☆ 4.7 Article

Epidemic waves in a discrete diffusive endemic model with treatment and external supplies

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2023)

Related references

Note: Only part of the references are listed.

Article Mathematics, Applied

Analysis of a diffusive HBV model with logistic proliferation and non-cytopathic antiviral mechanisms

Jinliang Wang et al.

Summary: Non-cytopathic antiviral mechanisms play a crucial role in blocking HBV infection by eliminating viral DNA from the liver, and this paper incorporates them into a classical infection model, validating the main results through numerical simulations.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Add to Collection

Article Mathematics, Applied

Traveling waves for a four-compartment lattice epidemic system with exposed class and standard incidence

Ran Zhang et al.

Summary: This paper investigates the problem of traveling wave solutions for an SEIR epidemic model with discrete diffusion, obtaining threshold conditions for the existence and nonexistence of TWS based on the threshold number R-0. It is shown that the critical wave speed c* can be found if R-0 > 1, with TWS existing for c > c* and not existing for c < c*. Furthermore, nonexistence of TWS is also demonstrated for R-0 <= 1, with biological explanations provided from an epidemiological perspective.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2022)

Add to Collection

Article Mathematics, Applied

Threshold dynamics of a nonlocal and time-delayed West Nile virus model with seasonality

Zhenguo Bai et al.

Summary: This paper studies a nonlocal periodic reaction-diffusion system that models the transmission of the West Nile virus between mosquitoes and birds. The study includes global stability analysis of the subsystem for mosquito growth, as well as analysis of the basic reproduction number and disease transmission dynamics for the full model. In addition, numerical simulations reveal the effects of diffusion, heterogeneity, and periodic delay on the reproduction number.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Add to Collection

Article Mathematics, Applied

Propagation dynamics for a periodic delayed lattice differential equation without quasi-monotonicity

Shi-Liang Wu et al.

Summary: This paper investigates the propagation dynamics of a periodic delayed lattice differential equation with age structures. In the case of quasi-monotonicity, the existence of the spreading speed and its coincidence with the minimal wave speed of periodic traveling fronts have been established. In this paper, we examine the spatial dynamics of the equation without quasi-monotonicity. We establish the existence of the spreading speed c* and prove the non-existence of periodic traveling waves with speeds in the interval (0, c*). Furthermore, we demonstrate the existence of periodic traveling waves using the asymptotic fixed point theorem. Our findings indicate that the spreading speed still equals the minimal wave speed in the non-quasi-monotone case. This study may be the first to explore the spatial dynamics of time-periodic and delayed lattice differential systems without quasi-monotonicity.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Add to Collection

Article Mathematics, Applied

WAVE PHENOMENA IN A COMPARTMENTAL EPIDEMIC MODEL WITH NONLOCAL DISPERSAL AND RELAPSE

Jia-Bing Wang et al.

Summary: This paper investigates wave phenomena in a compartmental epidemic model with nonlocal dispersal and relapse, showing the well-posedness of solutions and establishing a threshold result regarding the existence of strong traveling waves and the minimal wave speed. Numerical simulations indicate that relapse can encourage the spread of the disease.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2022)

Add to Collection

Article Mathematics, Applied

Traveling Wave Solutions for a Class of Discrete Diffusive SIR Epidemic Model

Ran Zhang et al.

Summary: This paper examines the conditions of existence and nonexistence of traveling wave solutions for a class of discrete diffusive epidemic model. The existence of traveling wave solutions is determined by the basic reproduction number and critical wave speed.

JOURNAL OF NONLINEAR SCIENCE (2021)

Add to Collection

Article Mathematics, Interdisciplinary Applications

The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence

Weixin Wu et al.

Summary: In this paper, a reaction-diffusion SIR epidemic model is proposed, taking into account factors such as individual mobility and time periodicity. The study focuses on the existence and nonexistence of periodic traveling wave solutions, with results extending and improving existing conclusions. Numerical experiments support the theoretical findings and differences between periodic and aperiodic coefficient systems are analyzed through simulations.

CHAOS SOLITONS & FRACTALS (2021)

Add to Collection

Article Mathematics, Applied

Traveling waves for a discrete diffusive SIR epidemic model with treatment

Dong Deng et al.

