

Tian¹,

Guo²,

Liu³

2021

DCDS-B

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<p style='text-indent:20px;'>This paper is devoted to an SEIR epidemic model with variable recruitment and both exposed and infected populations having infectious in a spatially heterogeneous environment. The basic reproduction number is defined and the existence of endemic equilibrium is obtained, and the relationship between the basic reproduction number and diffusion coefficients is established. Then the global stability of the endemic equilibrium in a homogeneous environment is investigated. Finally, the asymptotic profiles of endemic equilibrium are discussed, when the diffusion rates of susceptible, exposed and infected individuals tend to zero or infinity. The theoretical results show that limiting the movement of exposed, infected and recovered individuals can eliminate the disease in low-risk sites, while the disease is still persistent in high-risk sites. Therefore, the presence of exposed individuals with infectious greatly increases the difficulty of disease prevention and control.</p>

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On the Basic Reproduction Number of Reaction-Diffusion Epidemic Models

Cited by 87 publications

References 33 publications

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

Evaluating the effect of Chinese control measures on COVID-19 via temporal reproduction number estimation

Qualitative analysis of a diffusive SEIR epidemic model with linear external source and asymptomatic infection in heterogeneous environment

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