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Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-30
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We formulate and discuss models for the spread of infectious diseases with variable population sizes and vaccinations on the susceptible individuals.
First, we assume that the susceptible individuals are vaccinated continuously.
We establish the threshold-like results for the existence and global stability of the disease-free and the endemic equilibriums for these systems.
Especially, we prove the global stability of the endemic equilibriums by converting the systems into integrodifferential equations.
Second, we suppose that vaccinations occur once per time period.
We obtain the existence and global stability of the disease-free periodic solutions for such systems with impulsive effects.
By a useful bifurcation theorem, we acquire the existence of the endemic periodic solutions when the disease-related deaths do not occur.
At last, we compare the results with vaccinations and without vaccinations and illustrate our results by numerical simulations.
American Psychological Association (APA)
Shi, Peilin& Dong, Lingzhen. 2012. Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-993733
Modern Language Association (MLA)
Shi, Peilin& Dong, Lingzhen. Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations. Journal of Applied Mathematics No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-993733
American Medical Association (AMA)
Shi, Peilin& Dong, Lingzhen. Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-993733
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993733