The Stability of an SEI Epidemic System with Two Different Vertical Transmissions
碩士 === 東海大學 === 應用數學系 === 102 === In this thesis, we construct the autonomous SEI epidemic system with vertical transmission. We first analyze the local stability of the equilibriums. Secondly, we use the technique of Lyapunov function, LaSalle's Invariance Principle, and Ponicar$\grave{e}$-Ben...
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| Format: | Others |
| Language: | en_US |
| Published: |
2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/65349087772574075247 |
| Summary: | 碩士 === 東海大學 === 應用數學系 === 102 === In this thesis, we construct the autonomous SEI epidemic system with vertical transmission. We first analyze the local stability of the equilibriums. Secondly, we use the technique of Lyapunov function, LaSalle's Invariance Principle, and Ponicar$\grave{e}$-Bendixson Theorem to establish the global stability of the equilibriums. Furthermore, we obtain the basic reproductive number $\rho$ which determines whether the disease is extinct or not. Finally, we give some examples to illustrate our results.
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