ASYMPTOTIC STABILITY OF MALARIA DYNAMICS
WITH VIGILANT HUMAN COMPARTMENT
O.S. Obabiyi1, S. Olaniyi2 1Department of Mathematics
University of Ibadan
Ibadan, NIGERIA 2Department of Pure and Applied Mathematics
Ladoke Akintola University of Technology
PMB 4000, Ogbomoso, NIGERIA
Abstract. A continuous-time and discrete-age-structured compartmental model for malaria transmission in a two-interacting human and mosquito populations is formulated. The model incorporates a class of vigilant humans who adhere to the malaria vector control measures of the World Health Organization with a view to preventing the human-mosquito contacts. An epidemiological threshold called the basic reproduction number of the model is derived and a qualitative analysis of the model is carried out to investigate the asymptotic stability of the equilibria. A locally asymptotically stable disease-free equilibrium at the basic reproduction number less than unity is proved via the analysis of characteristic equation. Whereas, the existence of a locally asymptotically stable endemic equilibrium is established at the basic reproduction number greater than unity based on the use of center manifold theory of bifurcation. In addition, a sensitivity analysis is performed to examine the contributory effects of the model parameters on the transmission and spread of the malaria disease with respect to the basic reproduction number.
AMS Subject Classification: 92B05, 93D20
Key Words and Phrases: malaria, vigilant human, basic reproduction number, stability, sensitivity analysis
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