Industrial Mathematics

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Industrial Mathematics

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A Mathematical Model of a Yellow Fever Dynamics with Vaccination
(Journal of the Nigerian Association of Mathematical Physics, 2015-11) F. A. Oguntolu; N. I. Akinwande; S. A. Somma; F. Y. Eguda; T. T. Ashezua
In this paper, a mathematical model describing the dynamics of yellow fever epidemics, which involves the interactions of two principal communities of Hosts (Humans) and vectors (mosquitoes) is considered. The existence and uniqueness of solutions of the model were examined by actual solution. We conduct local stability analysis for the model. The results show that it is stable under certain conditions. The system of equations describing the phenomenon was solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It is discovered that improvement in Vaccination strategies will eradicate the epidemics.
Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach
(Advances in Systems Sciences and Applications (ASSA), 2022-12-30) Oguntolu, Festus Abiodun; Peter, Olumuyiwa James; Oshinubi, Kayode; Ayoola, Tawakalt Abosede; Oladapo, Asimiyu Olalekan; Ojo, Mayowa Michael
Tuberculosis (TB) is an infectious disease caused by mycobacterium disease which causes major ill health in humans. Control strategies like vaccines, early detention, treatment and isolation are required to minimize or eradicate this deadly pandemic disease. This article presents a novel mathematical modelling approach to tuberculosis disease using Vaccinated-Susceptible-Latent-Mild-Chronic-Isolated-Treated model. We examined if the epidemiology model is well posed and then obtained two equilibria points (disease free and endemic equilibrium). We also showed that TB disease free equilibrium is locally and globally asymptotically stable if . We solved the model analytically using Homotopy Perturbation Method (HPM) and the graphical representations and interpretations of various effects of the model parameters in order to measure the impact for effective disease control are presented. The findings show that infected populations will be reduced when the isolation and treatment rates and their effectiveness are high.
Analytical Study of Viscous Fluid Movement in a Rectangular Pipe using Diffusion Magnetic Resonance Equation
(Nigerian Journal of Theoretical and Environmental Physics, 2024-09) Yusuf S. I.
Silicene, a two-dimensional material analogous to graphene, has garnered Diffusion Magnetic Resonance Imaging (DMRI) equation is used in this research work to examine the flow of fluid in a rectangular. Having previously considered flow in cylindrical and spherical coordinates, this study explores the rectangular channel of a three dimensional - (3D) flow using DMRI equation evolved and solved analytically using the method of separation of variables (MSV) with appropriate boundary conditions applied. Relaxation times of three viscous fluids were used - crude oil, oil wax and black oil in the simulation and the values of magnetization registered by each fluid recorded. The results obtained showed that oil wax has the highest value of magnetization followed by crude oil and then black oil. The study underscores the multivarious ways diffusion MRI can be applied and its use in the analysis of flow of viscous fluid through different geometrical channels.
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.
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 Oguntolu
In 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.
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.
Effects of Undesired Course of Study on Students' Academic Achievement in Nigeria Using Binary Logistic Regression
(Journal of Science, Technology, Mathematics and Education, 2017-09) O. M. Adetutu; F. A. Oguntolu; U. Abdullahi
This study was conducted to examine the effects of undesired course of study on students' academic performance in tertiary institutions in Nigeria. The questionnaire method was used with stratified sampling scheme. The questionnaire was administered to 400 students in Federal University of Technology, Minna Nigeria. Factors such as gender, age, satisfaction and the course of study were examined whether these factors were having effect on students' academic performance. The student cumulative grade point average (CGPA) was used as a measure of academic performance. The data were analyzed using binary logistic regression and the results revealed that satisfaction with course of study and undesired course of study affected students' academic performance. However, age and gender difference did not affect students' academic performance.
Enhanced Cuckoo Intelligence Search Algorithm
(Research India Publications, 2021-06-30) Ibukun Isaac Aina; Olumuyiwa James Peter; Abayomi Ayotunde Ayoade; Festus Abiodun Oguntolu; Matthew Olanrewaju Oluwayemi
Cuckoo Search (CS) algorithm is a meta-heuristic technique that displays several merits. For example, it is easier to apply and less tuning parameters also, it is suitable for solving optimization problems. However, easily fall into local optimum has been established and has a slow convergence rate as a result of the cuckoo search parameters being kept constant. Therefore to handle this issue, an Enhanced Cuckoo Intelligence Search (ECIS) algorithm was developed which is an upgraded CS algorithm. The efficiency of ECIS was tested by some benchmark constrained optimization test functions and it was shown that ECIS gives a better optimal value than CS.
