Analysis of a malaria transmission mathematical model considering immigration

Volume 30, Issue 4, pp 390--406 http://dx.doi.org/10.22436/jmcs.030.04.08

Publication Date: April 04, 2023 Submission Date: July 04, 2022 Revision Date: October 19, 2022 Accteptance Date: January 30, 2023

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Authors

C. Taftaf - Lab-Mia, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco. H. Benazza - Lab-Mia, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco. Y. Louartassi - Superior School of Technology Sale, Mohammed V University in Rabat, LASTIMI, Z, Morocco. Z. Hamidi - Laboratory M2PA, Department of mathematics \(\&\) informatics, ENS. University Sidi Mohamed Ben Abdellah. Fez, Morocco.

Abstract

The aims of this paper are to study the local and global stability of the equilibrium points using a mathematical model for malaria disease. The model is based on five differential equations. The analysis of the stability was examined using the Lyapunov method. We prove that the disease free equilibrium point is locally and globally asymptotically stable when \(R_0<1\) and unstable when \(R_0>1\). On the other hand, the endemic equilibrium point is locally and globally asymptotically stable when \(R_0>1\).

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Keywords

• Malaria
• epidemic model
• Lyapunov
• endemic equilibrium
• disease-free equilibrium

MSC

•  92B05
•  92B10
•  93A10

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