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The impact of demography in a model of malaria with Transmission Blocking Drugs
  • Rachid Ouifki,
  • Jacek Banasiak,
  • Stéphane Tchoumi
Rachid Ouifki
North-West University - Mafikeng Campus
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Jacek Banasiak
University of Pretoria Department of Mathematics and Applied Mathematics

Corresponding Author:jacek.banasiak@up.ac.za

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Stéphane Tchoumi
University of Pretoria Department of Mathematics and Applied Mathematics
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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.
24 Oct 2023Submitted to Mathematical Methods in the Applied Sciences
25 Oct 2023Submission Checks Completed
25 Oct 2023Assigned to Editor
02 Nov 2023Review(s) Completed, Editorial Evaluation Pending
08 Nov 2023Reviewer(s) Assigned
26 Jan 2024Editorial Decision: Revise Minor
06 Feb 20241st Revision Received
13 Feb 2024Submission Checks Completed
13 Feb 2024Assigned to Editor
15 Mar 2024Review(s) Completed, Editorial Evaluation Pending