Industrial Mathematics
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Industrial Mathematics
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Item A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics(Elsevier BV, 2023-12) Adesoye Idowu Abioye; Olumuyiwa James Peter; Hammed Abiodun Ogunseye; Festus Abiodun Oguntolu; Tawakalt Abosede Ayoola; Asimiyu Olalekan OladapoThis study proposes a fractional-order mathematical model for malaria and COVID-19 co-infection using the Atangana–Baleanu Derivative. We explain the various stages of the diseases together in humans and mosquitoes, and we also establish the existence and uniqueness of the fractional order co-infection model solution using the fixed point theorem. We conduct the qualitative analysis along with an epidemic indicator, the basic reproduction number R0 of this model. We investigate the global stability at the disease and endemic free equilibrium of the malaria-only, COVID-19-only, and co-infection models. We run different simulations of the fractional-order co-infection model using a two-step Lagrange interpolation polynomial approximate method with the aid of the Maple software package. The results reveal that reducing the risk of malaria and COVID-19 by taking preventive measures will reduce the risk factor for getting COVID-19 after contracting malaria and will also reduce the risk factor for getting malaria after contracting COVID-19 even to the point of extinction.Item A non-linear differential equation model of COVID-19 and seasonal influenza co-infection dynamics under vaccination strategy and immunity waning(Elsevier BV, 2023-12) Rabiu Musa; Olumuyiwa James Peter; Festus Abiodun OguntoluThis study presents a mathematical model of the transmission dynamics of COVID-19 and influenza co-infection. The potential impacts of the influenza vaccine only on the co-infection dynamics and the potential impacts of both vaccines on the co-infection dynamics are thoroughly studied. The basic reproduction number for the two diseases using the next-generation matrix approach and the stability of the sub-model is examined. The model assessed the scenario whereby both diseases’ waning immunity occurs concurrently to check the epidemic peaks. The numerical simulation results show that the diseases would continue to be endemic in the population if the immunity waning rates increase. The epidemic peak can be reduced by increasing vaccination and vaccine efficacy rates. The results show that the COVID-19 contact rate significantly increases the epidemic level more than the co-infection contact rate. A similar result was obtained when it was observed that the COVID-19 post-recovery waning rate has more significant effects on the epidemic peak than the co-infection post-recovery waning rate. A possible reason for this counter-intuitive occurrence is that two infections cannot have the same viral load nor the same within-host competitiveness. This means an infectious co-infected person will transmit the infection with the highest within-host competitiveness. Here, it is suspected that COVID-19 has a within-host competitive advantage over influenza in the co-dynamics.Item AN OPTIMIZED SINGLE-STEP BLOCK HYBRID NYSTRÖM-TYPE METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS OF BRATU-TYPE(African Journal of Mathematics and Statistics Studies, 2023-12-12) Joel Olusegun Ajinuhi; Umaru Mohammed; Abdullahi Idris Enagi; Onanmayi Razaq JimohIn this paper, a global single-step implicit block hybrid Nyström-type method (BHNTM) for solving nonlinear second-order initial-boundary value problems of Bratu-type is developed. The mathematical derivation of the proposed BHNTM is based on the interpolation and multistep collocation techniques with power series polynomials as the trial function. Unlike previous approaches, BHNTM is applied without linearization or restrictive assumptions. The basic properties of the proposed method, such as zero stability, consistency and convergence are analysed. The numerical results from three test problems demonstrate its superiority over existing methods which emphasize the effectiveness and reliability in numerical simulations. Furthermore, as the step size decreases as seen in the test problems, the error drastically reduces, indicating BHNTM's precision. These findings underscore BHNTM's significance in numerical methods for solving differential equations, offering a more precise and dependable approach for addressing complex problems.Item 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. BelloIn 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.Item 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. OjedokunThis 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.Item 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. OgwumuIn 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.Item 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. AwojoyogbeMagnetic 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)=coswt 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.Item 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 AyoolaIn 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.Item 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.Item 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. BelloIn 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.Item Mathematical analysis of a novel fractional order vaccination model for Tuberculosis incorporating susceptible class with underlying ailment(International Journal of Modelling and Simulation (Taylor & Francis), 2024-07-10) El-Mesady, A.; Peter, Olumuyiwa James; Omame, Andrew; Oguntolu, Festus AbiodunTuberculosis (TB) is a communicable, airborne infection caused by the bacillus Mycobacterium tuberculosis. Pulmonary tuberculosis (PTB) is the most common presentation, although infection can spread anywhere to cause extra-pulmonary tuberculosis (EPTB). In this paper, a novel fractional order mathematical model is designed for the transmission dynamics of tuberculosis. Uninfected vulnerable individuals are categorized into the following: susceptible with underline ailment and susceptible without underline ailment. The research seeks to qualitatively and quantitatively analyze the proposed model and suggests comprehensive intervention measures for the control of tuberculosis among individuals with underline ailment. Some of the major highlights from the numerical investigation points out that TB vaccination is key to reducing the spread of TB among individuals with underline ailment. Furthermore, efforts to step down the spread of TB through awareness campaigns could significantly reduce the burden of the disease among individuals with co-morbidity.Item Mathematical Analysis of the Transmission Dynamics of Hepatitis B Virus(Springer Science and Business Media LLC, 2025-05-15) F.A. Oguntolu; O.J. Peter; D. Aldila; G. B. Balogun; O. P. Ogunmola; B. I. OmedeHepatitis B is a life-threatening hepatic illness induced by the Hepatitis B virus (HBV). This is a major worldwide health issue, especially in low- and middle-income nations in Africa and the Western Pacific, where prevalence rates are