Electron. J. Differential Equations, Vol. 2019 (2019), No. 09, pp. 1-10.

Global stability analysis of malaria transmission dynamics with vigilant compartment

Olawale S. Obabiyi, Samson Olaniyi

A deterministic compartmental model for the transmission dynamics of malaria incorporating vigilant human compartment is studied. The model is qualitatively analyzed to investigate its asymptotic behavior with respect to the equilibria. It is shown, using a linear Lyapunov function, that the disease-free equilibrium is globally asymptotically stable when the associated basic reproduction number is less than the unity. When the basic reproduction number is greater than the unity, under certain specifications on the model parameters, we prove the existence of a globally asymptotically stable endemic equilibrium with the aid of a suitable nonlinear Lyapunov function.

Submitted July 8, 2016. Published January 21, 2019.
Math Subject Classifications: 92B05, 93A30, 93D20.
Key Words: Global dynamics; malaria model; basic reproduction number; Lyapunov function; vigilant human compartment.

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Olawale S. Obabiyi
Department of Mathematics
University of Ibadan
email: obabiyios@yahoo.com
Samson Olaniyi
Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology, PMB 4000
Ogbomoso, Nigeria
email: solaniyi@lautech.edu.ng

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