Fractional order mathematical model of monkeypox transmission dynamics
(IOP Publishing, 2022-07-15) Olumuyiwa James Peter; Festus Abiodun Oguntolu; Mayowa M Ojo; Abdulmumin Olayinka Oyeniyi; Rashid Jan; Ilyas Khan
In this paper, we present a deterministic mathematical model of monkeypox virus by using both classical and fractional-order differential equations. The model includes all of the possible interactions that contribute to disease spread in the population. We investigate the model's stability results in the disease-free case when R0 < 1. When R0 < 1, we show that the model is stable, otherwise it is unstable. To obtain the best fit that describes the dynamics of this disease in Nigeria, the model is fitted using the nonlinear least square method on cumulative reported cases of monkeypox virus from Nigeria between January to December 2019. Furthermore, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We run numerous simulations of the proposed monkeypox model with varied input parameters to investigate the intricate dynamics of monkeypox infection under the effect of various system input parameters. We investigate the system's dynamical behavior to develop appropriate infection control policies. This allows the public to understand the significance of control parameters in the eradication of monkeypox in the population. Lowering the order of fractional derivatives has resulted in significant modifications. To the community's policymakers, we offered numerous parameters for the control of monkeypox.
Mathematical Analysis of Discontinuities in the Flow Field of Gas in a Cylindrical Pipe Using Diffusion MRI
(Nigeria Journal of Technological Research., 2019) Yusuf S. I., Aiyesimi Y. M., Jiya M., and Dada O. M.
In this study, Magnetic Resonance Imaging (MRI) is used to detect partial and total blockage of hydrogen gas in a cylindrical pipe. Diffusion Magnetic Resonance (DMR) equation is solved analytically for flow of fluid in a radially symmetric cylindrical pipe. Appropriate boundary conditions were imposed and the radial axis varied to depict partial and total blockage in the pipe. The results show that for free fluid flow, the magnetization is between 0.004 and 0.005. For partial blockage, the magnetization reduces (signal loss) in value to 0.00001 and for total blockage it is zero (0). This method is a viable alternative to other methods of detecting blockage in fluid pipelines in oil and gas industry due to its non-invasive analysis of flow in fluid. The MRI model also registers signal in its first few seconds or microseconds. The analysis can also be useful in process industries where different network of pipes are used or machines use cylindrical pipes or tubes in transporting materials especially when there is a partial or total blockage at any point in the network.
Mathematical Analysis of Jamming of Radio-Controlled Improvised Explosive Device (RCIED)
(Nigerian Journal of Physics, 2023-06) Ochijenu U. E., Yusuf S. I., Ibrahim J. A. and Jatto A. O.
In military operations especially counter insurgency operations, many soldiers including the civilian population have lost their lives due to explosions from Radio Controlled Improvised Explosive Devices (RCIED). This research work examines mathematically the concept of jamming an RCIED. The wave equation and the principle of superposition of waves were used to show how destructive interference can annul the effect of RCIED. It is obvious from the graphical presentations that the destructive effect of the waves from the jamming device effectively brought the waves from RCIED to nullity (zero) as the two graphs collapse at the point y=0.
Mathematical model and analysis of the soil-transmitted helminth infections with optimal control
(Springer Science and Business Media LLC, 2024-02) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Abubakar Yusuf; B. I. Omede; G. Bolarin; T. A. Ayoola
Soil-transmitted helminth diseases are highly prevalent in impoverished regions and pose a significant health burden on the global population. These diseases are primarily transmitted through the contamination of soil with human faces containing parasite eggs. This study presents a novel deterministic mathematical model to comprehensively investigate the dynamics of helminth infection transmission through the soil. The mathematical model exhibits two equilibrium points: the diseases-free equilibrium point (DFE) and the endemic equilibrium point (EEP). The DFE is proven to be locally and globally asymptotically stable when the basic reproduction number is less than one, indicating the potential for disease eradication. Conversely, the EEP is locally asymptotically stable when the basic reproduction number exceeds unity, representing a persistent endemic state. To explore effective intervention strategies for controlling the spread of these infections, optimal control theory is applied. The study incorporates two time-varying control variables derived from sensitivity analysis: the rate of hygiene consciousness in the susceptible class and the rate of hygiene consciousness in the infectious class. Numerical simulations demonstrate that implementing optimal control strategies can successfully curb and mitigate soil-transmitted helminth infections. Overall, this research highlights the importance of proactive and targeted interventions, emphasizing the significance of hygiene education and awareness campaigns. By implementing optimal control measures based on the proposed strategies, the burden of soil-transmitted helminth diseases can be significantly reduced, improving public health in affected regions.
