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Ahuod Alsheri


+44 (0)1483 683024
17 AA 04

My publications

Publications

Alsheri A, Gourley S (2017) A mathematical model for the transmission of
Louse-Borne Relapsing Fever,
European Journal of Applied Mathematics 29 (3) pp. 417-449 Cambridge University Press
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.