Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method
We are concerned with the estimation of the domain of attraction (DOA) for suboptimal immunity epidemic models. We establish a procedure to determine the maximal Lyapunov function in the form of rational functions. Based on the definition of DOA and the maximal Lyapunov function, a theorem and subse...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/508794 |
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| author | Chang Phang Yonghong Wu Benchawan Wiwatanapataphee |
| author_facet | Chang Phang Yonghong Wu Benchawan Wiwatanapataphee |
| author_sort | Chang Phang |
| collection | DOAJ |
| description | We are concerned with the estimation of the domain of attraction (DOA) for suboptimal immunity epidemic models. We establish a procedure to determine the maximal Lyapunov function in the form of rational functions. Based on the definition of DOA and the maximal Lyapunov function, a theorem and subsequently a numerical procedure are established to determine the maximal Lyapunov function and the DOA. Determination of the domain of attraction for epidemic models is very important for understanding the dynamic behaviour of the disease transmission as a function of the state of population distribution in different categories of disease states. We focus on suboptimal immunity epidemic models with saturated treatment rate and nonlinear incidence rate. Different from classical models, suboptimal immunity models are more realistic to explain the microparasite
infection diseases such as Pertussis and Influenza A. We show that, for certain values of the parameter, larger k value (i.e., the model is more toward the SIR model) leads to a smaller DOA. |
| format | Article |
| id | doaj-art-121f53ffc6774ee4af45a555043f8f37 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-121f53ffc6774ee4af45a555043f8f372025-08-20T02:01:54ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/508794508794Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function MethodChang Phang0Yonghong Wu1Benchawan Wiwatanapataphee2Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Batu Pahat, 86400 Johor, MalaysiaDepartment of Mathematics and Statistics, Curtin University, Perth, WA 6845, AustraliaDepartment of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandWe are concerned with the estimation of the domain of attraction (DOA) for suboptimal immunity epidemic models. We establish a procedure to determine the maximal Lyapunov function in the form of rational functions. Based on the definition of DOA and the maximal Lyapunov function, a theorem and subsequently a numerical procedure are established to determine the maximal Lyapunov function and the DOA. Determination of the domain of attraction for epidemic models is very important for understanding the dynamic behaviour of the disease transmission as a function of the state of population distribution in different categories of disease states. We focus on suboptimal immunity epidemic models with saturated treatment rate and nonlinear incidence rate. Different from classical models, suboptimal immunity models are more realistic to explain the microparasite infection diseases such as Pertussis and Influenza A. We show that, for certain values of the parameter, larger k value (i.e., the model is more toward the SIR model) leads to a smaller DOA.http://dx.doi.org/10.1155/2013/508794 |
| spellingShingle | Chang Phang Yonghong Wu Benchawan Wiwatanapataphee Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method Abstract and Applied Analysis |
| title | Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method |
| title_full | Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method |
| title_fullStr | Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method |
| title_full_unstemmed | Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method |
| title_short | Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method |
| title_sort | computation of the domain of attraction for suboptimal immunity epidemic models using the maximal lyapunov function method |
| url | http://dx.doi.org/10.1155/2013/508794 |
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