Industrial Mathematics

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Industrial Mathematics

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A decomposition approach for magnetohydrodynamics stagnation point flow over an inclined shrinking/stretching sheet with suction/injection
(International Journal of Mathematical Analysis and Modelling, 2023-09-27) A. Yusuf; G. Bolarin; F. A. Oguntolu; M. Jiya; Y. M. Aiyesimi
In this paper, the approximate solution to Magnetohydrodynamics Stagnation Point Flow over an inclined Shrinking/Stretching Sheet with Suction/injection was analyzed via the Adomian Decomposition. The governing partial differential equations (PDEs) were reduced with the help of similarity variables to non linear coupled ordinary differential equations (ODEs). The effects of various pertinent parameters were presented numerically and graphically. Numerical comparisons were carried out with the existing literature and a good agreement was established. The angle of inclination was found to enhance the velocity profile.
A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives
(Springer Science and Business Media LLC, 2022-04-26) Olumuyiwa James Peter; Abdullahi Yusuf; Mayowa M. Ojo; Sumit Kumar; Nitu Kumari; Festus Abiodun Oguntolu
In this paper, we develop a new mathematical model based on the Atangana Baleanu Caputo (ABC) derivative to investigate meningitis dynamics. We explain why fractional calculus is useful for modeling real-world problems. The model contains all of the possible interactions that cause disease to spread in the population. We start with classical differential equations and extended them into fractional-order using ABC. Both local and global asymptotic stability conditions for meningitis-free and endemic equilibria are determined. It is shown that the model undergoes backward bifurcation, where the locally stable disease-free equilibrium coexists with an endemic equilibrium. We also find conditions under which the model’s disease-free equilibrium is globally asymptotically stable. The approach of fractional order calculus is quite new for such a biological phenomenon. The effects of vaccination and treatment on transmission dynamics of meningitis are examined. These findings are based on various fractional parameter values and serve as a control parameter for identifying important disease-control techniques. Finally, the acquired results are graphically displayed to support our findings.
A Mathematical Modelling of Lymphatic Filariasis and Malaria Co-infection
(Abubakar Tafawa Balewa University, 2022-06-25) F. A. Oguntolu; D. W. Yavalah; C. F. Udom; T. A. Ayoola; A. A. Victor
Lymphatic Filariasis (LF) and Malaria continue to pose significant public health burden globally and are co-endemic in many sub-Saharan African regions. In this work, we developed and analyzed a mathematical model of Lymphatic filariasis and malaria co-infection model. Friedman and Lunge method was used to find the positivity of the solution, the disease-free equilibrium was obtained, the model stability was analyzed, and the basic reproductive number was also obtained. The findings suggest that with the use of a bed-net and insecticide as a control measure, the treatment of LF and malaria co-infection can be reduced to a minimum.
A Mathematical Study of HIV Transmission Dynamics with Counselling and Antiretroviral Therapy
(International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 2015-02) F. A. Oguntolu; R. O. Olayiwola; A. O. Bello
In this paper, a mathematical model of HIV transmission dynamics with counseling and Antiretroviral therapy (ART) as a major means of control of infection is presented. The existence and uniqueness of solutions of the model were examined by actual solution. The stability analysis of the critical points was conducted. The results show that it is globally asymptotically stable under certain conditions. The systems of equations were solved analytically using parameter-expanding method coupled with direct integration. The results are presently graphically and discussed. It is discovered that the parameters involved play a crucial role in the dynamics of the diseases which indicate that ART and counseling could be effective methods in the control and eradication of HIV.
Analytical Simulation of Cholera Dynamics Controls
(International Journal of Innovative Science, Engineering & Technology, 2015-03) F. A. Oguntolu; R. O. Olayiwola; O. A. Odebiyi; A. O. Bello
In this paper, an analytical simulation of cholera dynamics with control is presented. The model incorporates therapeutic treatment, water sanitation and Vaccination in curtailing the disease. We prove the existence and uniqueness of solution. The systems of equations were solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It shows clearly that improvement in treatment, water sanitation and Vaccination can eradicate cholera epidemic. It also observed that with proper combination of control measures the spread of cholera could be reduced.
