Chaos analysis and control for a class of SIR epidemic model with seasonal fluctuation. (English) Zbl 1354.92099
Summary: In this paper, the problems of chaos and chaos control for a class of susceptible-infected-removed (SIR) epidemic model with seasonal fluctuation are investigated. The seasonality in outbreak is natural among infectious diseases, as the common influenza, A type H1N1 influenza and so on. It is shown that there exist chaotic phenomena in the epidemic model. Furthermore, the tracking control method is used to control chaotic motions in the epidemic model. A feedback controller is designed to achieve tracking of an ideal output. Thus, the density of infected individuals can converge to zero, in other words, the disease can be disappeared. Finally, numerical simulations illustrate that the controller is effective.
MSC:
| 92D30 | Epidemiology |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 93B52 | Feedback control |
Keywords:
epidemic model; differential-algebraic system; seasonal fluctuation; chaos; tracking controlReferences:
| [1] | DOI: 10.1016/j.mbs.2004.01.003 · Zbl 1073.92040 · doi:10.1016/j.mbs.2004.01.003 |
| [2] | DOI: 10.1016/j.apm.2008.01.005 · Zbl 1205.34049 · doi:10.1016/j.apm.2008.01.005 |
| [3] | DOI: 10.1016/j.mbs.2004.10.011 · Zbl 1065.92040 · doi:10.1016/j.mbs.2004.10.011 |
| [4] | DOI: 10.1016/j.mcm.2003.10.047 · Zbl 1065.92041 · doi:10.1016/j.mcm.2003.10.047 |
| [5] | DOI: 10.1016/j.chaos.2007.08.056 · Zbl 1197.34123 · doi:10.1016/j.chaos.2007.08.056 |
| [6] | DOI: 10.1016/S0167-2789(02)00389-5 · Zbl 0993.92030 · doi:10.1016/S0167-2789(02)00389-5 |
| [7] | DOI: 10.1016/j.nonrwa.2010.12.021 · Zbl 1235.34216 · doi:10.1016/j.nonrwa.2010.12.021 |
| [8] | DOI: 10.1098/rspa.1927.0118 · JFM 53.0517.01 · doi:10.1098/rspa.1927.0118 |
| [9] | DOI: 10.1016/j.chaos.2005.09.024 · Zbl 1142.34352 · doi:10.1016/j.chaos.2005.09.024 |
| [10] | DOI: 10.1016/j.nonrwa.2010.08.017 · Zbl 1203.92058 · doi:10.1016/j.nonrwa.2010.08.017 |
| [11] | DOI: 10.1016/j.nonrwa.2008.10.041 · Zbl 1184.92044 · doi:10.1016/j.nonrwa.2008.10.041 |
| [12] | Nisbet R. M., Modelling Fluctuating Populations (1982) · Zbl 0593.92013 |
| [13] | DOI: 10.1007/BF00276232 · Zbl 0558.92013 · doi:10.1007/BF00276232 |
| [14] | Wang J., Proc. Chin. Soc. Electr. Eng. 21 pp 23– (2001) |
| [15] | DOI: 10.1016/0167-2789(85)90011-9 · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9 |
| [16] | DOI: 10.1016/j.nonrwa.2008.04.017 · Zbl 1163.92332 · doi:10.1016/j.nonrwa.2008.04.017 |
| [17] | DOI: 10.1016/j.amc.2007.09.053 · Zbl 1136.92336 · doi:10.1016/j.amc.2007.09.053 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
