Global analyses of a state-dependent impulsive system for an SIRS model with a nonlinear incidence rate.

Authors

Chenxi Huang, Sanyi Tang, Qianqian Zhang

Published in

Journal of biological dynamics. Volume 20. Issue 1. Pages 2732280. Dec 31, 2026. Epub Sep 18, 2026.

Abstract

This paper establishes a state-feedback control system based on a nonlinear incidence SIRS model to explore the regulatory mechanism of infectious disease control. We develop a state-dependent impulsive model with threshold-triggered vaccination and isolation interventions once the susceptible population exceeds a predefined level. After investigating the basic properties of the ODE subsystem, we define and classify the Poincaré map and analyze its domain, range and monotonicity, which provides a theoretical basis for studying positive periodic solutions of the impulsive system under different ODE dynamics. The results show that the disease-free periodic solution is globally asymptotically stable for $p>1$, where $p$ is a parameter directly related to the force of the infection. When $0<p<1$, however, the model may exhibit bistability between the disease-free periodic solution and an endemic periodic solution, where the final outcome depends sensitively on the initial infection size, which is consistent with the weak transmissibility and controllable low-level prevalence.

PMID:
42757765
Bibliographic data and abstract were imported from PubMed on 18 Sep 2026.

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