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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/824192 |
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| _version_ | 1832548327291355136 |
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| author | Peilin Shi Lingzhen Dong |
| author_facet | Peilin Shi Lingzhen Dong |
| author_sort | Peilin Shi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5ad72bc85ff9472590ad7261992bf2bb |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5ad72bc85ff9472590ad7261992bf2bb2025-02-03T06:14:17ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/824192824192Dynamical Models for Infectious Diseases with Varying Population Size and VaccinationsPeilin Shi0Lingzhen Dong1Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, ChinaWe 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.http://dx.doi.org/10.1155/2012/824192 |
| spellingShingle | Peilin Shi Lingzhen Dong Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations Journal of Applied Mathematics |
| title | Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations |
| title_full | Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations |
| title_fullStr | Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations |
| title_full_unstemmed | Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations |
| title_short | Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations |
| title_sort | dynamical models for infectious diseases with varying population size and vaccinations |
| url | http://dx.doi.org/10.1155/2012/824192 |
| work_keys_str_mv | AT peilinshi dynamicalmodelsforinfectiousdiseaseswithvaryingpopulationsizeandvaccinations AT lingzhendong dynamicalmodelsforinfectiousdiseaseswithvaryingpopulationsizeandvaccinations |