Multiple recurrent outbreak cycles in an autonomous epidemiological model due to multiple limit cycle bifurcation. (English) Zbl 1460.92227
The authors study a SI epidemiological model and analyze that the coexistence of multiple attractors attributes to the complex outbreak patterns. They first give the existence of an isolated center under some reasonable conditions, propose that the existence of Hopf bifurcation by properly perturbation, and obtain limit cycles around the center. They further prove that the maximum number of the coexisting limit cycles is three, and point out a corresponding set for the existence of the three limit cycles.
Reviewer: Hongying Shu (Xi’an)
MSC:
| 92D30 | Epidemiology |
| 34C07 | Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations |
| 34D45 | Attractors of solutions to ordinary differential equations |
Keywords:
epidemiology; infectious diseases; recurrent outbreaks; multiple attractors; multiple limit cyclesReferences:
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