Analytical Study of Leakage of Viscous Flow in a Cylindrical Pipe
(International Journal of Scientific Engineering and Applied Science (IJSEAS), 2022-03) Yusuf S. I., Ejeh S. & Olayiwola R.O
This research work presents the transient flow analysis of viscous fluid within a pipe. The model equations evolved were considered for leak and no leak conditions. The equations were further solved analytically using eigen vector expansion method. The results obtained were presented graphically and analyzed. The analyses were undertaken using flow velocity, pressure, density, measured inlet mass flow, measured outlet mass flow, elevation, leak rate, leak velocity and Reynolds’ number. Based on the results obtained, these fundamental tools of analysis proved effective in detecting, locating and describing the type and behaviour of leakage in a pipe.
Application of Diffusion Magnetic Resonance Imaging Equation to Compressible and Incompressible Fluid Particles in a Spherical Region
(International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2024) A. Saba, S. I. Yusuf, D. O. Olaoye, A. O. Jatto
n the previous work, the response of viscous and non-viscous fluids to magnetic resonance was examined. In this research work, Diffusion magnetic resonance imaging, MRI, is used to study, analyse and compare the response of particles of compressible and incompressible fluids in a spherical region. The fluids considered are hydrogen gas and paraffin oil. The general flow equation was evolved from the fundamental Bloch equations. The general flow equation was solved using the method of separation of variables and applied to spherical region leading to Legendre equation of the first and second kinds. From the results obtained, it can be concluded that the value of Magnetization for hydrogen gas ranges from 9.28819444503×1013 to 9.35×1014. However, appreciable change can be noticed when magnetization is 9.2881944500003 × 1013. For paraffin oil, the value of Magnetization ranges from 2.749305556000075×1014 to 2.75×1014 with appreciable change noticed at magnetization value of 2.7493055560000094 × 1014. The analytical solution of Diffusion MRI equation adopted in this research work has shown the difference in compressible (hydrogen gas) and incompressible (paraffin oil) fluids in a spherical region through the magnetization values that were generated. This is laying credence to the effectiveness and non-invasive properties of MRI.
Application of System of Linear Equation to A 3-Arm Roundabout Network Flows
(Journal of the Nigerian Association of Mathematical Physics, 2016-07) O. M. Adetutu; N. Nyor; O. A. Bello; F. A. Oguntolu
A mathematical model was presented and used to determine turning movements at roundabouts based on field data. Assumptions were made in order to simplify the model; such as U-turns from and to the same arm of a roundabout, total traffic into the roundabout is equal to the total traffic out of the roundabout and traffic is homogenous (i.e. mainly consisting of vehicles). Using Gaussian elimination, turning movements could be estimated from 3-arm roundabouts for the indeterminate traffic steam movements when inflows and outflows for each arm of the roundabout is known together with a flow stream on one internal circulating (weaving) section between any two arms of the roundabout. The model has practical use in reducing the number of detectors or counters (whether automatic, videoing technique or manual methods are in use) which are needed in collecting data to determine the estimated flows from and to the different parts of a roundabout. The reduction in the number of detectors (or traffic counts) could be due to site limitations caused by faulty or limited number of counters used, inaccessible sections for obtaining video images for later analysis (e.g. presence of sharp bends buildings or large trees obscuring vision). The benefits of saving costs could be significant in terms of time and man-power needed on site and this could depend on the amount of traffic flow through the roundabout.
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 of typhoid fever model with optimal control
(Elsevier BV, 2021-08) Olumuyiwa James Peter; Mohammed Olanrewaju Ibrahim; Helen Olaronke Edogbanya; Festus Abiodun Oguntolu; Kayode Oshinubi; Abdullahi Adinoyi Ibrahim; Tawakalt Abosede Ayoola; John Oluwasegun Lawal
In this paper, a model for direct and indirect transmission dynamics of typhoid fever with three control interventions is analyzed. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We proved the existence and uniqueness of optimal control paths and obtained these optimal paths analytically using Pontryagin’s Maximum Principle. We analyzed our results numerically to compare various strategies of proposed controls. It is observed that the implementation of the three controls among all strategies is most successful. Thus, we conclude that in order to reduce typhoid fever threat, all the three controls must be taken into consideration concurrently.
