Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality
We use a periodically forced SIS epidemic model with disease inducedmortality to study the combined effects of seasonal trends and death on theextinction and persistence of discretely reproducing populations. Weintroduce the epidemic threshold parameter, $R_0$, forpredicting disease dynamics in peri...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.385 |
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| author | John E. Franke Abdul-Aziz Yakubu |
| author_facet | John E. Franke Abdul-Aziz Yakubu |
| author_sort | John E. Franke |
| collection | DOAJ |
| description | We use a periodically forced SIS epidemic model with disease inducedmortality to study the combined effects of seasonal trends and death on theextinction and persistence of discretely reproducing populations. Weintroduce the epidemic threshold parameter, $R_0$, forpredicting disease dynamics in periodic environments. Typically, $R_01$ to extinction.Furthermore, we obtain conditions for the persistence of the totalpopulation. In addition, we use the Beverton-Holt recruitment function toshow that the infective population exhibits period-doubling bifurcationsroute to chaos where the disease-free susceptible population lives on a2-cycle (non-chaotic) attractor. |
| format | Article |
| id | doaj-art-20fff636c69d4353915205171632e791 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-20fff636c69d4353915205171632e7912025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018238540810.3934/mbe.2011.8.385Periodically forced discrete-time SIS epidemic model with diseaseinduced mortalityJohn E. Franke0Abdul-Aziz Yakubu1Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205We use a periodically forced SIS epidemic model with disease inducedmortality to study the combined effects of seasonal trends and death on theextinction and persistence of discretely reproducing populations. Weintroduce the epidemic threshold parameter, $R_0$, forpredicting disease dynamics in periodic environments. Typically, $R_01$ to extinction.Furthermore, we obtain conditions for the persistence of the totalpopulation. In addition, we use the Beverton-Holt recruitment function toshow that the infective population exhibits period-doubling bifurcationsroute to chaos where the disease-free susceptible population lives on a2-cycle (non-chaotic) attractor.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.385epidemicsinfectivesperiodic environmentssusceptibles. |
| spellingShingle | John E. Franke Abdul-Aziz Yakubu Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality Mathematical Biosciences and Engineering epidemics infectives periodic environments susceptibles. |
| title | Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality |
| title_full | Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality |
| title_fullStr | Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality |
| title_full_unstemmed | Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality |
| title_short | Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality |
| title_sort | periodically forced discrete time sis epidemic model with diseaseinduced mortality |
| topic | epidemics infectives periodic environments susceptibles. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.385 |
| work_keys_str_mv | AT johnefranke periodicallyforceddiscretetimesisepidemicmodelwithdiseaseinducedmortality AT abdulazizyakubu periodicallyforceddiscretetimesisepidemicmodelwithdiseaseinducedmortality |