Global threshold analysis of an age-space structured disease model with relapse

被引：0

作者：

Lyu, Guoyang ^{[1
]}

Guo, Yutong ^{[1
]}

Wang, Jinliang ^{[1
]}

机构：

[1] Heilongjiang Univ, Engn Res Ctr Agr Microbiol Technol, Sch Math Sci, Heilongjiang Prov Key Lab Ecol Restorat & Resource, Harbin 150080, Peoples R China

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2024年 / 29卷 / 05期

基金：

中国国家自然科学基金;

关键词：

age-space structured model; basic reproduction number; threshold dynamics; global asymptotic stability; EPIDEMIC MODEL; NONLINEAR INCIDENCE; INFECTION; STABILITY; TUBERCULOSIS; LATENCY;

D O I：

10.15388/namc.2024.29.36098

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an age-space structured disease model with age-dependent relapse rate is investigated. We first prove the well-posedness of the model including the existence and uniqueness of the solution, positivity, and boundedness. By performing the Laplace transformation to renewal equation, we derive the next generation operator, whose spectral radius is defined as the basic reproduction number. By checking the distribution of the roots of the characteristic equation, exploring the strong persistence property of the solution and designing the Lyapunov functionals, we establish the local and global dynamics of the model.

引用

页码：914 / 938

页数：25

共 27 条

[1] DELAYED NONLOCAL REACTION DIFFUSION MODEL FOR HEMATOPOIETIC STEM CELL DYNAMICS WITH DIRICHLET BOUNDARY CONDITIONS [J].

Adimy, M. ;

Chekroun, A. ;

Kuniya, T. .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2017, 12 (06) :1-22

[2] FIXED-POINT EQUATIONS AND NONLINEAR EIGENVALUE PROBLEMS IN ORDERED BANACH-SPACES [J].

AMANN, H .

SIAM REVIEW, 1976, 18 (04) :620-709

[3]

Cantrell R. S., 2003, Spatial ecology via reaction-diffusion equations

[4] An infection age-space structured SIR epidemic model with Neumann boundary condition [J].

Chekroun, Abdennasser ;

Kuniya, Toshikazu .

APPLICABLE ANALYSIS, 2020, 99 (11) :1972-1985

[5] Relapse in persons treated for drug-susceptible tuberculosis in a population with high coinfection with human immunodeficiency virus in New York City [J].

Driver, CR ;

Munsiff, SS ;

Li, JH ;

Kundamal, N ;

Osahan, SS .

CLINICAL INFECTIOUS DISEASES, 2001, 33 (10) :1762-1769

[6] Travelling wave solutions for an infection-age structured epidemic model with external supplies [J].

Ducrot, Arnaud ;

Magal, Pierre .

NONLINEARITY, 2011, 24 (10) :2891-2911

[7] PERSISTENCE DEFINITIONS AND THEIR CONNECTIONS [J].

FREEDMAN, HI ;

MOSON, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 109 (04) :1025-1033

[8]

Hale J.K., 1988, Asymptotic Behavior of Dissipative Systems, DOI [10.1090/surv/025, DOI 10.1090/SURV/025]

[9] Relapse and recurrent tuberculosis in the context of a National Tuberculosis Control Programme [J].

Harries, AD ;

Hargreaves, NJ ;

Kwanjana, JH ;

Salaniponi, FML .

TRANSACTIONS OF THE ROYAL SOCIETY OF TROPICAL MEDICINE AND HYGIENE, 2000, 94 (03) :247-249

[10] Global stability of an SEIR epidemic model with age-dependent latency and relapse [J].

Liu, Lili ;

Wang, Jinliang ;

Liu, Xianning .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 24 :18-35

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