Dynamic Properties and Chaos Control Analysis of Discrete Epidemic Models Affected by Media Coverage

Yanfang Liang and Wenlong Wang ()
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Yanfang Liang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Wenlong Wang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2025, vol. 13, issue 17, 1-17

Abstract: This study investigates the dynamic behavior of a discrete epidemic model as affected by media coverage through integrated analytical and numerical methods. The main objective is to quantitatively assess the impact of media coverage on disease outbreak models through mathematical modeling. We use the central manifold theorem and bifurcation theory to perform a rigorous analysis of the periodic solutions, focusing on the coefficients and conditions governing the flip bifurcation. On this basis, state feedback and hybrid control are utilized to control the system chaotically. Under certain conditions, the chaos and bifurcation of the system can be stabilized by the control strategy. Numerical simulations further reveal the bifurcation dynamics, chaotic behavior, and control techniques. Our results show that media coverage is a key factor in regulating the intensity and chaos of disease transmission. Control techniques can effectively prevent large-scale outbreaks of epidemics. Notably, enhanced media coverage can effectively increase public awareness and defensive behaviors, thus contributing to mitigating disease spread.

Keywords: media coverage; discrete epidemic model; bifurcation analysis; chaos control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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