Mathematical model for control of tuberculosis epidemiology
(Springer Science and Business Media LLC, 2022-04-22) Mayowa M. Ojo; Olumuyiwa James Peter; Emile Franc Doungmo Goufo; Hasan S. Panigoro; Festus Abiodun Oguntolu
Tuberculosis is an infectious disease caused by bacteria that most commonly affects the lungs. Due to its high mortality, it remains a global health issue, and it is one of the leading causes of death in the majority of sub-Saharan African countries. We formulate a six-compartmental deterministic model to investigate the impact of vaccination on the dynamics of tuberculosis in a given population. The qualitative behaviors of the presented model were examined, and the respective threshold quantity was obtained. The tuberculosis-free equilibrium of the system is said to be locally asymptotically stable when the effective reproduction number and unstable otherwise. Furthermore, we examined the stability of the endemic equilibrium, and the conditions for the existence of backward bifurcation are discussed. A numerical simulation was performed to demonstrate and support the theoretical findings. The result shows that reducing the effective contact with an infected person and enhancing the rate of vaccinating susceptible individuals with high vaccine efficacy will reduce the burden of tuberculosis in the population.
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 Oshinubi
In 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.
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.
Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination
(Springer Science and Business Media LLC, 2023-03-06) Olumuyiwa James Peter; Hasan S. Panigoro; Afeez Abidemi; Mayowa M. Ojo; Festus Abiodun Oguntolu
This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate, the rate of first vaccine dose, the second dose vaccination rate and the recovery rate due to the second dose of vaccination are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population.
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. Philip
A 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.
Mathematical modelling for the transmission dynamics of Rift Valley fever virus with human host
(Universitas Negeri Gorontalo, 2022-06-28) Festus Abiodun Oguntolu; Deborah W. Yavalah; Collins F. Udom; Olumuyiwa James Peter; Kayode Oshinubi
Rift Valley Fever (RVF) is a viral zoonosis spread primarily by mosquitos that primarily affects livestock but has the potential to affect humans. Because of its potential to spread quickly and become an epidemic, it has become a public concern. In this article, the transmission dynamics of RVF with mosquito, livestock and human host using a compartmental model is studied and analyzed. The basic reproduction number R0 is computed using next generation matrix and the disease-free equilibrium state is found to be locally asymptotically stable if R0 < 1 which implies that rift valley fever could be put under control in a population where the reproduction number is less than 1. The numerical simulations give insightful results to further explore the dynamics of the disease based on the effect of three interventions; efficacy of vaccination, culling of livestock and trapping of mosquitoes introduced in the model.
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-Mesady
Meningitis 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.
Modeling tuberculosis dynamics with vaccination and treatment strategies
(Elsevier BV, 2025-03-19) Olumuyiwa James Peter; Dipo Aldila; Tawakalt Abosede Ayoola; Ghaniyyat Bolanle Balogun; Festus Abiodun Oguntolu
Tuberculosis (TB) remains a leading cause of morbidity and mortality worldwide, worsened by the emergence of drug-resistant strains. The implementation of vaccination and observed treatment still becomes the most popular intervention in many countries. This study develops a mathematical model to analyze TB dynamics by considering the impact of integrated intervention vaccination and treatment strategy, and also taking into account the possibility of treatment failure and drug–resistant. The model constructed by dividing the population into six compartments: susceptible S, vaccinated V, latent L, active TB (I), drug-resistant TB Dr, and recovered R. Through a mathematical analysis of the dynamical properties of the proposed model, we demonstrated that the disease-free equilibrium point is always locally asymptotically stable when the basic reproduction number is less than one and unstable when it exceeds one. Moreover, the endemic equilibrium point is shown to exist uniquely only when the basic reproduction number is greater than one, and once it exists, it is always locally stable. For better visualization of the stability properties, we perform continuation simulations to generate a bifurcation diagram of our model, utilizing various bifurcation parameters. The Partial Rank Correlation Coefficient (PRCC) approach is used to carry out sensitivity analyses to determine the most sensitive parameters to the disease control. Simulation results show that increased vaccination rates efficiently reduce the susceptible population to increase the vaccinated population, decreasing disease transmission and lowering the burden of active and drug-resistant tuberculosis. Recovery rates after second-line treatment have a substantial impact on the dynamics of drug-resistant tuberculosis. Higher recovery rates result in faster rises in the recovered population and improved disease control. The findings emphasize the need for integrated measures, such as vaccination campaigns and enhanced treatment procedures, to reduce tuberculosis incidence, minimize drug resistance, and improve public health outcomes. These findings lay the groundwork for enhancing tuberculosis control programs, especially in countries with limited resources.