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A mathematical model for the transmission of louse-borne relapsing fever

Published online by Cambridge University Press:  24 August 2017

AHUOD ALSHERI  and
STEPHEN A. GOURLEY
AHUOD ALSHERI
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK emails: a.alsheri@surrey.ac.uk, s.gourley@surrey.ac.uk
STEPHEN A. GOURLEY
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK emails: a.alsheri@surrey.ac.uk, s.gourley@surrey.ac.uk
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Abstract

We present a detailed derivation and analysis of a model consisting of seven coupled delay differential equations for louse-borne relapsing fever (LBRF), a disease transmitted from human to human by the body louse Pediculus humanus humanus. Delays model the latency stages of LBRF in humans and lice, which vary in duration from individual to individual, and are therefore modelled using distributed delays with relatively general kernels. A particular feature of the transmission of LBRF to a human is that it involves the death of the louse, usually by crushing which has the effect of releasing the infected body fluids of the dead louse onto the hosts skin. Careful attention is paid to this aspect. We obtain results on existence, positivity, boundedness, linear and nonlinear stability, and persistence. We also derive a basic reproduction number R0 for the model and discuss its dependence on the model parameters. Our analysis of the model suggests that effective louse control without crushing should be the best strategy for LBRF eradication. We conclude that simple measures and precautions should, in general, be sufficient to facilitate disease eradication.

Keywords

Louse-borne relapsing fevervector-borne diseaseepidemicdelaystabilitybasic reproduction number
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Issue 3 , June 2018 , pp. 417 - 449
Copyright
Copyright © Cambridge University Press 2017 

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