Browsing by Author "O. J. Peter"

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Approximate Solution of Typhoid Fever Model by Variational Iteration Method
(ATBU, Journal of Science, Technology & Education (JOSTE), 2018-09) A. F. Adebisi; O. J. Peter; T. A. Ayoola; F. A. Oguntolu; C. Y. Ishola
In this paper, a deterministic mathematical model involving the transmission dynamics of typhoid fever is presented and studied. Basic idea of the disease transmission using compartmental modeling is discussed. The aim of this paper is to apply Variational Iteration Method (VIM) to solve typhoid fever model for a given constant population. This mathematical model is described by nonlinear first order ordinary differential equations. First, we find the solution of the model by using Variation Iteration Method (VIM). The validity of the VIM in solving the model is established by classical fourth-order Runge-Kutta method (RK4) implemented in Maple 18. In order to show the efficiency of the method we compare the solutions obtained by VIM and RK4. We illustrated the profiles of the solutions of each of the compartments, from which we speculate that the VIM and RK4 solutions agreed well.
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.
Differential Transform Method for Solving Mathematical Model of SEIR and SEI Spread of Malaria
(International Journal of Sciences: Basic and Applied Research (IJSBAR), 2018-07-18) A. I. Abioye; M. O. Ibrahim; O. J. Peter; S. Amadiegwu; F. A. Oguntolu
In this paper, we use Differential Transformation Method (DTM) to solve two dimensional mathematical model of malaria human variable and the other variable for mosquito. Next generation matrix method was used to solve for the basic reproduction number and we use it to test for the stability that whenever the disease-free equilibrium is globally asymptotically stable otherwise unstable. We also compare the DTM solution of the model with Fourth order Runge-Kutta method (R-K 4) which is embedded in maple 18 to see the behaviour of the parameters used in the model. The solutions of the two methods follow the same pattern which was found to be efficient and accurate.
Direct and Indirect Transmission Dynamics of Typhoid Fever Model by Differential Transform Method
(ATBU, Journal of Science, Technology & Education (JOSTE), 2018-03) O. J. Peter; M. O. Ibrahim; F. A. Oguntolu; O. B. Akinduko; S. T. Akinyemi
The aim of this paper is to apply the Differential Transformation Method (DTM) to solve typhoid fever model for a given constant population. This mathematical model is described by nonlinear first order ordinary differential equations. First, we find the solution of this model by using the differential transformation method (DTM). In order to show the efficiency of the method, we compare the solutions obtained by DTM and RK4. We illustrated the profiles of the solutions, from which we speculate that the DTM and RK4 solutions agreed well.
Exploring the dynamics of lymphatic filariasis through a mathematical model and analysis with Holling type II treatment functions
(Iranian Journal of Numerical Analysis and Optimization, 2025-06) F. A. Oguntolu; O. J. Peter; B. I. Omede; T. A. Ayoola; G. B. Balogun
This paper presents a robust deterministic mathematical model incorporat-ing Holling type II treatment functions to comprehensively investigate the dynamics of Lymphatic filariasis. Through qualitative analysis, the model demonstrates the occurrence of backward bifurcation when the basic re-production number is less than one. Moreover, numerical simulations are employed to illustrate and validate key analytical findings. These simula-tion results emphasize the significance of accessible medical resources and the efficacy of prophylactic drugs in eradicating Lymphatic filariasis. The findings show that, enhancing medical resource availability and implement-ing effective treatment strategies in rural areas and regions vulnerable to Lymphatic filariasis is crucial for combating the transmission and control of this disease.
Mathematical model for the control of infectious disease
(African Journals Online (AJOL), 2018-05-03) O. J. Peter; O. B. Akinduko; F. A. Oguntolu; C. Y. Ishola
We proposed a mathematical model of infectious disease dynamics. The model is a system of first order ordinary differential equations. The population is partitioned into three compartments of Susceptible S(t) , Infected I(t) and Recovered R(t). Two equilibria states exist: the disease-free equilibrium which is locally asymptotically stable if Ro < 1 and unstable if Ro > 1. Numerical simulation of the model shows that an increase in vaccination leads to low disease prevalence in a population.
Mathematical model for the control of measles
(African Journals Online (AJOL), 2018-05-03) O. J. Peter; O. A. Afolabi; A. A. Victor; C. E. Akpan; F. A. Oguntolu
We proposed a mathematical model of measles disease dynamics with vaccination by considering the total number of recovered individuals either from natural recovery or recovery due to vaccination. We tested for the existence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the disease free equilibrium (DFE) and the endemic equilibrium (EE) for the system of the equations and vaccination reproduction number are given. Numerical simulation of the model shows that vaccination is capable of reducing the number of exposed and infectious population.
Multi-Step Homotopy Analysis Method for Solving Malaria Model
(Universiti Sultan Zainal Abidin (Malaysian Journal of Applied Sciences), 2018-12-30) O. J. Peter; A. F. Adebisi; F. A. Oguntolu; S. Bitrus; C. E. Akpan
In this paper, we consider the modified epidemiological malaria model proposed by Abadi and Harald. The multi-step homotopy analysis method (MHAM) is employed to compute an approximation to the solution of the model of fractional order. The fractional derivatives are described in the Caputo sense. We illustrated the profiles of the solutions of each of the compartments. Figurative comparisons between the MHAM and the classical fourth-order reveal that this method is very effective.
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.