Industrial Mathematics

Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/188

Industrial Mathematics

Browse

Now showing 1 - 20 of 29

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.
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.
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.
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.
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.
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.
Semi-analytical solution for the mathematical modeling of yellow fever dynamics incorporating secondary host
(Communication in Mathematical Modeling and Applications (CMMA), 2019-04-15) Samuel Abu Somma; Ninuola Ifeoluwa Akinwande; Roseline Toyin Abah; Festus Abiodun Oguntolu; Florence Dami Ayegbusi
In this paper we use Differential Transformation Method (DTM) to solve the mathematical modeling of yellow fever dynamics incorporating secondary host. The DTM numerical solution was compared with the MAPLE RungeKutta 4-th order. The variable and parameter values used for analytical solution were estimated from the data obtained from World Health Organization (WHO) and UNICEF. The results obtained are in good agreement with Runge-Kutta. The solution was also presented graphically and gives better understanding of the model. The graphical solution showed that vaccination rate and recovery rate play a vital role in eradicating the yellow fever in a community.
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.
Stability and optimal control analysis of an SCIR epidemic model
(SCIK Publishing Corporation, 2020-10-16) Olumuyiwa James Peter; Ratchada Viriyapong; Festus Abiodun Oguntolu; Pensiri Yosyingyong; Helen Olaronke Edogbanya; Michael Oyelami Ajisope
In this paper, we proposed a deterministic model of SCIR governed by a system of nonlinear differential equations. Two equilibria (disease-free and endemic) are obtained and the basic reproduction number R0 is calculated. If R0 is less than one, then the disease-free equilibrium state is globally stable i.e. the disease will be eradicated eventually. However, when R0 is greater than unity, the disease persists and the endemic equilibrium point is globally stable. Furthermore, the optimal control problem is applied into the model. The focus of this study is to determine what control method can be implemented to significantly slow the incidence of the epidemic disease, therefore we take into account various possible combinations of such three controls which are prevention via proper hygiene, screening of the infected carriers which enable them to know their health conditions and to go for early treatment and treatment of the infected individuals. The possible strategies of using combinations of the three controls on the spread of the disease, one at a time or two at a time is also discussed. Our numerical analysis of the optimal approach suggests that the best method is to incorporate all three controls in order to control the disease epidemic.
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.
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.
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.
Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate
(Elsevier BV, 2022) Oluwatosin Babasola; Oshinubi Kayode; Olumuyiwa James Peter; Faithful Chiagoziem Onwuegbuche; Festus Abiodun Oguntolu
COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection.
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.
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 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.
Modelling heat and mass transfer of a CO2 binary mixture: a mathematical approach. International Journal of Mathematical Analysis and Modelling
(International Journal of Mathematical Analysis and Modelling, 2023-09-28) R. O. Olayiwola; A. T. Cole; M. D. Shehu; F. A. Oguntolu; E. E. Iyeme; A. W. Abubakar
This paper presents an analytical solutions for describing heat and mass transfer between a droplet of organic solvent and a compressed antisolvent taking into consideration the viscous energy dissipation and heat and mass transfer between the surface and the droplet by convection. The solvent and antisolvent are assumed to be fully miscible and have the same temperature. Both the initial temperature of the mixture and the initial carbon dioxide concentration are also assumed to depend on the space variable. The governing equations formulated based on the conservation of total mass, chemical species, momentum and energy were solved analytically using polynomial approximation method. The results obtained are presented graphically and discussed. The results revealed the effects of operating parameters on droplet lifetime. These results might be used for interpretation or experiments planning of the more complex real supercritical antisolvent process.