Volume 4, Issue 2
Bifurcation and Sensitivity Analysis of Immunity Duration in an Epidemic Model

NICHOLAS PIAZZA AND HAO WANG

Int. J. Numer. Anal. Mod. B, 4 (2013), pp. 179-202

Published online: 2013-04

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  • Abstract
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.
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37Mxx 92Bxx 37Nxx 65Yxx 65Pxx

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@Article{IJNAMB-4-179, author = {NICHOLAS PIAZZA AND HAO WANG}, title = {Bifurcation and Sensitivity Analysis of Immunity Duration in an Epidemic Model}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {2}, pages = {179--202}, abstract = {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.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/252.html} }
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.
NICHOLAS PIAZZA AND HAO WANG. (1970). Bifurcation and Sensitivity Analysis of Immunity Duration in an Epidemic Model. International Journal of Numerical Analysis Modeling Series B. 4 (2). 179-202. doi:
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