Traveling waves of an epidemic model with general nonlinear incidence rate and infection-age structure

Tian, Xuan; Guo, Shangjiang

doi:10.1007/s00033-022-01804-x

Cited by 4 publications

(2 citation statements)

References 46 publications

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“…In order to take into account both age and spatial heterogeneity, more complicated models were developed [55][56][57][58]. In particular, the age-structured SIS epidemic model with diffusion [55] where k(a, σ, x, y) denotes the rate of disease transmission from an infective individual of age σ in position y to a susceptible individual of age a in position x.…”

Section: Age-structured Epidemic Modelsmentioning

confidence: 99%

“…Age-structured epidemic models should be mentioned as well. Such models are based on integro-differential equations in order to incorporate both spatial and age dimensions for modeling the spread of infectious diseases (see [55][56][57][58] and papers cited therein). These models aim to understand the complex dynamics of disease transmission in relation to age-specific factors and spatial patterns.…”

Section: Introductionmentioning

confidence: 99%

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Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

Davydovych,

Dutka,

Cherniha

2023

Symmetry

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The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.

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Section: Age-structured Epidemic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

Davydovych,

Dutka,

Cherniha

2023

Symmetry

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Existence of periodic traveling waves in a nonlocal convection–diffusion model with chemotaxis and delay effect

Liu,

Guo

2023

Z. Angew. Math. Phys.

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We focus upon the existence of periodic traveling waves in a nonlocal reaction-diffusion model with chemotaxis and nonlocal delay effect. Based on the perturbation method, the existence of periodic traveling waves with large wave speed are obtained by the Lyapunov-Schmidt reduction and the implicit function theorem. The trick of the proof is to treat the wave profile as a solution of an operator in a suitable Banach space. Keywords nonlocal convection-diffusion model • chemotaxis • delay • periodic traveling waves • perturbation method Mathematics Subject Classification (2000) 35K57 • 34K05.

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Spatio-temporal patterns in a ring network with delay and square symmetry

Li¹,

Guo²

2024

DCDS-B

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Traveling waves of an epidemic model with general nonlinear incidence rate and infection-age structure

Cited by 4 publications

References 46 publications

Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

Existence of periodic traveling waves in a nonlocal convection–diffusion model with chemotaxis and delay effect

Spatio-temporal patterns in a ring network with delay and square symmetry

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