Sir epidemic and predator - prey models of fractional-order
Recently, many deterministic mathematical models such as ordinary differential equations have been extended to fractional models, which are transformed using fractional differential equations. It was believed that these fractional models are more realistic to represent the daily life phenomena. The...
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| Format: | Thesis |
| Language: | English English |
| Published: |
2018
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| Online Access: | http://eprints.uthm.edu.my/327/1/24p%20owoyemi%20abiodun%20ezekiel.pdf http://eprints.uthm.edu.my/327/2/OWOYEMI%20ABIODUN%20EZEKIEL%20WATERMARK.pdf |
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| Summary: | Recently, many deterministic mathematical models such as ordinary differential equations have been extended to fractional models, which are transformed using fractional differential equations. It was believed that these fractional models are more realistic to represent the daily life phenomena. The main focus of this report is to extend the model of a predator-prey and the SIR epidemic models to fractional model. More specifically, the fractional predator-prey model which depend on the availability of a biotic resources was discussed. On the other hand, fractional SIR epidemic model with sub-optimal immunity, nonlinear incidence and saturated recovery rate was also discussed. The fractional ordinary differential equations were defined in the sense of the Caputo derivative. Stability analysis of the equilibrium points of the models for the fractional models were analyzed. Furthermore, the Hopf bifurcation analysis of each model was investigated . The result obtained showed that the model undergo Hopf bifurcation for some values. Throughout the project, the Adams-type predictor-corrector method to obtain the numerical solutions of the fractional models was applied. All computations were done by using mathematical software, Maple 18. |
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