On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy
In this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights in...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/7191487 |
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| author | Jalil Rashidinia Mehri Sajjadian Jorge Duarte Cristina Januário Nuno Martins |
| author_facet | Jalil Rashidinia Mehri Sajjadian Jorge Duarte Cristina Januário Nuno Martins |
| author_sort | Jalil Rashidinia |
| collection | DOAJ |
| description | In this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal-type iterated maps with a striking biological meaning is detected among those dynamical regimes of the densities of the susceptibles. Using the theory of symbolic dynamics, these iterated maps are characterized based on the computation of an important numerical invariant, the topological entropy. The introduction of a degree (or amplitude) of seasonality, ε, is responsible for inducing complexity into the population dynamics. The resulting dynamical behaviors are studied using some of the previous tools for particular values of the strength of the seasonality forcing, ε. Finally, we carry out a study of the discrete SIR epidemic model under a planned constant vaccination strategy. We examine what effect this vaccination regime will have on the periodic and chaotic dynamics originated by seasonally forced epidemics. |
| format | Article |
| id | doaj-art-cfffc237bd904a8490e48bf35c964010 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-cfffc237bd904a8490e48bf35c9640102025-02-03T01:12:22ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/71914877191487On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination StrategyJalil Rashidinia0Mehri Sajjadian1Jorge Duarte2Cristina Januário3Nuno Martins4School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranInstituto Superior de Engenharia de Lisboa (ISEL), Department of Mathematics, Rua Conselheiro Emídio Navarro 1, 1949-014 Lisboa, PortugalInstituto Superior de Engenharia de Lisboa (ISEL), Department of Mathematics, Rua Conselheiro Emídio Navarro 1, 1949-014 Lisboa, PortugalCenter for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalIn this article, we consider the discretized classical Susceptible-Infected-Recovered (SIR) forced epidemic model to investigate the consequences of the introduction of different transmission rates and the effect of a constant vaccination strategy, providing new numerical and topological insights into the complex dynamics of recurrent diseases. Starting with a constant contact (or transmission) rate, the computation of the spectrum of Lyapunov exponents allows us to identify different chaotic regimes. Studying the evolution of the dynamical variables, a family of unimodal-type iterated maps with a striking biological meaning is detected among those dynamical regimes of the densities of the susceptibles. Using the theory of symbolic dynamics, these iterated maps are characterized based on the computation of an important numerical invariant, the topological entropy. The introduction of a degree (or amplitude) of seasonality, ε, is responsible for inducing complexity into the population dynamics. The resulting dynamical behaviors are studied using some of the previous tools for particular values of the strength of the seasonality forcing, ε. Finally, we carry out a study of the discrete SIR epidemic model under a planned constant vaccination strategy. We examine what effect this vaccination regime will have on the periodic and chaotic dynamics originated by seasonally forced epidemics.http://dx.doi.org/10.1155/2018/7191487 |
| spellingShingle | Jalil Rashidinia Mehri Sajjadian Jorge Duarte Cristina Januário Nuno Martins On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy Complexity |
| title | On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy |
| title_full | On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy |
| title_fullStr | On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy |
| title_full_unstemmed | On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy |
| title_short | On the Dynamical Complexity of a Seasonally Forced Discrete SIR Epidemic Model with a Constant Vaccination Strategy |
| title_sort | on the dynamical complexity of a seasonally forced discrete sir epidemic model with a constant vaccination strategy |
| url | http://dx.doi.org/10.1155/2018/7191487 |
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