Backwards bifurcations and catastrophe in simple models of fatal diseases
type: Item
instance of: scholarly article
title: Backwards bifurcations and catastrophe in simple models of fatal diseases
zbMATH Open document ID: 0917.92022
author: Jonathan Dushoff
author: Wenzhang Huang
author: Carlos Castillo-Chavez
published in: Journal of Mathematical Biology
publication date: 1999-07-06T00:00:00Z
review text: Our purpose in writing this paper was to provide an intuitive explanation of the mechanisms that drive backwards bifurcations in some simple disease models, and thus to make it possible to explore in what circumstances such bifurcations might occur in more realistic disease models and hence in what circumstances we should look for the dynamical signature of the backwards bifurcations -- breakpoints above which the disease can persist for certain values of \(R_0\), and the possibility of `catastrophic' fast dynamics as underlying parameters change slowly -- in real-world disease systems. The original models on which our analysis is based are AIDS models. It is natural to consider the possibility that backwards bifurcations of the type discussed here may occur in AIDS, with men making up the core groups and women the victim groups, since male homosexual transmission is thought to be very important to the spread of AIDS in many places. For this to cause backwards bifurcations, however, AIDS would need to change the population structure in such a way as to increase the proportion of men's sexual contacts that were with other men. This is certainly possible, but does not intuitively seem likely. In general, models of sexual mixing involve complicating social factors beyond the scope of this discussion. An exploration of the possibility of core/victim backwards bifurcations in AIDS would certainly be of interest, however. Another difficulty with AIDS modeling is that, directly contrary to our discussion of slow-changing parameters, it seems likely that behavioral `parameters' in a disease like AIDS change quickly compared to the time scale of disease spread itself. For a wide variety of other diseases, it is at least plausible that a `core' group of healthier, more active people might be both more important than other groups at spreading the disease, and less affected by it. For backwards bifurcations to be caused by the mechanism discussed here, however, it would be nece…
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1140135
zbMATH Keywords: backwards bifurcations
zbMATH Keywords: AIDS models
Wikidata QID: Q43857988
MaRDI profile type: Publication
full work available at URL: s002850050099
OpenAlex ID: W2010825494
DOI: 10.1007/S002850050099
description: scientific article; zbMATH DE number 1140135