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- Title
Complex dynamics of a discrete‐time seasonally forced SIR epidemic model.
- Authors
Naik, Parvaiz Ahmad; Eskandari, Zohreh; Madzvamuse, Anotida; Avazzadeh, Zakieh; Zu, Jian
- Abstract
In this paper, a discrete‐time seasonally forced SIR epidemic model with a nonstandard discretization scheme is investigated for different types of bifurcations. Although many researchers have already suggested numerically that this model can exhibit chaotic dynamics, not much focus is given to the bifurcation theory of the model. We prove analytically and numerically the existence of different types of bifurcations in the model. First, one and two parameters bifurcations of this model are investigated by computing their critical normal form coefficients. Second, the flip, Neimark–Sacker, and strong resonance bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complete complex dynamical behavior of the model is investigated. The model is discretized by a novel technique, namely a nonstandard finite difference discretization scheme (NSFD). Some graphical representations of the model are presented to verify the obtained results.
- Subjects
FINITE differences; EPIDEMICS; BIFURCATION theory; MODEL theory
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 6, p7045
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.8955