Industrial Mathematics

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Industrial Mathematics

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    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.
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    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.
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    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.
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    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.
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    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.
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    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. Omede
    Hepatitis 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.
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    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.
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    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.
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    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.
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    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.