Industrial Mathematics

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Industrial Mathematics

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    Some New Results on a Free Boundary Value Problem Related to Auto Ignition of Combustible Fluid in Insulation Materials
    (International Conference on Mathematical Analysis and Optimization, 2019-03) R. O. Olayiwola; A. T. Cole; M. D. Shehu; F. A. Oguntolu; J. T. Fadepo; F. E. Okoosi
    Auto ignition of combustible fluids in insulation materials is one of the major problems facing the processing industries and many developing nations because it leads to serious environmental problem. This paper presents an analytical solutions to a free boundary value problem related to auto ignition of combustible fluids in insulation materials. The aim is to ascertain whether such a system is safe or if it will undergo ignition for a particular set of conditions. The conditions for this existence of unique solution of the model is established by actual solution method. The properties of solutions is examined. The analytical solution is obtained via polynomial approximation method, which show the influence of the parameters such as the Lewis numbers and Nusselt number are presented graphically and discussed.
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    Stability Analysis of Rotavirus Model with Co-infection and Control Measures
    (Journal of Science, Technology, Mathematics and Education, 2021-06) R. O. Olayiwola; F. A. Kuta; F. A. Oguntolu; O. N. Emuoyibofarhe; F. T. Olayiwola
    A mathematical model of the spread of rotavirus diarrhea based on a continuous time ordinary differential equation modeled two viral strains of influenza is presented. The existing influenza models is extended to include the case of co-infection when a single individual is infected with both strains of rotavirus and to explore the effects of maternal antibodies, vaccination and seasonality. The model exhibits two equilibria, disease-free equilibrium (DFE) and the endemic equilibrium (EE). Equilibrium analysis is conducted in the case with constant controls for both epidemic and endemic dynamics. By the use of Lyapunov function, it is shown that if the effective reproduction number, R0<1, the DFE is globally asymptotically stable and in such a case, the EE is unstable. Moreover, if R0 >1, the endemic equilibrium is globally asymptotically stable.
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    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.
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    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.
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    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.
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    Properties of Some Distributions Using Chebyshev’s Inequality Approach
    (Journal of Science, Technology, Mathematics and Education, 2014-08) K. Rauf; F. A. Oguntolu; A. Isah; U. Y. Abubakar
    In this article, we give a simpler proof of Chebyshev inequality and use the result to obtain some properties of Binomial, Poisson and Geometric distributions. Furthermore, analysis of the results has shown that Chebyshev inequality is effective for determining convergence bound of the distributions. Some recent sharpened results are complemented.2010 Mathematics Subject Classification, 41A50.
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    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.
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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.
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    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.
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    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.