TY - JOUR
T1 - Bifurcation and Sensitivity Analysis of Immunity Duration in an Epidemic Model
AU - NICHOLAS PIAZZA AND HAO WANG
JO - International Journal of Numerical Analysis Modeling Series B
VL - 2
SP - 179
EP - 202
PY - 2013
DA - 2013/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/252.html
KW - immunity duration
KW - bifurcation
KW - sensitivity
KW - SIR
KW - disease transmission
AB - Most disease transmission models assume no immunity or permanent immunity for simplicity, however, hosts have temporary immunity for most diseases. In this note we find that the
immunity duration is actually the most sensitive parameter for dynamics of disease transmission.
We provide numerical schemes to sketch Hopf bifurcations (forward or backward), sensitivity
surfaces, periodicity diagrams (one dimensional or two dimensional parameter space) for a disease
transmission model with immunity delay. The methods introduced here can be easily modified
for a specific disease transmission model. We also test how different incidence functions change
dynamics via bifurcation diagrams.