Summary: This paper explores the existence of traveling waves for a discrete diffusive SIR epidemic model with treatment, obtaining more accurate results compared to previous work. It is shown that when the basic reproduction number is greater than 1, nontrivial traveling wave solutions exist, while they do not exist for a basic reproduction number less than 1.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

Add to Collection

Article Mathematics, Applied

Global stability of travelling waves for a class of monostable epidemic models

Zhaoquan Xu

Summary: The study investigates the stability of travelling wave solutions for a monostable reaction-diffusion system describing the spatial spread of bacterial and viral diseases in the human-environment. Global stability of travelling wave solutions with any admissible wave speed, including the critical wave speed, is proven mathematically. Numerical computation of the critical wave speed and solutions of the Cauchy problem further demonstrate the global stability of travelling wave solutions with noncritical wave speed and critical wave speed.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

Add to Collection

Article Mathematics, Applied

Traveling waves of a diffusive SIR epidemic model with general nonlinear incidence and infinitely distributed latency but without demography

Haijun Hu et al.

Summary: This paper investigates the existence/non-existence of traveling waves in a diffusive SIR epidemic model, showing that the existence of traveling waves is determined by the basic reproduction number of the corresponding spatial-homogeneous system of delay differential equations, influenced by recovery rate, local properties of f and g, and a minimal wave speed c affected by distributed delay. The proof of existence uses Schauder's fixed point theorem, while the proof of nonexistence is completed with the aid of the bilateral Laplace transform.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

Add to Collection

Article Mathematics, Applied

RECENT DEVELOPMENTS ON SPATIAL PROPAGATION FOR DIFFUSION EQUATIONS IN SHIFTING ENVIRONMENTS

Jia-Bing Wang et al.

Summary: This review discusses recent developments in spatial propagation for diffusion problems in shifting environments, covering various models and equations. These topics are relevant for modeling the impact of global climate change, industrialization, pathophoresis, and invasion processes. Open problems and potential research directions are also highlighted.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2021)

Add to Collection

Article Mathematics, Applied

TRAVELING WAVES FOR A TWO-GROUP EPIDEMIC MODEL WITH LATENT PERIOD AND BILINEAR INCIDENCE IN A PATCHY ENVIRONMENT

Xuefeng San et al.

Summary: This paper examines the transmission patterns of a two-group SIR epidemic model with bilinear incidence in a patchy environment, discussing the dependence of minimum speed c* on parameters.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2021)

Add to Collection

Article Mathematics, Applied

Asymptotic boundary and nonexistence of traveling waves in a discrete diffusive epidemic model

Jingdong Wei

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS (2020)

Add to Collection

Article Biology

Traveling wave solutions in a two-group SIR epidemic model with constant recruitment

Lin Zhao et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2018)

Add to Collection

Article Physics, Mathematical

Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence

Shou-Peng Zhang et al.

JOURNAL OF MATHEMATICAL PHYSICS (2018)

Add to Collection

Article Mathematics

Existence of traveling waves with the critical speed for a discrete diffusive epidemic model

Chin-Chin Wu

JOURNAL OF DIFFERENTIAL EQUATIONS (2017)

Add to Collection

Article Mathematics, Applied

Traveling waves for a lattice dynamical system arising in a diffusive endemic model

Yan-Yu Chen et al.

NONLINEARITY (2017)

Add to Collection

Article Mathematics, Applied

Traveling wave solutions in a two-group epidemic model with latent period

Lin Zhao et al.

NONLINEARITY (2017)

Add to Collection

Article Mathematics, Applied

Traveling waves for a diffusive SIR model with delay

Sheng-Chen Fu

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2016)

Add to Collection

Article Mathematics, Applied

Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay

Zhenguo Bai et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2015)

Add to Collection

Article Mathematics, Applied

Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission

Jia-Bing Wang et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2015)

Add to Collection

Article Mathematics, Applied

TRAVELING WAVES OF A DELAYED DIFFUSIVE SIR EPIDEMIC MODEL

Yan Li et al.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2015)

Add to Collection

Article Mathematics, Applied

Existence of traveling wave solutions for influenza model with treatment

Tianran Zhang et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)

Add to Collection

Article Mathematics, Applied

Travelling wave solutions for an infection-age structured epidemic model with external supplies

Arnaud Ducrot et al.

NONLINEARITY (2011)

Add to Collection

Article Mathematics, Applied

Travelling wave solutions for an infection-age structured model with diffusion

A. Ducrot et al.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2009)

Add to Collection

Article Mathematics

Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models

HR Thieme et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2003)

Add to Collection

Article Mathematics

Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

XF Chen et al.

MATHEMATISCHE ANNALEN (2003)

Add to Collection

© Peeref 2019-2024. All rights reserved.