A Simple Epidemic Model with Surprising Dynamics
A simple model incorporating demographic and epidemiologicalprocesses is explored. Four re-parameterized quantities the basicdemographic reproductive number ($\R_d$), the basic epidemiologicalreproductive number ($\R_0$), the ratio ($\nu$) between the averagelife spans of susceptible and infective...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.133 |
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| author | F. Berezovskaya G. Karev Baojun Song Carlos Castillo-Chavez |
| author_facet | F. Berezovskaya G. Karev Baojun Song Carlos Castillo-Chavez |
| author_sort | F. Berezovskaya |
| collection | DOAJ |
| description | A simple model incorporating demographic and epidemiologicalprocesses is explored. Four re-parameterized quantities the basicdemographic reproductive number ($\R_d$), the basic epidemiologicalreproductive number ($\R_0$), the ratio ($\nu$) between the averagelife spans of susceptible and infective class, and the relativefecundity of infectives ($\theta$), are utilized in qualitativeanalysis. Mathematically, non-analytic vector fields are handled byblow-up transformations to carry out a complete and global dynamicalanalysis. A family of homoclinics is found, suggesting that adisease outbreak would be ignited by a tiny number of infectiousindividuals. |
| format | Article |
| id | doaj-art-291d745845f84a5e9584409b9a5895e8 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-291d745845f84a5e9584409b9a5895e82025-01-24T01:47:55ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-10-012113315210.3934/mbe.2005.2.133A Simple Epidemic Model with Surprising DynamicsF. Berezovskaya0G. Karev1Baojun Song2Carlos Castillo-Chavez3Department of Mathematics, Howard University, Washington D.C., 20059Oak Ridge Institute for Science and Education (ORISE) 8600 Rockville Pike, Bldg. 38A, Rm. 5N511N, Bethesda, MD 20894Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287A simple model incorporating demographic and epidemiologicalprocesses is explored. Four re-parameterized quantities the basicdemographic reproductive number ($\R_d$), the basic epidemiologicalreproductive number ($\R_0$), the ratio ($\nu$) between the averagelife spans of susceptible and infective class, and the relativefecundity of infectives ($\theta$), are utilized in qualitativeanalysis. Mathematically, non-analytic vector fields are handled byblow-up transformations to carry out a complete and global dynamicalanalysis. A family of homoclinics is found, suggesting that adisease outbreak would be ignited by a tiny number of infectiousindividuals.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.133dynamical systembifurcation analysisglobalstability.epidemic model |
| spellingShingle | F. Berezovskaya G. Karev Baojun Song Carlos Castillo-Chavez A Simple Epidemic Model with Surprising Dynamics Mathematical Biosciences and Engineering dynamical system bifurcation analysis globalstability. epidemic model |
| title | A Simple Epidemic Model with Surprising Dynamics |
| title_full | A Simple Epidemic Model with Surprising Dynamics |
| title_fullStr | A Simple Epidemic Model with Surprising Dynamics |
| title_full_unstemmed | A Simple Epidemic Model with Surprising Dynamics |
| title_short | A Simple Epidemic Model with Surprising Dynamics |
| title_sort | simple epidemic model with surprising dynamics |
| topic | dynamical system bifurcation analysis globalstability. epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.133 |
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