Stability analysis of an SEIQV epidemic model with saturated incidence rate

Abstract In this article, an SEIQV epidemic model with saturated incidence rate is considered. The basic reproduction number R 0 is found. If  R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable; if  R 0 > 1 , endemic equilibrium is globally asymptotically stable and the disease is persistent. Numerical simulations are carried out to illustrate the feasibility of the obtained results, especially the effect of vaccination to eliminate the disease.

[1]  Lansun Chen,et al.  The dynamics of an epidemic model for pest control with impulsive effect , 2010 .

[2]  G. Serio,et al.  A generalization of the Kermack-McKendrick deterministic epidemic model☆ , 1978 .

[3]  Paul Waltman,et al.  Persistence in dynamical systems , 1986 .

[4]  Philip K Maini,et al.  Non-linear incidence and stability of infectious disease models. , 2005, Mathematical medicine and biology : a journal of the IMA.

[5]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[6]  Shaokai Wang,et al.  Global dynamics of delay epidemic models with nonlinear incidence rate and relapse , 2011 .

[7]  Murray E. Alexander,et al.  Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence , 2005, SIAM J. Appl. Math..

[8]  James S. Muldowney,et al.  A Geometric Approach to Global-Stability Problems , 1996 .

[9]  Bimal Kumar Mishra,et al.  Fuzzy epidemic model for the transmission of worms in computer network , 2010 .

[10]  Lu-Xing Yang,et al.  A novel computer virus model and its dynamics , 2012 .

[11]  M. Fan,et al.  Global stability of an SEIS epidemic model with recruitment and a varying total population size. , 2001, Mathematical biosciences.

[12]  Zhien Ma,et al.  Qualitative analyses of SIS epidemic model with vaccination and varying total population size , 2002 .

[13]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[14]  Lourdes Esteva,et al.  A MODEL FOR VECTOR TRANSMITTED DISEASES WITH SATURATION INCIDENCE , 2001 .

[15]  Xiao-Qiang Zhao,et al.  Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments , 2008 .

[16]  Ge Yu,et al.  Discrete-Time Simulation Method for Worm Propagation Model with Pulse Quarantine Strategy , 2011 .

[17]  Kaifa Wang,et al.  Global properties of an improved hepatitis B virus model , 2010 .

[18]  Xiao-Qiang Zhao,et al.  Chain Transitivity, Attractivity, and Strong Repellors for Semidynamical Systems , 2001 .

[19]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[20]  Abraham J. Arenas,et al.  An exact global solution for the classical SIRS epidemic model , 2010 .

[21]  Fangwei Wang,et al.  Stability analysis of a SEIQV epidemic model for rapid spreading worms , 2010, Comput. Secur..

[22]  Chengjun Sun,et al.  Global stability for an special SEIR epidemic model with nonlinear incidence rates , 2007 .

[23]  Jing Hui,et al.  Dynamics of Seis Epidemic Models with Varying Population Size , 2007, Int. J. Bifurc. Chaos.

[24]  Michael Y. Li,et al.  Global stability for the SEIR model in epidemiology. , 1995, Mathematical biosciences.

[25]  Toshikazu Kuniya,et al.  Global dynamics of a class of SEIRS epidemic models in a periodic environment , 2010 .

[26]  Robert H. Martin.  Logarithmic norms and projections applied to linear differential systems , 1974 .

[27]  G F Medley,et al.  Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence , 2005, Journal of mathematical biology.

[28]  S. Levin,et al.  Dynamical behavior of epidemiological models with nonlinear incidence rates , 1987, Journal of mathematical biology.

[29]  James S. Muldowney,et al.  On Bendixson′s Criterion , 1993 .

[30]  Navnit Jha,et al.  SEIQRS model for the transmission of malicious objects in computer network , 2010 .

[31]  Shigui Ruan,et al.  Global analysis of an epidemic model with nonmonotone incidence rate , 2006, Mathematical Biosciences.

[32]  Lu-Xing Yang,et al.  A delayed computer virus propagation model and its dynamics , 2012 .

[33]  Abba B. Gumel,et al.  The effect of incidence functions on the dynamics of a quarantine/isolation model with time delay , 2010, Nonlinear Analysis: Real World Applications.