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A mathematical model for the transmission of Louse-Borne Relapsing Fever

Alsheri, Ahuod and Gourley, Stephen (2017) A mathematical model for the transmission of Louse-Borne Relapsing Fever European Journal of Applied Mathematics.

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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 hu- manus. 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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Alsheri, Ahuoda.alsheri@surrey.ac.ukUNSPECIFIED
Gourley, StephenS.Gourley@surrey.ac.ukUNSPECIFIED
Date : 24 July 2017
Identification Number : 10.1017/S0956792517000237
Copyright Disclaimer : Copyright 2017 Cambridge University Press
Uncontrolled Keywords : Louse Borne Relapsing Fever; Vector-Borne Disease; Epidemic; Delay; Stability; Basic Reproduction Number.
Depositing User : Melanie Hughes
Date Deposited : 25 Jul 2017 12:26
Last Modified : 29 Sep 2017 16:55
URI: http://epubs.surrey.ac.uk/id/eprint/841748

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