Industrial Mathematics

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Industrial Mathematics

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End date: 2024Subject: search.filters.subject.Stability

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    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. Bello
    In 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.
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    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 Shaba
    Lassa 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.
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    Transmission dynamics of Monkeypox virus: a mathematical modelling approach
    (Springer Science and Business Media LLC, 2021-10-15) Olumuyiwa James Peter; Sumit Kumar; Nitu Kumari; Festus Abiodun Oguntolu; Kayode Oshinubi; Rabiu Musa
    Monkeypox (MPX), similar to both smallpox and cowpox, is caused by the monkeypox virus (MPXV). It occurs mostly in remote Central and West African communities, close to tropical rain forests. It is caused by the monkeypox virus in the Poxviridae family, which belongs to the genus Orthopoxvirus. We develop and analyse a deterministic mathematical model for the monkeypox virus. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. It is shown that the model undergo backward bifurcation, where the locally stable disease-free equilibrium co-exists with an endemic equilibrium. Furthermore, we determine conditions under which the disease-free equilibrium of the model is globally asymptotically stable. Finally, numerical simulations to demonstrate our findings and brief discussions are provided. The findings indicate that isolation of infected individuals in the human population helps to reduce disease transmission.
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    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 Abiodun
    Tuberculosis (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.
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    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 Ayoola
    Leptospirosis 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.