Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays

被引：2

作者：

Dai, Huan ^{[1
]}

Liu, Yuying ^{[2
]}

Wei, Junjie ^{[2
]}

机构：

[1] Harbin Inst Technol Weihai, Sch Sci, Weihai 264209, Peoples R China

[2] Harbin Inst Thchnol, Dept Math, Harbin 150001, Peoples R China

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2020年 / 17卷 / 04期

基金：

中国国家自然科学基金;

关键词：

epidemic; two delays; Hopf bifurcation; normal form; GLOBAL STABILITY; SYSTEM; DYNAMICS; WAVES;

D O I：

10.3934/mbe.2020229

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A diffusive epidemic model with two delays subjecting to Neumann boundary conditions is considered. First we obtain the existence and the stability of the positive constant steady state. Then we investigate the existence of Hopf bifurcations by analyzing the distribution of the eigenvalues. Furthermore, we derive the normal form on the center manifold near the Hopf bifurcation singularity. Finally, some numerical simulations are carried out to illustrate the theoretical results.

引用

页码：4127 / 4146

页数：20

共 36 条

[1]

BERETTA E, 1995, J MATH BIOL, V33, P250, DOI 10.1007/BF00169563

[2] A REACTION-DIFFUSION SYSTEM ARISING IN MODELING MAN-ENVIRONMENT DISEASES [J].

CAPASSO, V ;

KUNISCH, K .

QUARTERLY OF APPLIED MATHEMATICS, 1988, 46 (03) :431-450

[3] Analysis of a reaction-diffusion system modeling man-environment-man epidemics [J].

Capasso, V ;

Wilson, RE .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (02) :327-346

[4]

CAPASSO V, 1979, REV EPIDEMIOL SANTE, V27, P121

[5] On a Generalized Time-Varying SEIR Epidemic Model with Mixed Point and Distributed Time-Varying Delays and Combined Regular and Impulsive Vaccination Controls [J].

De la Sen, M. ;

Agarwal, Ravi P. ;

Ibeas, A. ;

Alonso-Quesada, S. .

ADVANCES IN DIFFERENCE EQUATIONS, 2010,

[6] ON SOME STRUCTURES OF STABILIZING CONTROL LAWS FOR LINEAR AND TIME-INVARIANT SYSTEMS WITH BOUNDED POINT DELAYS AND UNMEASURABLE STATES [J].

DELASEN, M .

INTERNATIONAL JOURNAL OF CONTROL, 1994, 59 (02) :529-541

[7] Two delays induce Hopf bifurcation and double Hopf bifurcation in a diffusive Leslie-Gower predator-prey system [J].

Du, Yanfei ;

Niu, Ben ;

Wei, Junjie .

CHAOS, 2019, 29 (01)

[8] Global stability of an SEIS epidemic model with recruitment and a varying total population size [J].

Fan, M ;

Li, MY ;

Wang, K .

MATHEMATICAL BIOSCIENCES, 2001, 170 (02) :199-208

[9]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[10] The mathematics of infectious diseases [J].

Hethcote, HW .

SIAM REVIEW, 2000, 42 (04) :599-653

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