Yang, JIn, Guan, Likun, Chen, Zhou, Tan, Yuanshun, Liu, Zijian and Cheke, Robert ORCID: 0000-0002-7437-1934 (2023) Bifurcation analysis of a nonlinear pulse SIR model with media coverage. Nonlinear Dynamics. ISSN 0924-090X (Print), 1573-269X (Online) (doi:https://doi.org/10.1007/s11071-023-08869-x)

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Abstract

In this study, we propose a nonlinear pulse SIR model with media coverage to describe the effects of vaccination and isolation measures determined by the numbers of susceptible individuals. The dynamic behaviour of themodel without impulse is discussed and the basic reproduction number defined. The existence and stability of disease-free periodic solutions (DFPS) are investigated when R0 < 1. Even if R0 > 1 the DFPS is still stable when SH < 1/R0, which indicates that a state-dependent pulse strategy is still effective in preventing the outbreak of infectious diseases by choosing suitable SH. Further, by defining the Poincaré map and using the bifurcation theorem, transcritical and pitchfork bifurcations near the DFPS with respect to some key parameters were investigated. We found that complex dynamic behaviour, with important biological significance, and the rich biological significance, can be exhibitedwith the introduction of impulse control into the model.

Item Type:	Article
Uncontrolled Keywords:	SIR model; media coverage; nonlinear pulse; Bifurcations; Poincaré map
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science R Medicine > RA Public aspects of medicine > RA0421 Public health. Hygiene. Preventive Medicine
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > Natural Resources Institute Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Last Modified:	20 Sep 2023 12:24
URI:	http://gala.gre.ac.uk/id/eprint/44145

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