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\begin{document}

\title{A singularly perturbed vector-bias malaria model incorporating bed-net
control}



\author[1]{Sanaa Salman}%
\affil[1]{Alexandria University}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
A malaria transmission disease model with host selectivity and
Insecticide treated bed nets (ITNs), as an intervention for controlling
the disease, is formulated. Since the vector is an insect, the vector
time scale is much more expeditious than the host time scale. This leads
to a singularly perturbed model with two distinctive intrinsic time
scales, two-slow for the host and one-fast for the vector. The basic
reproduction number R0 is calculated and the local stability analysis is
performed at equilibria of the model when the perturbation parameter e
\selectlanguage{english}\textgreater{} 0. The model is analyzed when e - \selectlanguage{english}0 using asymptotic
expansions technique. Merging bed-net control, vector-bias, and singular
perturbation have a notable effect on the model dynamics. It is shown
that if over \%30 of humans use ITNs, malaria disease burden can be
reduced. The dynamics on the slow surface indicate that the infected
vectors decays very fast when e \selectlanguage{english}= 0.001 according to the numerical
simulations.%
\end{abstract}%



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