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Nonlinear pulse vaccination in an SIR epidemic model with resource limitation

Nonlinear pulse vaccination in an SIR epidemic model with resource limitation

Qin, Wenjie, Tang, Sanyi and Cheke, Robert A. ORCID: 0000-0002-7437-1934 (2013) Nonlinear pulse vaccination in an SIR epidemic model with resource limitation. Abstract and Applied Analysis, 2013:670263. ISSN 1085-3375 (Print), 1687-0409 (Online) (doi:https://doi.org/10.1155/2013/670263)

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Abstract

Mathematical models can assist in the design and understanding of vaccination strategies when resources are limited. Here we propose and analyse an SIR epidemic modelwith a nonlinear pulse vaccination to examine how a limited vaccine resource affects the transmission and control of infectious diseases, in particular emerging infectious diseases. The threshold condition for the stability of the disease free steady state is given. Latin Hypercube Sampling/Partial Rank Correlation Coefficient uncertainty and sensitivity analysis techniques were employed to determine the key factors which are most significantly related to the threshold value. Comparing this threshold value with that without resource limitation, our results indicate that if resources become limited pulse
vaccination should be carried out more frequently than when sufficient resources are available to eradicate an infectious disease. Once the threshold value exceeds a critical level, both susceptible and infected populations can oscillate periodically. Furthermore, when the pulse vaccination period is chosen as a bifurcation parameter, the SIR model with nonlinear pulse vaccination reveals
complex dynamics including period doubling, chaotic solutions, and coexistence of multiple attractors. The implications of our findings with respect to disease control are discussed.

Item Type: Article
Additional Information: [1] Citation: Wenjie Qin, Sanyi Tang, and Robert A. Cheke, “Nonlinear Pulse Vaccination in an SIR Epidemic Model with Resource Limitation,” Abstract and Applied Analysis, vol. 2013, Article ID 670263, 13 pages, 2013. doi:10.1155/2013/670263. [2] Copyright © 2013 Wenjie Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Uncontrolled Keywords: model, SIR, vaccination, pulse
Faculty / Department / Research Group: Faculty of Engineering & Science > Natural Resources Institute
Faculty of Engineering & Science > Natural Resources Institute > Agriculture, Health & Environment Department
Related URLs:
Last Modified: 02 May 2016 08:06
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/10874

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