Industrial Mathematics

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Industrial Mathematics

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    A Fractional Order Model for the Transmission Dynamics of Meningococcal Meningitis With Real Statistical Data
    (Wiley, 2026-01-30) F. A. Oguntolu; O. J. Peter; B. I. Omede; G. B. Balogun; Z. O. Dere; S. Qureshi
    In this paper, we propose a Caputo-based fractional-order derivative model for the transmission dynamics of meningo coccal meningitis (MM), incorporating the environmental concentration of Neisseria meningitidis as well as factors such as vaccination and the hygiene consciousness of susceptible individuals. The existence and uniqueness of solutions to the model are established using Banach’s and Schauder’s fixed-point theorems. Additionally, we compute the basic reproduction number and examine the local asymptotic stability of the disease-free equilibrium using the Routh–Hurwitz criterion. We analyze the stability of the fractional-order meningitis model using the Ulam–Hyers–Rassias stability method. Furthermore, we fit the model to the cumulative confirmed cases of cere brospinal meningitis in Nigeria using data obtained from the Nigeria Centre for Disease Control (NCDC) to validate the model. The model demonstrates a good fit with the reported cumulative cases. Numerical simulations are conducted for various values of the fractional order. The results reveal an inverse relationship between the fractional order and the total number of asymptomatic infected individuals (carriers), symptomatic infected individuals, and the environmental concentration of Neisseria meningitidis. This implies that increasing the order of the fractional derivative leads to a decrease in the number of infections and bacterial concentration. Moreover, increasing vaccine uptake and improving hygiene consciousness among susceptible individuals significantly reduce both the number of infections and the environmental concentration of Neisseria meningitidis.
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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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    Modelling and optimal control analysis of typhoid fever
    (SCIK Publishing Corporation, 2021-08-19) Tawakalt Abosede Ayoola; Helen Olaronke Edogbanya; Olumuyiwa James Peter; Festus Abiodun Oguntolu; Kayode Oshinubi; Mutiu Lawal Olaosebikan
    In this paper, we formulate a deterministic mathematical model to describe the transmission dynamics of typhoid fever by incorporating some control strategies. In order to study the impact of these control strategies on the dynamics of typhoid fever, the model captures vaccination and educational campaign as control variables. We show that the model is mathematically and epidemiologically well positioned in a biologically feasible region in human populations. We carry out a detailed analysis to determine the basic reproduction number necessary for the control of the disease. The optimal control strategies are used to minimize the infected carriers and infected individuals and the adverse side effects of one or more of the control strategies. We derive a control problem and the conditions for optimal control of the disease using Pontryagin’s Maximum Principle and it was shown that an optimal control exists for the proposed model. The optimality system is solved numerically, the numerical simulation of the model shows that possible optimal control strategies become more effective in the control and containment of typhoid fever when vaccination and educational campaign are combined optimally would reduce the spread of the disease.