Industrial Mathematics
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Industrial Mathematics
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Item Modeling prevalence of meningitis control strategies through evaluating with available data on meningitis cases reported in Nigeria(Springer Science and Business Media LLC, 2025-05-14) O.J. Peter; F.A. Oguntolu; N. Nyerere; A. El-MesadyMeningitis is a major public health concern, especially in developing nations, due to its devastating consequences for human health. Although modeling studies have examined disease transmission dynamics, little attention has been paid to how control strategies affect the behavior of different population groups, including carriers, symptomatic individuals, hospitalized patients, and those in intensive care. This study proposes a computational framework that compares the effectiveness of vaccination of people at risk of the disease versus treating symptomatic infected persons. The basic reproduction number is used to evaluate the equilibrium points. Assess the precision of the proposed model’s illustration to data. We fit the meningitis model using the information at our disposal on meningitis cases reported in Nigeria from the first week of January to the last week of December 2023; this was obtained from the Nigerian Center for Disease Control (NCDC) database. We also performed a sensitivity analysis using a normalized forward sensitivity index to see which parameters had significant effects on the effective reproduction number. The results of both analytical techniques and numerical simulations reveal that recruitment rate, vaccination, progression from carrier to symptomatic stages, and disease-induced death all significantly reduce the incidence and prevalence of meningitis in the community. The study findings could be used to inform decisions about meningitis control initiatives.Item 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. AkinyemiThe 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.Item 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. IsholaIn 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.Item Bifurcation Analysis on the Mathematical Model of Measles Disease Dynamics(Horizon Research Publishing Co., Ltd., 2013-12) Samuel Abubakar; Ninuola Ifeoluwa Akinwande; Sirajo Abdulrahman; Festus Abiodun OguntoluIn this paper we proposed a Mathematical model of Measles disease dynamics. The Disease Free Equilibrium (DFE) state, Endemic Equilibrium (EE) states and the characteristic equation of the model were obtained. The condition for the stability of the Disease Free equilibrium state was obtained. We analyze the bifurcation of the Disease Free Equilibrium (DFE) and the result of the analysis was presented in a tabular form.Item 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. OguntoluWe 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.Item 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. AkpanIn 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.Item 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. AmadiegwuA 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.Item Mathematical Modeling of Polio Virus Infection Incorporating Immigration and Vaccination(Faculty of Physical Sciences, University of Ilorin, 2019-12-01) G. Bolarin; I. U. Omatola; A. Yusuf; C. E. Odo; F. A. Oguntolu; M. A. PhilipA deterministic mathematical model for polio infection dynamics with emphasis on immigration and vaccination was formulated and analyzed. We derived the basic reproduction number, of the model formulated. The effective reproduction number was computed using the next generation matrix to enable a qualitative analysis to be carried out on the model. Also, the disease-free equilibrium and endemic equilibrium points were computed. On analyzing the equilibrium points, we found that the disease-free equilibrium point is locally asymptotically stable if and the condition for existence on an Endemic Equilibrium point was also established. More so, numerical simulations showed that vaccination coverage of about 75% would be enough to eradicate polio from the population.Item Modelling fire spread reaction rate in atmospheric-weather condition(Science World Journal, 2021-08-11) A. B. Zhiri; R. O. Olayiwola; S. A. Somma; F. A. OguntoluFire spread in any fire environment is a thing of great concern as wind is arguably the most important weather factor that influences the spread of fire. In this paper, we present equations governing the phenomenon and assume the fire depends on the space variable x . Analytical solution is obtained via perturbation method, direct integration and eigenfunction expansion technique, which depicts the influence of parameters involved in the system. The effect of change in parameters such as Peclet mass number and Equilibrium wind velocity are presented graphically and discussed. The results obtained revealed that both Peclet mass number and Equilibrium wind velocity enhanced oxygen concentration during fire spread.Item Mathematical model for the control of lymphatic filariasis transmission dynamics(SCIK Publishing Corporation, 2021-02-23) Festus Abiodun Oguntolu; Gbolahan Bolarin; Olumuyiwa James Peter; Abdullah Idris Enagi; Kayode OshinubiIn this paper, a mathematical model for the transmission dynamics of lymphatic filariasis is presented by incorporating the infected without symptom, the infected with symptom and treatment compartments. The model is shown to have two equilibrium states: the disease-free equilibrium (DFE) and the endemic equilibrium states. An explicit formula for the effective reproduction number was obtained in terms of the demographic and epidemiological parameters of the model. Using the method of linearization, the disease-free equilibrium state was found to be locally asymptotically stable if the basic reproduction number is less than unity. By constructing a suitable Lyapunov function, the disease-free equilibrium state was found to be globally asymptotically stable. This means that lymphatic filariasis could be put under control in a population when the effective reproduction number is less than one. The endemic equilibrium state was found to be locally asymptotically stable. By constructing yet another Lyapunov function, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions. Sensitivity analysis was carried out on the effective reproduction number, the most sensitive parameters were the treatment rate of human population and the infected rate of human population. Results from the simulation carried out showed that treatment level coverage of human population should target a success rate of 75% for LF to be under control in the population.