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\begin{document}

\title{The impact of demography in a model of malaria with Transmission
Blocking Drugs}



\author[1]{Rachid Ouifki}%
\author[2]{Jacek Banasiak}%
\author[2]{Stéphane Tchoumi}%
\affil[1]{North-West University - Mafikeng Campus}%
\affil[2]{University of Pretoria Department of Mathematics and Applied Mathematics}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
In this paper, we develop and analyze a mathematical model for spreading
malaria, including treatment with Transmission Blocking Drugs (TBDs).
The paper's main aim is to demonstrate the impact the chosen model for
demographic growth has on the disease's transmission and the effect of
its treatment with TBDs. We calculate the model's control reproduction
number and equilibria, and perform a global stability analysis of the
disease-free equilibrium point. The mathematical analysis reveals that,
depending on the model's demography, the model can exhibit forward,
backward and even some unconventional types of bifurcation, where
disease elimination can occur for both small and large values of the
reproduction number. We also conduct a numerical analysis to explore the
short-time behavior of the model. A key finding is that for one type of
demographic growth, the population experienced a significantly higher
disease burden than the others, and when exposed to high levels of
treatment with TBDs, only this population succeeded in effectively
eliminating the disease within a reasonable timeframe.%
\end{abstract}%



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