A simple vaccination model with multiple endemic states.
A simple two-dimensional SIS model with vaccination exhibits a backward bifurcation for some parameter values. A two-population version of the model leads to the consideration of vaccination policies in paired border towns. The results of our mathematical analysis indicate that a vaccination campaign &phi; meant to reduce a disease's reproduction number R(&phi;) below one may fail to control the disease. If the aim is to prevent an epidemic outbreak, a large initial number of infective persons can cause a high endemicity level to arise rather suddenly even if the vaccine-reduced reproduction number is below threshold. If the aim is to eradicate an already established disease, bringing the vaccine-reduced reproduction number below one may not be sufficient to do so. The complete bifurcation analysis of the model in terms of the vaccine-reduced reproduction number is given, and some extensions are considered.
Kribs-Zaleta
C M
CM
Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA. kribs@uta.edu
Velasco-Hernández
J X
JX
D016915:AIDS Vaccines / Q000009:adverse effects / Q000592:standards*; D004196:Disease Outbreaks / Q000517:prevention & control; D015658:HIV Infections / Q000517:prevention & control; D006801:Humans; D008800:Mexico / Q000453:epidemiology; D018448:Models, Immunological; D011634:Public Health; D012409:Rubella / Q000517:prevention & control; D012411:Rubella Vaccine / Q000009:adverse effects / Q000592:standards; D014481:United States / Q000453:epidemiology; D014611:Vaccination / Q000009:adverse effects / Q000592:standards*
D016915:AIDS Vaccines; D012411:Rubella Vaccine