TRAVELING WAVE SOLUTION FOR A DIFFUSIVE SIMPLE EPIDEMIC MODEL WITH A FREE BOUNDARY

被引：0

作者：

Enatsu, Yoichi ^{[1
]}

Ishiwata, Emiko ^{[1
]}

Ushijima, Takeo ^{[2
]}

机构：

[1] Tokyo Univ Sci, Fac Sci, Dept Appl Math, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 1628601, Japan

[2] Tokyo Univ Sci, Fac Sci & Technol, Dept Math, 2641 Yamazaki, Noda, Chiba 2788510, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2021年 / 14卷 / 03期

关键词：

Traveling wave; free boundary; epidemic model; spreading phenomena; reaction diffusion system of prey-predator type; SPEED; CONVERGENCE; EQUATION; SYSTEM; RISK;

D O I：

10.3934/dcdss.2020387

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we proved existence and nonexistence of traveling wave solution for a diffusive simple epidemic model with a free boundary in the case where the diffusion coefficient d of susceptible population is zero and the basic reproduction number is greater than 1. We obtained a curve in the parameter plane which is the boundary between the regions of existence and nonexistence of traveling wave. We numerically observed that in the region where the traveling wave exists the disease successfully propagate like traveling wave but in the region of no traveling wave disease stops to invade. We also numerically observed that as d increases the speed of propagation slows down and the parameter region of propagation narrows down.

引用

页码：835 / 850

页数：16

共 21 条

[1]

Allen LJS, 2008, DISCRETE CONT DYN-A, V21, P1

[2]

Aronson D. G., 1975, LECT NOTES MATH, V446, P5, DOI DOI 10.1007/BFB0070595

[3] Spreading in space time periodic media governed by a monostable equation with free boundaries, Part 1: Continuous initial functions [J].

Ding, Weiwei ;

Du, Yihong ;

Liang, Xing .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (10) :4988-5021

[4] Spreading and vanishing in nonlinear diffusion problems with free boundaries [J].

Du, Yihong ;

Lou, Bendong .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (10) :2673-2724

[5] NONLINEAR DIFFUSION PROBLEMS WITH FREE BOUNDARIES: CONVERGENCE, TRANSITION SPEED, AND ZERO NUMBER ARGUMENTS [J].

Du, Yihong ;

Lou, Bendong ;

Zhou, Maolin .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (05) :3555-3584

[6] Spreading speed and profile for nonlinear Stefan problems in high space dimensions [J].

Du, Yihong ;

Matsuzawa, Hiroshi ;

Zhou, Maolin .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2015, 103 (03) :741-787

[7] Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II [J].

Du, Yihong ;

Guo, Zongming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (12) :4336-4366

[8] SPREADING-VANISHING DICHOTOMY IN THE DIFFUSIVE LOGISTIC MODEL WITH A FREE BOUNDARY [J].

Du, Yihong ;

Lin, Zhigui .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (01) :377-405

[9] Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type [J].

Ducrot, Arnaud ;

Giletti, Thomas ;

Matano, Hiroshi .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (04)

[10] Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population [J].

Ducrot, Arnaud ;

Giletti, Thomas .

JOURNAL OF MATHEMATICAL BIOLOGY, 2014, 69 (03) :533-552

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