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/lp/oxford-university-press/analysis-of-a-malaria-model-with-a-distributed-delay-e0OGqRHTHs
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- Publisher
- Oxford University Press
- Copyright
- The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
- Subject
- Articles
- ISSN
- 0272-4960
- eISSN
- 1464-3634
- DOI
- 10.1093/imamat/hxt009
- Publisher site
- See Article on Publisher Site
Abstract
We consider a vectorhost model for the transmission dynamics of malaria with a gamma-distributed delay representing the incubation period of the disease in the vector. We analyse the impact of the delay on the steady states and their stability, and determine a threshold value for the mean delay at which the system undergoes either a transcritical or a backward bifurcation. We show that, the critical value depends on the shape parameter of the gamma distribution implying that the eradication or establishment of malaria does not depend only on the mean value of the delay but also on the shape parameter. A sensitivity analysis is performed by calculating the sensitivity index of the basic reproductive number and the endemic steady states to compare the effect of the mean delay and shape parameter on the initial disease transmission and the disease prevalence at the equilibrium. Numerical simulations are carried out to confirm the theoretical findings to investigate the impact of the delay on the prevalence of the disease.
Journal
IMA Journal of Applied Mathematics – Oxford University Press
Published: Dec 5, 2014
Keywords: malaria model distributed delay basic reproduction number equilibrium stability transcritical bifurcation backward bifurcation