Backward bifurcation for some general recovery functions

We consider an epidemic model for the dynamics of an infectious disease that incorporates a nonlinear function h(I), which describes the recovery rate of infectious individuals. We show that in spite of the simple structure of the model, a backward bifurcation may occur if the recovery rate h(I) dec...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-03, Vol.40 (5), p.1505-1515
Main Authors: Villavicencio Pulido, Geiser, Barradas, Ignacio, Luna, Beatriz
Format: Article
Language:English
Subjects:
Allocations
backward bifurcation
Bifurcations
epidemic model
Epidemics
Infectious diseases
Mathematical analysis
Mathematical models
multiple endemic state
Nonlinearity
Recovery
recovery function
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider an epidemic model for the dynamics of an infectious disease that incorporates a nonlinear function h(I), which describes the recovery rate of infectious individuals. We show that in spite of the simple structure of the model, a backward bifurcation may occur if the recovery rate h(I) decreases and the velocity of the recovery rate dh(0)dI is below a threshold value in the beginning of the epidemic. These functions would represent a weak reaction or slow treatment measures because, for instance, of limited allocation of resources o sparsely distributed populations. This includes commonly used functionals, as the monotone saturating Michaelis–Menten, and non monotone recovery rates, used to represent a recovery rate limited by the increasing number of infected individuals. We are especially interested in control policies that can lead to recovery functions that avoid backward bifurcation. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4074