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Global dynamics of a piece-wise epidemic model with switching vaccination strategy

Global dynamics of a piece-wise epidemic model with switching vaccination strategy

Wang, Aili, Xiao, Yanni and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2014) Global dynamics of a piece-wise epidemic model with switching vaccination strategy. Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 19 (9). pp. 2915-2940. ISSN 1531-3492 (Print), 1553-524X (Online) (doi:https://doi.org/10.3934/dcdsb.2014.19.2915)

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Abstract

A piece-wise epidemic model of a switching vaccination program, implemented once the number of people exposed to a disease-causing virus reaches a critical level, is proposed. In addition, variation or uncertainties in interventions are examined with a perturbed system version of the model. We also analyzed the global dynamic behaviors of both the original piece-wise system and the perturbed version theoretically, using generalized Jacobian theory, Lyapunov constants for a non-smooth vector field and a generalization of Dulac's criterion. The main results show that, as the critical value varies, there are three possibilities for stabilization of the piece-wise system: (i) at the disease-free equilibrium; (ii) at the endemic states for the two subsystems or (iii) at a generalized equilibrium which is a novel global attractor for non-smooth systems. The perturbed system exhibits new global attractors including a pseudo-focus of parabolic-parabolic (PP) type, a pseudo-equilibrium and a crossing cycle surrounding a sliding mode region. Our findings demonstrate that an infectious disease can be eradicated either by increasing the vaccination rate or by stabilizing the number of infected individuals at a previously given level, conditional upon a suitable critical level and the parameter values.

Item Type: Article
Additional Information: [1] This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B (DCDS-B) following peer review. The definitive publisher-authenticated version Wang, Aili, Xiao, Yanni and Cheke, Robert A. (2014) Global dynamics of a piece-wise epidemic model with switching vaccination strategy. Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 19 (9). pp. 2915-2940. ISSN 1531-3492 (Print), 1553-524X (Online) (doi:10.3934/dcdsb.2014.19.2915) is available online at: http://dx.doi.org/10.3934/dcdsb.2014.19.2915. [2] The authors are supported by the National Natural Science Foundation of China (NSFC, 11171268(YX)), by the Fundamental Research Funds for the Central Universities(GK 08143042 (YX)) and by the International Development Research Center, Ottawa, Canada (104519-010).
Uncontrolled Keywords: piece-wise epidemic model, vaccination, generalized equilibrium, global dynamics, perturbed system, limit cycle
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Engineering & Science
Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Related URLs:
Last Modified: 27 Apr 2016 17:10
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/12198

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