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

被引：62

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

[21]

Iannelli M., 1994, APPL MATH MONOGRAPHS, V7

[22] Non-linear incidence and stability of infectious disease models [J].

Korobeinikov, A ;

Maini, PK .

MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA, 2005, 22 (02) :113-128

[23] Global properties of infectious disease models with nonlinear incidence [J].

Korobeinikov, Andrei .

BULLETIN OF MATHEMATICAL BIOLOGY, 2007, 69 (06) :1871-1886

[24] Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission [J].

Korobeinikov, Andrei .

BULLETIN OF MATHEMATICAL BIOLOGY, 2006, 68 (03) :615-626

[25] Global attractors and steady states for uniformly persistent dynamical systems [J].

Magal, P ;

Xiao, XQ .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 37 (01) :251-275

[26] Eventual compactness for semiflows generated by nonlinear age-structured models [J].

Magal, P ;

Thieme, HR .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2004, 3 (04) :695-727

[27] Lyapunov functional and global asymptotic stability for an infection-age model [J].

Magal, P. ;

McCluskey, C. C. ;

Webb, G. F. .

APPLICABLE ANALYSIS, 2010, 89 (07) :1109-1140

[28] GLOBAL STABILITY OF AN SIR EPIDEMIC MODEL WITH DELAY AND GENERAL NONLINEAR INCIDENCE [J].

McCluskey, C. Connell .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2010, 7 (04) :837-850

[29] GLOBAL STABILITY FOR AN SEIR EPIDEMIOLOGICAL MODEL WITH VARYING INFECTIVITY AND INFINITE DELAY [J].

McCluskey, C. Connell .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2009, 6 (03) :603-610

[30] A note on heroin epidemics [J].

Mulone, Giuseppe ;

Straughan, Brian .

MATHEMATICAL BIOSCIENCES, 2009, 218 (02) :138-141

← 1 2 3 4 5 →