Industrial Mathematics
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Industrial Mathematics
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Item A Mathematical Model Analysis of Meningitis with Treatment and Vaccination in Fractional Derivatives(Springer Science and Business Media LLC, 2022-04-26) Olumuyiwa James Peter; Abdullahi Yusuf; Mayowa M. Ojo; Sumit Kumar; Nitu Kumari; Festus Abiodun OguntoluIn this paper, we develop a new mathematical model based on the Atangana Baleanu Caputo (ABC) derivative to investigate meningitis dynamics. We explain why fractional calculus is useful for modeling real-world problems. The model contains all of the possible interactions that cause disease to spread in the population. We start with classical differential equations and extended them into fractional-order using ABC. Both local and global asymptotic stability conditions for meningitis-free and endemic equilibria are determined. It is shown that the model undergoes backward bifurcation, where the locally stable disease-free equilibrium coexists with an endemic equilibrium. We also find conditions under which the model’s disease-free equilibrium is globally asymptotically stable. The approach of fractional order calculus is quite new for such a biological phenomenon. The effects of vaccination and treatment on transmission dynamics of meningitis are examined. These findings are based on various fractional parameter values and serve as a control parameter for identifying important disease-control techniques. Finally, the acquired results are graphically displayed to support our findings.Item Modeling the impact of control strategies on malaria and COVID-19 coinfection: insights and implications for integrated public health interventions(Springer Science and Business Media LLC, 2023-12-27) Adesoye Idowu Abioye; Olumuyiwa James Peter; Emmanuel Addai; Festus Abiodun Oguntolu; Tawakalt Abosede AyoolaThis work discusses the challenge posed by the simultaneous occurrence of malaria and COVID-19 coinfection on global health systems. We propose a novel fractional order mathematical model malaria and COVID-19 coinfection. To assess the impact of control strategies on both diseases, we consider two control strategies which are, personal protection against mosquito bites ($$u_{1}(t)$$) and preventive measures for COVID-19 ($$u_{2}(t)$$). Numerical simulations demonstrate that consistent application of these measures leads to significant reductions in disease transmission. Using insecticide-treated nets and repellents during day and night effectively reduces malaria transmission, while implementing facial masks and hand hygiene controls COVID-19 spread. The most substantial impact is observed when both sets of protection measures are simultaneously adopted, highlighting the importance of integrated strategies. The study provides valuable insights into malaria and COVID-19 coinfection dynamics and emphasizes the impact of the control measures. of individual behavior and consistent adoption of personal protection measures to control both diseases. It underscores the need for integrated public health interventions to combat the dual burden of malaria and COVID-19, contributing to the development of targeted and efficient control measures.Item A decomposition approach for magnetohydrodynamics stagnation point flow over an inclined shrinking/stretching sheet with suction/injection(International Journal of Mathematical Analysis and Modelling, 2023-09-27) A. Yusuf; G. Bolarin; F. A. Oguntolu; M. Jiya; Y. M. AiyesimiIn this paper, the approximate solution to Magnetohydrodynamics Stagnation Point Flow over an inclined Shrinking/Stretching Sheet with Suction/injection was analyzed via the Adomian Decomposition. The governing partial differential equations (PDEs) were reduced with the help of similarity variables to non linear coupled ordinary differential equations (ODEs). The effects of various pertinent parameters were presented numerically and graphically. Numerical comparisons were carried out with the existing literature and a good agreement was established. The angle of inclination was found to enhance the velocity profile.Item A Mathematical Modelling of Lymphatic Filariasis and Malaria Co-infection(Abubakar Tafawa Balewa University, 2022-06-25) F. A. Oguntolu; D. W. Yavalah; C. F. Udom; T. A. Ayoola; A. A. VictorLymphatic Filariasis (LF) and Malaria continue to pose significant public health burden globally and are co-endemic in many sub-Saharan African regions. In this work, we developed and analyzed a mathematical model of Lymphatic filariasis and malaria co-infection model. Friedman and Lunge method was used to find the positivity of the solution, the disease-free equilibrium was obtained, the model stability was analyzed, and the basic reproductive number was also obtained. The findings suggest that with the use of a bed-net and insecticide as a control measure, the treatment of LF and malaria co-infection can be reduced to a minimum.Item Exploring the dynamics of lymphatic filariasis through a mathematical model and analysis with Holling type II treatment functions(Iranian Journal of Numerical Analysis and Optimization, 2025-06) F. A. Oguntolu; O. J. Peter; B. I. Omede; T. A. Ayoola; G. B. BalogunThis paper presents a robust deterministic mathematical model incorporat-ing Holling type II treatment functions to comprehensively investigate the dynamics of Lymphatic filariasis. Through qualitative analysis, the model demonstrates the occurrence of backward bifurcation when the basic re-production number is less than one. Moreover, numerical simulations are employed to illustrate and validate key analytical findings. These simula-tion results emphasize the significance of accessible medical resources and the efficacy of prophylactic drugs in eradicating Lymphatic filariasis. The findings show that, enhancing medical resource availability and implement-ing effective treatment strategies in rural areas and regions vulnerable to Lymphatic