Document Type
Article
Source Publication Title
Mathematical Biosciences
First Page
183
Last Page
201
DOI
http://dx.doi.org/10.1016/S0025-5564(00)00003-1
Abstract
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 φ meant to reduce a disease's reproduction number R(φ) 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.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
1-1-2000
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Kribs, Christopher and Velasco-Hernandez, Jorge X., "A simple vaccination model with multiple endemic states" (2000). Mathematics Faculty Publications. 8.
https://mavmatrix.uta.edu/math_facpubs/8
Comments
JXVH acknowledges support from a CONACYT grant 1998 and UAM-I internal grant. CMKZ research was partially supported by an REP grant from the University of Texas at Arlington during the summer of 1998.