Olawale S. Obabiyi, Samson Olaniyi
Abstract:
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 Nigeria 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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