|Table of Contents|

Backward Bifurcation in an Epidemic Model(PDF)

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

Issue:
2017年03期
Page:
5-
Research Field:
·数学·
Publishing date:

Info

Title:
Backward Bifurcation in an Epidemic Model
Author(s):
Bai ChanWan Hui
Jiangsu Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
Keywords:
vaccinationepidemic modelmedical resourceequilibriumstabilitybackward bifurcation
PACS:
175.12
DOI:
10.3969/j.issn.1001-4616.2017.03.002
Abstract:
In this paper,we formulate a SIVS epidemic model with special recovery rate to study the impact of limited medical resource on the transmission dynamics of diseases with vaccination. The basic investigation of the model has been finished. The backward bifurcation has been proved precisely. It is shown that limited medical resource leads to vital dynamics,such as bistability. Backward bifurcation implies that even if the basic reproduction number is smaller than unity,there may be a stable endemic equilibrium and the basic reproductive number itself is not enough to describe whether a disease will prevail or not and we should pay more attention to the initial conditions. It is also shown that sufficient medical services and medicines are very important for the disease control and eradication. Besides,the impact of vaccination has been explored too.

References:

[1] CUI J,MU X,WAN H. Saturation recovery leads to multiple endemic equilibria and backward bifurcation[J]. Journal of theoretical biology,2008,254:275-283.
[2]KRIBS Z C,VELASCO H J. A simple vaccination model with multiple endemic states[J]. Math Biosci,2000,164:183-201.
[3]LIU X,TAKEUCHI Y,IWAMI S. SVIR epidemic models with vaccination strategies[J]. Journal of theoretical biology,2008,253:1-11.
[4]LI J,ZHAO Y,ZHU H. Bifurcation of an SIS model with nonlinear contact rate[J]. J Math Anal Appl,2015,432:1 119-1 138.
[5]LI G,LI G F. Bifurcation analysis of an SIR epidemic model with the contact transmissions function[J]. Abstract and applied analysis,2014,Article ID 930541.
[6]MAGPANTAY F M G,RIOLO M A,DOMENECH de CELLS M,et al. Epidemiological consequences of imperfect vaccines for immunizing Iinfection[J]. SIAM Journal on applied mathematics,2014,74:1 810-1 830.
[7]ERIKA R,ERIC A,GERARDO G. Stability and bifurcation analysis of a SIR model with saturated incidence rate and saturated treatment[J]. Mathematics and computers in simulation,2016,121:109-132.
[8]SHAN C,ZHU H. Bifurcations and complex dynamics of an SIR model with the impact of the number of hospital beds[J]. J differential equations,2014,257:1 662-1 688.
[9]SHAN C,ZHU H. Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources[J]. J differential equations,2016,260:4 339-4 365.
[10]WAN H,CUI J. Rich Dynamics of an epidemic model with saturation recovery[J]. Journal of applied mathematics,2013,Article ID 314958,9 pages.
[11]XIAO Y,TANG S. Dynamics of infection with nonlinear incidence in a simple vaccination model[J]. Nonlinear analysis:real world applications,2010,11:4 154-4 163.
[12]ZHOU T,ZHANG W,LU Q. Bifurcation analysis of an SIS epidemic model with saturated incidence rate and saturated treatment function[J]. J applied mathematics and computation,2014,226:288-305.
[13]VAN DEN DRIESSCHE P,WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental model of disease transmission[J]. J Math Biosci,2002,180:29-48.
[14]CASTILLO C C,SONG B. Dynamical models of tuberculosis and their applications[J]. Mathematical biosciences and enginieering,2004(1):361-404.

Memo

Memo:
-
Last Update: 2017-09-30