Abstract
In this study, a new discrete SI epidemic model is proposed and established from SI fractional-order epidemic model. The existence conditions, the stability of the equilibrium points and the occurrence of bifurcation are analyzed. By using the center manifold theorem and bifurcation theory, it is shown that the model undergoes flip and Neimark–Sacker bifurcation. The effects of step size and fractional-order parameters on the dynamics of the model are studied. The bifurcation analysis is also conducted and our numerical results are in agreement with theoretical results.
Highlights
Mathematical modeling plays an important role in understanding the dynamics of many infectious diseases
Using the discretized-time SI model with fractional order is a new topic, this paper provides a new contribution to the literature
8 Discussion and conclusion A new discrete-time SI epidemic model has been discussed in this paper
Summary
Mathematical modeling plays an important role in understanding the dynamics of many infectious diseases. A discrete-time SI is established by SI fractional-order epidemic model. Using the discretized-time SI model with fractional order is a new topic, this paper provides a new contribution to the literature. This model is constructed by Iwami et al [29] to explain the spreads of avian influenza through the bird world and describes the interactions between them. The fractional-order form of the SI epidemic model (2.1) can be formulated as follows: Dαt S(t) = – μS – βSI, (2.2). Remark 3.1 It should be noticed that if α → 1 in (3.7), the Euler discretization of SI model is obtained
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