Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates

Dongpo Hu, Xuexue Liu, Kun Li, Ming Liu and Xiao Yu ()
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Dongpo Hu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Xuexue Liu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Kun Li: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Ming Liu: Institute of Automation, Qufu Normal University, Qufu 273165, China
Xiao Yu: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2023, vol. 11, issue 19, 1-24

Abstract: In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. Parameter conditions for the occurrence of codimension-two bifurcations are obtained by constructing the corresponding approximate normal form with translation and transformation of several parameters and variables. To further confirm the accuracy of our theoretical analysis, numerical simulations such as phase portraits, bifurcation diagrams, and maximum Lyapunov exponents diagrams are provided. In particular, the coexistence of bistability states is observed by giving local attraction basins diagrams of different fixed points under different integral step sizes. It is possible to more clearly illustrate the model’s complex dynamic behavior by combining theoretical analysis and numerical simulation.

Keywords: discrete-time SIR model; codimension-two bifurcation; fold-flip bifurcation; 1:3 resonance; 1:4 resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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