the greatest. Nevertheless, the existence of an efficacious vaccination, Hepatitis B persists in inflicting significant morbidity and death owing to a deficiency of awareness regarding the illness. Thus, we developed a deterministic mathematical model to elucidate the transmission dynamics of Hepatitis B, integrating elements such as vertical transmission, re-infection, and environmental viral concentration. The study starts with the calculation of the basic reproduction number and the assessment of the local stability of the disease-free equilibrium employing the Routh-Hurwitz criteria. A comprehensive examination of the model indicates that the model may experience backward bifurcation phenomena under some specific conditions. This trait presents considerable challenges in the proper management of Hepatitis B infection among the population. Assuming no re-infection of Hepatitis B post-recovery, the disease-free equilibrium point is globally asymptotically stable when the basic reproduction number is less than or equal to one. The sensitivity analysis of the basic reproduction number was conducted to assess the influence of each fundamental parameter in the model that contributes to disease transmission. Utilizing the optimal control theory to effectively curb the spread of Hepatitis B, we incorporated two time-varying control strategies, namely the prevention of susceptible individuals from acquiring HBV (through safe sex practice, regular washing of hands, and using protective hand gloves when handling blood, body fluid and semen) and the sensitization on individuals on personal hygiene, sterilization and proper disposal of medical and dental equipment like syringes in order to reduce the shedding of HBV in the environment. The numerical simulations indicated that Hepatitis B infection may be effectively managed and mitigated within the community if both control measures are correctly implemented.Item Mathematical model for the dynamics of COVID-19 Pandemic Incorporating Isolation and Non-Linear Recovery Rate(ISEP Porto-Portugal, 2024-06-22) N. I. Akinwande; T. T. Ashezua; S. A. Somma; O. N. Abdurrahman; F. A. Oguntolu; O. M. Adetutu; R. I. Gweryina; R. O. Olayiwola; T. P. Adajime; F. A. Kuta; S. Abdulrahman; A. I. Enagi; G. A. Bolarin; M. D. Shehua; A. Usman.COVID-19 has in recent times created a major health concern in both developed and developing parts of the world. In this wise, there is every need to theoretically explore ways that will provide some insights into curtailing the spread of the disease in the population. In this paper, we present a population model for COVID-19 pandemic incorporating isolation and nonlinear recovery rate. The reproduction number was obtained using the next generation method. The disease-free equilibrium (DFE) of the model (1) was found to be locally and globally asymptotically stable whenever the associated reproduction number is less than unity. Results from the sensitivity analysis of the model, using the reproduction number, RC show that the top parameters that largely drive the dynamics of COVID-19 in the population are COVID-19 transmission rate and the proportion of individuals progressing to the class of reported symptomatic infectious individuals. Numerical simulations of the model shows that increasing the recovery rate of infected patients in the population will lead to an initial decrease in the number of hospitalized patients before subsequent increase. The reason for this could be attributed to the number of unreported symptomatic infectious individuals who are progressing to reported symptomatic infectious stage of infection for immediate isolation.Item 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 KhanThe 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.Item 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. ShehuCOVID-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 𝑅0𝑐<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 𝑅0𝑐>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.Item 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 OguntoluMeasles 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.Item Mathematical model on the transmission dynamics of leptospirosis in human and animal population with optimal control strategies using real statistical data(Springer Science and Business Media LLC, 2024-12-07) Festus Abiodun Oguntolu; Olumuyiwa James Peter; Benjamin Idoko Omede; Ghaniyyat Bolanle Balogun; Tawakalt Abosede AyoolaLeptospirosis poses a significant public health challenge, with a growing incidence in both human and animal populations. The complex interplay between reservoir hosts, environmental factors, and human activities complicates efforts to curb the spread of the disease. Consequently, this paper presents a deterministic mathematical model for the transmission dynamics of leptospirosis within the intertwined human and animal populations. A comprehensive examination of the model revealed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is below one. Utilizing center manifold theory, we demonstrated that the Leptospirosis model displays forward bifurcation. Consequently, the epidemiological significance of this forward bifurcation suggests that eradicating leptospirosis from the community is feasible, provided the reproduction number remains below one. We conducted a sensitivity analysis on the basic reproduction number of Leptospirosis to identify parameters that contribute positively to the disease’s spread. Furthermore, We validated our Leptospirosis model by fitting it with confirmed cases reported in Kerala State, India, covering the period from January 2021 to December 2022. This calibration process ensures the model’s accuracy and reliability in reflecting real-world epidemiological dynamics within the specified region and timeframe. In addition, we enhanced the Leptospirosis model by incorporating three time-dependent control measures. These controls encompass the vaccination of animals, environmental sanitation, and preventive actions such as using hand gloves and goggles when handling animals, as well as wearing rubber boots during periods of flooding or heavy rainfall. Results obtained from numerical simulations indicate that implementing the vaccination of animals as a standalone control strategy has no discernible effect on the number of infected humans or the bacteria population. However, when the three time-dependent control measures are combined, there is a substantial and meaningful impact on reducing the number of infected humans, infected animals, and the overall bacteria population within a relatively short timeframe. This underscores the effectiveness of the integrated approach in mitigating the spread of leptospirosis across both human and animal populations.Item 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 AyoolaIn 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.Item 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. OguntoluThe 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.Item 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 ShabaLassa 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.