Stability Analysis of an Seirs Epidemic Model with Relapse, Immune and General Incidence Rates

被引：1

作者：

Bernoussi, Amine ^{[1
]}

Elkhaiar, Soufiane ^{[2
]}

Jerry, Chakib ^{[3
]}

机构：

[1] Ibn Tofail Univ, Fac Sci, Lab Equat Derivees Partielles Algebre & Geometrie, BP 133, Kenitra 14000, Morocco

[2] Fac Appl Sci, Dept Math, POB 6146, Ait Mellon, Morocco

[3] Moulay Ismail Univ Meknes, Fac Law Econ & Socials Sci, Team OMEGA, BP 3102 Toulal, Meknes, Morocco

来源：

JOURNAL OF APPLIED NONLINEAR DYNAMICS | 2022年 / 11卷 / 01期

关键词：

General nonlinear incidence rate; Relapse; Infective's immigrants; Lyapunov function; Geometric approach; GLOBAL-STABILITY; MATHEMATICAL-THEORY; SIR; MEDIA; IMPACT;

D O I：

10.5890/JAND.2022.03.013

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper has the goal to broaden the incidence rate of an SEIRS epidemic model to a wide range of monotonic, concave incidence rates and some non-monotonic or concave cases. These incidence functions could reflect media education or psychological effect or mass action. The model takes into account relapse, recovery and immunity rates but without disease-induced death one. Applying the novel geometric approach we establish the global stability of the SEIRS model. Our analytical results reveal that the basic reproduction number completely determines the global stability of equilibria. Our conclusions are applied to two special incidence functions reflecting media and mass action. (C) 2022 L&H Scientific Publishing, LLC. All rights reserved.

引用

页码：217 / 231

页数：15

共 32 条

[1] Periodicity in an epidemic model with a generalized non-linear incidence [J].

Alexander, ME ;

Moghadas, SM .

MATHEMATICAL BIOSCIENCES, 2004, 189 (01) :75-96

[2]

Anderson R.M., 1979, NATURE, V180, P316

[3] REGULATION AND STABILITY OF HOST-PARASITE POPULATION INTERACTIONS .1. REGULATORY PROCESSES [J].

ANDERSON, RM ;

MAY, RM .

JOURNAL OF ANIMAL ECOLOGY, 1978, 47 (01) :219-247

[4]

[Anonymous], 1965, Stability and asymptotic behavior of differential equations

[5]

[Anonymous], 1984, Lecture Notes in Biomath

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

CAPASSO, V ;

SERIO, G .

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

[7] The impact of media on the control of infectious diseases [J].

Cui, Jingan ;

Sun, Yonghong ;

Zhu, Huaiping .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2008, 20 (01) :31-53

[8]

Freedman H. I., 1994, Journal of Dynamics and Differential Equations, V6, P583, DOI DOI 10.1007/BF02218848

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

Hethcote, HW .

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

[10] BIFURCATIONS OF AN SIRS EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE [J].

Hu, Zhixing ;

Bi, Ping ;

Ma, Wanbiao ;

Ruan, Shigui .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2011, 15 (01) :93-112

← 1 2 3 4 →