Stability and Bifurcation in a Delayed Malaria Model with Threshold Control

Ying Qiao, Yuelin Gao, Jimin Li (), Zhixin Han and Bo Zhang
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Ying Qiao: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Yuelin Gao: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Jimin Li: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Zhixin Han: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Bo Zhang: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China

Mathematics, 2025, vol. 13, issue 20, 1-17

Abstract: In this paper, we develop a delayed malaria model that integrates a discrete time delay and a non-smooth threshold-based control strategy. Using the time delay τ as a bifurcation parameter, we investigate the local stability of the endemic equilibrium through analysis of the characteristic equation. We establish sufficient conditions for the occurrence of Hopf bifurcation, demonstrating how stability switches emerge as τ varies. Furthermore, when the infected population exceeds a critical threshold I m , a sliding mode domain arises. We analyze the dynamics within this sliding region using the Utkin equivalent control method. Numerical simulations are provided to support the theoretical findings, illustrating the complex dynamical behaviors induced by both delay and threshold control.

Keywords: malaria model; time delay; threshold control; local stability; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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