Epidemic models with nonlinear infection forces

Epidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model...

Full description

Saved in:
Bibliographic Details
Main Author: Wendi Wang
Format: Article
Language:English
Published: AIMS Press 2005-10-01
Series:Mathematical Biosciences and Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.267
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832590261092352000
author Wendi Wang
author_facet Wendi Wang
author_sort Wendi Wang
collection DOAJ
description Epidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model may admit a stable disease-free equilibrium and a stable endemic equilibrium at the same time. If we vary a recovery rate, numerical simulations show that the boundaries of the region for the persistence of the disease undergo the changes from the separatrix of a saddle to an unstable limit cycle. If the inhibition effect from behavior changes is weak, we find two limit cycles and obtain bifurcations of the model as the population size changes. We also find that the disease may die out although there are two endemic equilibria.
format Article
id doaj-art-6f7f9c55e8ac4005b3732be7488c688c
institution Kabale University
issn 1551-0018
language English
publishDate 2005-10-01
publisher AIMS Press
record_format Article
series Mathematical Biosciences and Engineering
spelling doaj-art-6f7f9c55e8ac4005b3732be7488c688c2025-01-24T01:51:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013126727910.3934/mbe.2006.3.267Epidemic models with nonlinear infection forcesWendi Wang0Department of Mathematics, Southwest Normal University, Chongqing, 400715, PREpidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model may admit a stable disease-free equilibrium and a stable endemic equilibrium at the same time. If we vary a recovery rate, numerical simulations show that the boundaries of the region for the persistence of the disease undergo the changes from the separatrix of a saddle to an unstable limit cycle. If the inhibition effect from behavior changes is weak, we find two limit cycles and obtain bifurcations of the model as the population size changes. We also find that the disease may die out although there are two endemic equilibria.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.267basic reproduction numberepidemiccycles.stabilitynonlinear incidence
spellingShingle Wendi Wang
Epidemic models with nonlinear infection forces
Mathematical Biosciences and Engineering
basic reproduction number
epidemic
cycles.
stability
nonlinear incidence
title Epidemic models with nonlinear infection forces
title_full Epidemic models with nonlinear infection forces
title_fullStr Epidemic models with nonlinear infection forces
title_full_unstemmed Epidemic models with nonlinear infection forces
title_short Epidemic models with nonlinear infection forces
title_sort epidemic models with nonlinear infection forces
topic basic reproduction number
epidemic
cycles.
stability
nonlinear incidence
url https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.267
work_keys_str_mv AT wendiwang epidemicmodelswithnonlinearinfectionforces