filariasis is crucial for combating the transmission and control of this disease.Item Modelling heat and mass transfer of a CO2 binary mixture: a mathematical approach. International Journal of Mathematical Analysis and Modelling(International Journal of Mathematical Analysis and Modelling, 2023-09-28) R. O. Olayiwola; A. T. Cole; M. D. Shehu; F. A. Oguntolu; E. E. Iyeme; A. W. AbubakarThis paper presents an analytical solutions for describing heat and mass transfer between a droplet of organic solvent and a compressed antisolvent taking into consideration the viscous energy dissipation and heat and mass transfer between the surface and the droplet by convection. The solvent and antisolvent are assumed to be fully miscible and have the same temperature. Both the initial temperature of the mixture and the initial carbon dioxide concentration are also assumed to depend on the space variable. The governing equations formulated based on the conservation of total mass, chemical species, momentum and energy were solved analytically using polynomial approximation method. The results obtained are presented graphically and discussed. The results revealed the effects of operating parameters on droplet lifetime. These results might be used for interpretation or experiments planning of the more complex real supercritical antisolvent process.Item Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate(Elsevier BV, 2022) Oluwatosin Babasola; Oshinubi Kayode; Olumuyiwa James Peter; Faithful Chiagoziem Onwuegbuche; Festus Abiodun OguntoluCOVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection.Item Global Stability and Sensitivity Analysis of Basic Reproduction Number of a Malaria Model(Advances in Systems Sciences and Applications (ASSA), 2023-12-31) Abioye, Adesoye I.; Peter, Olumuyiwa J.; Oguntolu, Festus A.; Ayoola, Tawakalt A.; Oladapo, Asimiyu O.This paper explores a mathematical model of malaria, focusing on the basic reproduction number R0 and employing Lyapunov functions to assess the global stability of disease-free and endemic equilibria. Sensitivity analysis of key parameters is conducted to evaluate their impact on disease control. The results indicate an active malaria outbreak with decreasing human classes signifying disease progression and increasing mosquito classes suggesting heightened transmission risk. Effective control measures, including mosquito control and treatment of infected individuals, are essential to mitigate the outbreak.Item Mathematical analysis on the vertical and horizontal transmission dynamics of HIV and Zika virus co-infection(Elsevier BV, 2024-03) Benjamin Idoko Omede; Bolarinwa Bolaji; Olumuyiwa James Peter; Abdullahi A. Ibrahim; Festus Abiodun OguntoluThe co-infection of HIV and Zika virus (ZIKV) poses a complex and understudied health challenge, requiring a comprehensive investigation into the synergistic effects, potential complications, and the impact on affected individuals. Consequently, This paper introduces a novel deterministic mathematical model that examines the transmission dynamics of HIV and Zika virus co-infection, considering both vertical and horizontal transmission. The analysis begins with two sub-models: one for HIV-only and another for ZIKV-only. Qualitative examination indicates that the HIV only sub-model achieves a globally asymptotically stable disease-free equilibrium when the associated reproduction number is below unity. In contrast, the ZIKV only sub-model exhibits a backward bifurcation phenomenon, where both stable disease-free and stable endemic equilibria co-exist when the associated reproduction number of the ZIKV only sub-model is less than unity. Thus, the backward bifurcation property makes effective control of ZIKV infection in the population difficulty when the associated reproduction number is less than unity. It is shown, using the center manifold theory that the full HIV-ZIKV co-infection model undergoes the phenomenon of backward bifurcation. We carried out the sensitivity analysis of the HIV and ZIKV basic reproduction numbers to determine the parameters that positively influence the spread of the two diseases. It is also revealed that an increase in HIV infection in the population will positively influence the transmission of ZIKV. We validated the ZIKV only sub-model by fitting the ZIKV only sub-model to the confirmed cases of ZIKV data in Brazil. The outcome of the numerical simulations of HIV-ZIKV co-infection model reveals that the two diseases co-exist when their basic reproduction number surpasses one. Furthermore, increasing HIV treatment rate significantly reduces the burden of co-infection with the Zika virus.Item Optimizing tuberculosis control: a comprehensive simulation of integrated interventions using a mathematical model(Mathematical Modelling and Numerical Simulation with Applications, 2024-09-30) Olumuyiwa James Peter; Afeez Abidemi; Fatmawati Fatmawati; Mayowa M. Ojo; Festus Abiodun OguntoluTuberculosis (TB) remains a formidable global health challenge, demanding effective control strategies to alleviate its burden. In this study, we introduce a comprehensive mathematical model to unravel the intricate dynamics of TB transmission and assess the efficacy and cost-effectiveness of diverse intervention strategies. Our model meticulously categorizes the total population into seven distinct compartments, encompassing susceptibility, vaccination, diagnosed infectious, undiagnosed infectious, hospitalized, and recovered individuals. Factors such as susceptible individual recruitment, the impact of vaccination, immunity loss, and the nuanced dynamics of transmission between compartments are considered. Notably, we compute the basic reproduction number, providing a quantitative measure of TB transmission potential. Through this comprehensive model, our study aims to offer valuable insights into optimal control measures for TB prevention and control, contributing to the ongoing global efforts to combat this pressing health challenge.