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Global Stability Analysis of the Mathematical Model for Malaria Transmission between Vector and Host Population

¹ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
² Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
³ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
⁴ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
⁵ Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

American Journal of Computational Mathematics·Volume 14 (2024)·Pages 275–289·Published 7 May 2024·DOI10.4236/ajcm.2024.142012

Abstract

In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R 0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.

KeywordsMalaria TransmissionGlobal StabilityLyapunov Function

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Global Stability Analysis of the Mathematical Model for Malaria Transmission between Vector and Host Population

Abstract

References (15)