SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects
We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impuls...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/542154 |
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| author | Tongqian Zhang Xinzhu Meng Tonghua Zhang |
| author_facet | Tongqian Zhang Xinzhu Meng Tonghua Zhang |
| author_sort | Tongqian Zhang |
| collection | DOAJ |
| description | We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input. |
| format | Article |
| id | doaj-art-fc8d3d7cda984024984040a1be5ed140 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fc8d3d7cda984024984040a1be5ed1402025-02-03T01:23:41ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/542154542154SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive EffectsTongqian Zhang0Xinzhu Meng1Tonghua Zhang2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaShandong University of Science and Technology, Qingdao 266590, ChinaDepartment of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, VIC 3122, AustraliaWe first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input.http://dx.doi.org/10.1155/2014/542154 |
| spellingShingle | Tongqian Zhang Xinzhu Meng Tonghua Zhang SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects Abstract and Applied Analysis |
| title | SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects |
| title_full | SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects |
| title_fullStr | SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects |
| title_full_unstemmed | SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects |
| title_short | SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects |
| title_sort | sveirs a new epidemic disease model with time delays and impulsive effects |
| url | http://dx.doi.org/10.1155/2014/542154 |
| work_keys_str_mv | AT tongqianzhang sveirsanewepidemicdiseasemodelwithtimedelaysandimpulsiveeffects AT xinzhumeng sveirsanewepidemicdiseasemodelwithtimedelaysandimpulsiveeffects AT tonghuazhang sveirsanewepidemicdiseasemodelwithtimedelaysandimpulsiveeffects |