Effects of Relaxation Times from the Bloch Equations on Age Related Changes in White and Grey Matter
(International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2024) S. I. Yusuf, D. O. Olaoye, M. O. Dada, A. Saba, K. J. Audu, J. A. Ibrahim, A. O. Jatto
This research work presented the analytical method of using T1 and T2 relaxation rates of white matter and grey matter to distinguish the passage of time on human organs. A time dependent model equation evolved from the Bloch Nuclear Magnetic Resonance equation was solved under the influence of the radio frequency magnetic field [rf B1(x, t)̸ = 0] and in the absence of radio frequency magnetic field [rf B1(x, t) = 0]. The general solution was considered in three cases. Analysis of the solutions obtained revealed that the rate of decrease of the white matter was faster than that of the grey matter. Between 100 and 400 seconds the difference is more noticeable.
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.
Forecasting of COVID-19 pandemic in Nigeria using real statistical data
(SCIK Publishing Corporation, 2021) Adesoye Idowu Abioye; Mfon David Umoh; Olumuyiwa James Peter; Helen Olaronke Edogbanya; Festus Abiodun Oguntolu; Oshinubi Kayode; Sylvanus Amadiegwu
In this paper, we used data released by Nigeria Center for Disease Control (NCDC) every 24 hours for the past consecutive two months to forecast the Coronavirus disease 2019 (COVID-19) cases for the months (September – October 2020). The linear regression forecasting model and R software package are used for the forecast and simulations respectively. The COVID-19 cases in Nigeria is on a decreasing trend and the forecast result show that in the next two months, there is going to be a decrease in new COVID-19 cases in Nigeria. COVID-19 in Nigeria can be drastically reduced if the organizations, management, government or policymakers are constantly proactive concerning these research findings.
Global Stability Analysis of Typhoid Fever Model
(Advances in Systems Sciences and Applications (ASSA), 2020-06-30) Peter, Olumuyiwa James; Adebisi, Ajimot Folasade; Ajisope, Michael Oyelami; Ajibade, Fidelis Odedishemi; Abioye, Adesoye Idowu; Oguntolu, Festus Abiodun
We analyze with four compartments a deterministic nonlinear mathematical model of typhoid fever transmission dynamics. Using the Lipchitz condition, we verified the existence and uniqueness of the model solutions to establish the validity of the model and derive the equilibria states of the model, i.e. disease-free equilibrium (DFE) and endemic equilibrium (EE). The computed basic reproductive number R0 was used to establish that the disease-free equilibrium is globally asymptotically stable when its numerical values are less than one while the endemic equilibrium is locally asymptotically stable when its values are greater than one. In addition, the Lyapunov function was applied to investigate the stability property for the (DFE). The model was numerically simulated to validate the results of the analysis.
Global Stability and Sensitivity Analysis of Basic Reproduction Number of a Malaria Model
(Advances in Systems Sciences and Applications (ASSA), 2023-12-31) Abioye, Adesoye I.; Peter, Olumuyiwa J.; Oguntolu, Festus A.; Ayoola, Tawakalt A.; Oladapo, Asimiyu O.
This paper explores a mathematical model of malaria, focusing on the basic reproduction number R0 and employing Lyapunov functions to assess the global stability of disease-free and endemic equilibria. Sensitivity analysis of key parameters is conducted to evaluate their impact on disease control. The results indicate an active malaria outbreak with decreasing human classes signifying disease progression and increasing mosquito classes suggesting heightened transmission risk. Effective control measures, including mosquito control and treatment of infected individuals, are essential to mitigate the outbreak.
Mathematical analysis on the vertical and horizontal transmission dynamics of HIV and Zika virus co-infection
(Elsevier BV, 2024-03) Benjamin Idoko Omede; Bolarinwa Bolaji; Olumuyiwa James Peter; Abdullahi A. Ibrahim; Festus Abiodun Oguntolu
The co-infection of HIV and Zika virus (ZIKV) poses a complex and understudied health challenge, requiring a comprehensive investigation into the synergistic effects, potential complications, and the impact on affected individuals. Consequently, This paper introduces a novel deterministic mathematical model that examines the transmission dynamics of HIV and Zika virus co-infection, considering both vertical and horizontal transmission. The analysis begins with two sub-models: one for HIV-only and another for ZIKV-only. Qualitative examination indicates that the HIV only sub-model achieves a globally asymptotically stable disease-free equilibrium when the associated reproduction number is below unity. In contrast, the ZIKV only sub-model exhibits a backward bifurcation phenomenon, where both stable disease-free and stable endemic equilibria co-exist when the associated reproduction number of the ZIKV only sub-model is less than unity. Thus, the backward bifurcation property makes effective control of ZIKV infection in the population difficulty when the associated reproduction number is less than unity. It is shown, using the center manifold theory that the full HIV-ZIKV co-infection model undergoes the phenomenon of backward bifurcation. We carried out the sensitivity analysis of the HIV and ZIKV basic reproduction numbers to determine the parameters that positively influence the spread of the two diseases. It is also revealed that an increase in HIV infection in the population will positively influence the transmission of ZIKV. We validated the ZIKV only sub-model by fitting the ZIKV only sub-model to the confirmed cases of ZIKV data in Brazil. The outcome of the numerical simulations of HIV-ZIKV co-infection model reveals that the two diseases co-exist when their basic reproduction number surpasses one. Furthermore, increasing HIV treatment rate significantly reduces the burden of co-infection with the Zika virus.
