Industrial Mathematics

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Industrial Mathematics

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Effect of Transverse Relaxation Rate on Time-Dependent Magnetic Resonance Imaging
(African Journal of Physical Science, 2011) S. I. Yusuf, Y.M. Aiyesimi and O. B. Awojoyogbe
Magnetic Resonance Imaging (MRI), developed from nuclear magnetic resonance involves a non-invasive medical approach towards studying the anatomy, physiology and pathology of human tissues. In this study, attempt is made at expressing mathematically the processes involved in MRI for diagnosis and possible treatment of diseases within the human body. A time-dependent second -order non-homogeneous linear differential equation from the Bloch (NMR) equation is evolved. The parameters in the equations are M_0, radio frequency rfB_1 f(x,t) field, gyromagnetic ratio of blood spin γ as well as T_1 and T_2 relaxation times. the solution obtained will be examined when the system is under an influence of a driving force, F_0 cos wt and γB_1 (t)=cos⁡wt is the radio frequency field. However, for the purpose of this study, only relaxation times are varied and analyzed for measurement of the signals in relation to its effect on human anatomy.
n Inequality to Generate Some Statistical Distributions
(Asian Journal of mathematics and Applications, 2013) A. F. Oguntolu; U. Y. Abubakar; A. Isah; L. A. Nafiu; K. Rauf
In this work, we established Markov inequality via Binomial, Poisson and Geometric Distribution. Results obtained were used to obtain probability bound for some random variables. Our results are in agreement with the existing works.
Approximate Solution of SIR Infectious Disease Model Using Homotopy Pertubation Method (HPM)
(Pacific Journal of Science and Technology, 2013-11) S. Abubakar; N. I. Akinwande; O. R. Jimoh; F. A. Oguntolu; O. D. Ogwumu
In this paper we proposed a SIR model for general infectious disease dynamics. The analytical solution is obtained using the Homotopy Perturbation Method (HPM). We used theMATLAB computer software package to obtain the graphical profiles of the three compartments while varying some salient parameters. The analysis revealed that the efforts at eradication or reduction of disease prevalence must always match or even supersede the infection rate.
Application of Bootstrap Re-sampling Method to a Categorical Data of HIV/AIDS Spread across different Social-Economic Classes
(Scientific & Academic Publishing, 2015) A. O. Bello; F. A. Oguntolu; O. M. Adetutu; J. P. Ojedokun
This research reports on the relationship and significance of social-economic factors (age, gender, employment status) and modes of HIV/AIDS transmission to the HIV/AIDS spread. Logistic regression model, a form of probabilistic function for binary response was used to relate social-economic factors (age, sex, employment status) to HIV/AIDS spread. The statistical predictive model was used to project the likelihood response of HIV/AIDS spread with a larger population using 10,000 Bootstrap re-sampled observations.
Modeling Economic Growht In Sub-Saharan Africa: A Panel Data Approach
(chool of Physical Science (SPSBIC) Biennial International Conference, Federal Univerisity of Technology, Minna, 2017-05-05) S. I. Onot; I. G. Sule; M. O. Adetut; O. A. Bello; F. A. Oguntolu
The debate on the effectiveness of macro-economic variables as a tool for promoting growth and development remains inconclusive given conflicting results of recent studies. Thus, the controversy is yet to be settled. Against this background, this study sought to fit a model to best predict economic growth in sub-Saharan Africa considering Government revenue, Trade Openness, Urbanization and Fiscal Freedom as the predictor variables and hence further explains the combined effect of the variables on economic growth. The study made use of secondary data of sub-Saharan African Countries in panel least squares. The hypotheses were linearly tested while adopting the panel data estimation under fixed-effect assumptions. Findings reveal that all the variables except fiscal freedom has a positive and significant effect on the economic growth of sub-Saharan Africa when the countries were pooled together. Only government revenue has a negative and insignificant effect on the economic growth of the countries in the fixed-effect model which considers the heterogeneity of individuality of the countries. The study therefore recommended that Governments of sub-Saharan African countries should engage in critical check on the revenue generated. Improving and strengthening the fiscal freedom so as to attract inflows of investors in order to boost the economic growth and improving the standard of living of the citizens is also recommended.
On the Dynamical Analysis of a Deterministic Typhoid Fever Infection Model
(Transactions of NAMP, 2017-11) F. A. Oguntolu; G. Gbolarin; S. O. Jaiyeola; O. M. Adetutu
In this paper, we develop a deterministic model of typhoid fever. The existence and uniqueness of solutions of the model were examined by actual solutions. Mathematical analysis is carried out to determine the transmission dynamics of typhoid in a community. We conduct local stability analysis for the model. The results show that the disease-free equilibrium which is locally asymptotically stable if R0 < 1 and unstable if R0 >1.
Analytic Solution of typhoid fever infection via homotopy perturbation method (HPM)
(Journal of Science, Technology, Mathematics and Education, 2018-03) F. A. Oguntolu; G. Gbolarin; O. M. Adetutu; A. O. Bello
In this paper, a deterministic mathematical model of typhoid fever infection was formulated with a control strategies. We find the analytical solution of the proposed model by Homotopy perturbation method which is one of the best method for finding the solution of the nonlinear problem to obtain the approximate solution of the model. The results are presented graphically and discussed. It is discovered that the epidemic is sustained in the population. Implications of these results indicate that treatment sustain the carrier infectives who in turn sustains the epidemic in the population in the long run.
Local Stability Analysis of a River Blindness Disease Model with Control
(The Pacific Journal of Science and Technology, 2018-05) F. A. Oguntolu; G. Bolarin; S. A. Somma; A.O. Bello
In this paper, a mathematical model to study the dynamics of River Blindness is presented. The existence and uniqueness of solutions of the model were examined by actual solution. The effective reproduction number was obtained using the next generation matrix. The Disease Free Equilibrium (DFE) State was obtained and analysed for stability. It was found that, the DFE State is Locally Asymptotically Stable (LAS) if the effective reproduction number R0 < 1 and unstable if R0 > 1.
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.
Semi analytical method for solving lymphatic filariasis epidemic model
(African Journals Online (AJOL), 2019-03-08) F. A. Oguntolu; N. I. Akinwande; N. O. Olayiwola; F. A. Faruq
In this paper, we present a deterministic model on the transmission dynamics of Lymphatic Filariasis. Non-Standard Finite Difference Method (NSFDM) is employed to attempt the solution of the model. The validity of the NSFDM in solving the model is established by using the computer in-built classical fourth-order Runge-Kutta method. The comparism between Non-Standard Finite Difference Method solution and Runge-Kutta (RK4) were performed which were found to be efficient, accurate and rapidly convergence.
Modelling and optimal control analysis of Lassa fever disease
(Elsevier BV, 2020) Olumuyiwa James Peter; Adesoye Idowu Abioye; Festus Abiodun Oguntolu; Titilayo Abimbola Owolabi; Michael Oyelami Ajisope; Abdullaziz Glabe Zakari; Timilehin Gideon Shaba
Lassa fever is a severe hemorrhagic viral infection whose agents belong to Mastomys natelensis. Generally, humans contract Lassa virus through exposure to food or household products that have been contaminated with the excreta of the infected rodents. Lassa fever is endemic in some West African countries including Nigeria. A basic model is proposed to examine the transmission of the disease. The proposed model is subjected to qualitative study via the theory of differential equations and the threshold quantity that denotes the dominant eigenvalue was derived using next-generation matrix approach. The basic model is further extended to an optimal control model with four controls namely, the fumigation of the environment with pesticide, the use of condom to prevent human to human transmission during sexual activities, early treatment and the use of indoor residual spray. The theory of optimal control was explored to establish the necessary conditions for curtailing the transmission of Lassa fever. Numerical simulation was conducted and the results showed that if the Lassa fever transmission and spread were to be reduced significantly in the endemic region, all the control measures must be taken with all seriousness.
Modelling and optimal control analysis of typhoid fever
(SCIK Publishing Corporation, 2021-08-19) Tawakalt Abosede Ayoola; Helen Olaronke Edogbanya; Olumuyiwa James Peter; Festus Abiodun Oguntolu; Kayode Oshinubi; Mutiu Lawal Olaosebikan
In this paper, we formulate a deterministic mathematical model to describe the transmission dynamics of typhoid fever by incorporating some control strategies. In order to study the impact of these control strategies on the dynamics of typhoid fever, the model captures vaccination and educational campaign as control variables. We show that the model is mathematically and epidemiologically well positioned in a biologically feasible region in human populations. We carry out a detailed analysis to determine the basic reproduction number necessary for the control of the disease. The optimal control strategies are used to minimize the infected carriers and infected individuals and the adverse side effects of one or more of the control strategies. We derive a control problem and the conditions for optimal control of the disease using Pontryagin’s Maximum Principle and it was shown that an optimal control exists for the proposed model. The optimality system is solved numerically, the numerical simulation of the model shows that possible optimal control strategies become more effective in the control and containment of typhoid fever when vaccination and educational campaign are combined optimally would reduce the spread of the disease.
Mathematical model of COVID-19 in Nigeria with optimal control
(Elsevier BV, 2021-09) Adesoye Idowu Abioye; Olumuyiwa James Peter; Hammed Abiodun Ogunseye; Festus Abiodun Oguntolu; Kayode Oshinubi; Abdullahi Adinoyi Ibrahim; Ilyas Khan
The novel Coronavirus Disease 2019 (COVID-19) is a highly infectious disease caused by a new strain of severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2). In this work, we proposed a mathematical model of COVID-19. We carried out the qualitative analysis along with an epidemic indicator which is the basic reproduction number () of this model, stability analysis of COVID-19 free equilibrium (CFE) and Endemic equilibrium (EE) using Lyaponuv function are considered. We extended the basic model into optimal control system by incorporating three control strategies. These are; use of face-mask and hand sanitizer along with social distancing; treatment of COVID-19 patients and active screening with testing and the third control is prevention against recurrence and reinfection of humans who have recovered from COVID-19. Daily data given by Nigeria Center for Disease Control (NCDC) in Nigeria is used for simulation of the proposed COVID-19 model to see the effects of the control measures. The biological interpretation of this findings is that, COVID-19 can be effectively managed or eliminated in Nigeria if the control measures implemented are capable of taking or sustaining the basic reproductive number to a value below unity. If the three control strategies are well managed by the government namely; NCDC, Presidential Task Force (PTF) and Federal Ministry of Health (FMOH) or policymakers, then COVID-19 in Nigeria will be eradicated.
Fractional order of pneumococcal pneumonia infection model with Caputo Fabrizio operator
(Elsevier BV, 2021-10) Olumuyiwa James Peter; Abdullahi Yusuf; Kayode Oshinubi; Festus Abiodun Oguntolu; John Oluwasegun Lawal; Adesoye Idowu Abioye; Tawakalt Abosede Ayoola
In this study, we present the Pneumococcal Pneumonia infection model using fractional order derivatives in the Caputo-Fabrizio sense. We use fixed-point theory to prove the existence of the solution and investigate the uniqueness of the model variables. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional order derivative, the numerical results are presented.
Transmission dynamics of Monkeypox virus: a mathematical modelling approach
(Springer Science and Business Media LLC, 2021-10-15) Olumuyiwa James Peter; Sumit Kumar; Nitu Kumari; Festus Abiodun Oguntolu; Kayode Oshinubi; Rabiu Musa
Monkeypox (MPX), similar to both smallpox and cowpox, is caused by the monkeypox virus (MPXV). It occurs mostly in remote Central and West African communities, close to tropical rain forests. It is caused by the monkeypox virus in the Poxviridae family, which belongs to the genus Orthopoxvirus. We develop and analyse a deterministic mathematical model for the monkeypox virus. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. It is shown that the model undergo backward bifurcation, where the locally stable disease-free equilibrium co-exists with an endemic equilibrium. Furthermore, we determine conditions under which the disease-free equilibrium of the model is globally asymptotically stable. Finally, numerical simulations to demonstrate our findings and brief discussions are provided. The findings indicate that isolation of infected individuals in the human population helps to reduce disease transmission.
Thermal Explosion with Convection in Porous Media: A Mathematical Approach
(International Journal of Mathematical Analysis and Modelling, 2022) R. O. Olayiwola, S. I. Yusuf, A. D. Abubakar, K. J. Audu, I. B. S. Mohammed, E. O. Anyanwu, U. A. Abdullahi and J. P. Oyubu
This paper studies the interaction between natural convection and thermal explosion in porous media. The model consists of the heat equation with a nonlinear source term describing heat production due to an exothermic chemical reaction coupled with the Darcy law. The conditions for the existence of unique solutions of the energy equation are established by thr Lipschitz continuity approach. The analytical solution is obtained via Olayiwola’s generalized polynomial approximation method (OGPAM), which shows the influence of the parameters involved on the system. The effects of changes in values of parameterssuch as Frank-Kamenetski number, Rayleigh number and inverse of Vadasz number are presented graphically and discussed. The results revealed that convection can change the conditions of thermal explosion.
Investigation of Dispersal Rate of Curry and Thyme
(Journal of Science, Technology, Mathematics and Education, 2022) Yusuf, S. I., Abdulsalam T.O., K. J. Audu, Jatto, A. O. and Ibrahim J. A.
This is a study of the rate of dispersal of curry and thyme in a medium using coefficient of diffusion of curry leaves and thyme leaves. The study was carried out by solving diffusion equation using the method of separation of variables and with appropriate boundary conditions and the coefficient of diffusion applied for curry and thyme. The result shows that curry leaves diffuse faster than thyme leaves under the same conditions. The research establishes why nutritionists and cooks would choose curry ahead of thyme when considering appropriate spices for cooking in order to attract attention.
Mathematical model of measles transmission dynamics using real data from Nigeria
(Informa UK Limited, 2022-05-25) Olumuyiwa James Peter; Mayowa M. Ojo; Ratchada Viriyapong; Festus Abiodun Oguntolu
Measles is a highly contagious and life-threatening disease caused by a virus called morbillivirus, despite the availability of a safe and cost-effective vaccine, it remains a leading cause of death, especially in children. Measles spreads easily from person to person via infected people's coughs and sneezes. It can also be transmitted through direct contact with the mouth or contaminated surfaces. To have a better knowledge of measles epidemiology in Nigeria, we develop a deterministic mathematical model to study the transmission dynamics of the disease in the population. The boundary of the model solution is performed, both equilibrium points are calculated, and the basic reproduction number ℛ0 is determined. We have proved that when ℛ0<1, the disease-free equilibrium point is both locally and globally stable. When ℛ0>1, the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. We demonstrate the model's effectiveness by using a real-life application of the disease spread in Nigeria. We fit the proposed model using available data from Nigeria Center for Disease Control (NCDC) from January to December 2020 to obtain the best fit, this help us to determine the accuracy of the proposed model's representation to the real-world data. We investigate the impact of vaccination rate and hospitalization of infected individuals on the dynamics of measles in the population. The result shows that the combined control strategies reduce the peak of infection faster than the single control strategy.
Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination
(Elsevier BV, 2022-11) N.I. Akinwande; T.T. Ashezua; R.I. Gweryina; S.A. Somma; F.A. Oguntolu; A. Usman; O.N. Abdurrahman; F.S. Kaduna; T.P. Adajime; F.A. Kuta; S. Abdulrahman; R.O. Olayiwola; A.I. Enagi; G.A. Bolarin; M.D. Shehu
COVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ω is suspended (Ω=0) is globally asymptotically stable when the effective reproduction number 𝑅0⁢𝑐<1 and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment (Ω>0), the endemic equilibrium using the centre manifold theory is shown to be stable globally whenever 𝑅0⁢𝑐>1. The model is extended into optimal control system and analyzed analytically using Pontryagin's Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.
Modeling and optimal control of monkeypox with cost-effective strategies
(Springer Science and Business Media LLC, 2022-11-22) Olumuyiwa James Peter; Chinwendu E. Madubueze; Mayowa M. Ojo; Festus Abiodun Oguntolu; Tawakalt Abosede Ayoola
In this work, we develop and analyze a deterministic mathematical model to investigate the dynamics of monkeypox. We examine the local and global stability of the basic model without control variables. The outcome demonstrates that when the reproduction number , the model’s disease-free equilibrium would be locally and globally asymptotically stable. We further analyze the effective control of monkeypox in a given population by formulating and analyzing an optimal control problem. We extend the basic model to include four control variables, namely preventive strategies for transmission from rodents to humans, prevention of infection from human to human, isolation of infected individuals, and treatment of isolated individuals. We established the necessary conditions for the existence of optimal control using Pontryagin’s maximal principle. To illustrate the impact of different control combinations on the spread of monkeypox, we use the fourth-order Runge–Kutta forward–backward sweep approach to simulate the optimality system. A cost-effectiveness study is conducted to educate the public about the most cost-effective method among various control combinations. The results suggest that, of all the combinations considered in this study, implementing preventive strategies for transmission from rodents to humans is the most economical and effective among all competing strategies.