Industrial Mathematics
Permanent URI for this collectionhttp://197.211.34.35:4000/handle/123456789/94
Industrial Mathematics
Browse
5 results
Search Results
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 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 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 OlaosebikanIn 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.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 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.