Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations
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 st...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/824192 |
| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |