Browsing by Author "A. A. Ayoade"

Now showing 1 - 3 of 3

Derivation of the Reproduction Numbers for Cholera Model
(Journal of the Nigerian Association of Mathematical Physcis (TNAMP), 2018-03) A. A. Ayoade; O. J. Peter; F. A. Oguntolu; C. Y. Ishola
It is expected of the epidemiologists to predict whether a disease will spread in a community or not and at the same time, forecast the degree of severity of the disease if it spreads in the community. By that, a cholera model is formulated and the procedure for obtaining the effective reproduction number and the basic reproduction number of the model is presented following the Next Generational MAtrix approach. The two reproduction numbers (the effective reproduction number and the basic reproduction number) are successfully derived. While the effective reproduction number can be used to predict the effectiveness of intervention strategies in inhibiting the spread of cholera disease, the basic reproduction number can be used to forecast the severity of cholera spread in a community where the intervention strategies are not on ground.
On the Global Stability of Cholera Model with Prevention and Control
(Malaysian Journal of Computing (MJoC), 2018-06-05) A. A. Ayoade; M. O. Ibrahim; O. J. Peter; F. A. Oguntolu
In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if Rq0 < 1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever Rq0 > 1 for the extended model or R0 > 1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of Rq0 > 1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.
On the verification of existence of backward bifurcation for a mathematical model of cholera dynamics
(African Journals Online, 2023-09-12) A. A. Ayoade; O. J. Peter; F. A. Oguntolu; C.Y. Ishola; S. Amadiegwu
A cholera transmission model, which incorporates preventive measures, is studied qualitatively. The stability results together with the center manifold theory are used to investigate the existence of backward bifurcation for the model. The epidemiological consequence of backward bifurcation is that the disease may still persist in the population even when the classical requirement of the reproductive number being less than one is satisfied.