A Heroin Epidemic Model: Very General Non Linear Incidence, Treat-Age, and Global Stability

被引：63

作者：

Djilali, Salih ^{[1
]}

Touaoula, Tarik Mohammed ^{[1
]}

Miri, Sofiane El-Hadi ^{[2
]}

机构：

[1] Univ Tlemcen, Dept Math, Fac Sci, Lab Anal Non Lineaire & Math Appl, Tilimsen, Algeria

[2] Univ Tlemcen, Dept GEE, Fac Technol, Lab Anal Non Lineaire & Math Appl, Tilimsen, Algeria

来源：

ACTA APPLICANDAE MATHEMATICAE | 2017年 / 152卷 / 01期

关键词：

General nonlinear incidence; Global stability; Treat age; ARBITRARILY DISTRIBUTED PERIODS; INFECTIOUS-DISEASE MODELS; NONLINEAR INCIDENCE; ASYMPTOTIC PROPERTIES; ENDEMIC MODELS; SIR; DELAY; TRANSMISSION; PERSISTENCE; SEMIFLOWS;

D O I：

10.1007/s10440-017-0117-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an age structured heroin epidemic model, in a population divided into three sub-populations: the susceptible individuals, the drug users and the drug users under treatment, interacting as follows: Our main contribution consists in considering a nonlinear incidence function in its very general form. Global dynamics of the obtained problem is analyzed.

引用

页码：171 / 194

页数：24

共 43 条

[1]

[Anonymous], NONLINEAR ANAL

[2]

[Anonymous], 2008, MATH EPIDEMIOLOGY

[3]

[Anonymous], 2011, GRAD STUD MATH

[4]

Bailey N. T., 1975, The mathematical theory of infectious diseases and its applications., V2nd

[5]

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

[6]

Brauer F., 2000, Mathematical Models in Population Biology and Epidemiology

[7] DYNAMICS OF AN AGE-OF-INFECTION CHOLERA MODEL [J].

Brauer, Fred ;

Shuai, Zhisheng ;

van den Driessche, P. .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2013, 10 (5-6) :1335-1349

[8] GLOBAL ANALYSIS OF AGE-STRUCTURED WITHIN-HOST VIRUS MODEL [J].

Browne, Cameron J. ;

Pilyugin, Sergei S. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (08) :1999-2017

[9] EPIDEMIC MODELS WITH AGE OF INFECTION, INDIRECT TRANSMISSION AND INCOMPLETE TREATMENT [J].

Cai, Liming ;

Martcheva, Maia ;

Li, Xue-Zhi .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (09) :2239-2265

[10] GENERALIZATION OF THE KERMACK-MCKENDRICK DETERMINISTIC EPIDEMIC MODEL [J].

CAPASSO, V ;

SERIO, G .

MATHEMATICAL BIOSCIENCES, 1978, 42 (1-2) :43-61

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