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 Modeling on the Transmission Dynamics of Diphtheria with Optimal Control Strategies
(Department of Mathematics, Universitas Negeri Gorontalo, 2025-03-29) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Benjamin Idoko Omede; Ghaniyyat Bolanle Balogun; Aminat Olabisi Ajiboye; Hasan S. Panigoro
Diphtheria is an acute bacterial infection caused by Corynebacterium diphtheriae, characterized by the formation of a pseudo-membrane in the throat, which can lead to airway obstruction and systemic complications. Despite the availability of effective vaccines, diphtheria remains a significant public health concern in many regions, particularly in areas with low immunization coverage. In this study, we formulated and rigorously analyzed a deter ministic epidemiological mathematical model to gain insight into the transmission dynamics of Diphtheria infection, incorporating the concentration of Corynebacterium Diphtheriae in the environment. The analysis of the model begins with the computation of the basic reproduction number and the examination of the local stability of the disease-free equilibrium using the Routh-Hurwitz criterion. An in-depth analysis of the model reveals that the model undergoes the phenomenon of backward bifurcation. This characteristic poses significant hurdles in effectively controlling Diph theria infection within the population. However, under the assumption of no re-infection of Diphtheria infection after recovery, the disease-free equilibrium point is globally asymptotically stable whenever the basic reproduction num ber is less than one. Furthermore, the sensitivity analysis of the basic reproduction number was carried out in order to determine the impact of each of the model basic parameters that contribute to the transmission of the disease. Utilizing the optimal control theory to effectively curb the spread of Diphtheria, We introduced two time dependent control measures, to mitigate the spread of Diphtheria. These time dependent control measures represent preventive actions, such as public enlightenment campaign to sensitize and educate the general public on the dynamics of Diph theria and proper personal hygiene which includes regular washing of hands to prevent susceptible individuals from acquiring Diphtheria, and environmental sanitation practices such as cleaning of surfaces and door handle to reduced the concentration of Corynebacterium diphtheriae in the environment. The results from the numerical simulations reveal that Diphtheria infection can successfully be controlled and mitigated within the population if we can increase the vaccination rate and the decay rate of Corynebacterium Diphtheriae in the environment, as well as properly and effectively implementing these optimal control measures simultaneously.
Modeling the impact of control strategies on malaria and COVID-19 coinfection: insights and implications for integrated public health interventions
(Springer Science and Business Media LLC, 2023-12-27) Adesoye Idowu Abioye; Olumuyiwa James Peter; Emmanuel Addai; Festus Abiodun Oguntolu; Tawakalt Abosede Ayoola
This work discusses the challenge posed by the simultaneous occurrence of malaria and COVID-19 coinfection on global health systems. We propose a novel fractional order mathematical model malaria and COVID-19 coinfection. To assess the impact of control strategies on both diseases, we consider two control strategies which are, personal protection against mosquito bites ($$u_{1}(t)$$) and preventive measures for COVID-19 ($$u_{2}(t)$$). Numerical simulations demonstrate that consistent application of these measures leads to significant reductions in disease transmission. Using insecticide-treated nets and repellents during day and night effectively reduces malaria transmission, while implementing facial masks and hand hygiene controls COVID-19 spread. The most substantial impact is observed when both sets of protection measures are simultaneously adopted, highlighting the importance of integrated strategies. The study provides valuable insights into malaria and COVID-19 coinfection dynamics and emphasizes the impact of the control measures. of individual behavior and consistent adoption of personal protection measures to control both diseases. It underscores the need for integrated public health interventions to combat the dual burden of malaria and COVID-19, contributing to the development of targeted and efficient control measures.