Mathematics
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Mathematics
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Item Application of Adomian Decomposition Method (ADM) for solving Mathematical Model of Measles(National Mathematical Center, 2021-03-22) Abdurrahman, Nurat Olamide; Somma S. A.; Ayegbusi F. D.; Gana P.; Adama P. W.; Yisa E. M.Item A 4-STAGE RUNGE-KUTTA TYPE METHOD FOR SOLUTION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS(Pan-American Journal of Mathematics, 2024) RAIHANATU MUHAMMAD; ABDULMALIK OYEDEJIIn this paper, a 2 step implicit block hybrid linear multistep method was reformulated into a 4-stage block hybrid Runge-Kutta Type Method via the butcher analysis. The method can be used to solve first order stiff ordinary differential equations. A numerical example solved with the proposed method showed a better result in comparison with an existing methodItem Modelling the impacts of media campaign and double dose vaccination in controlling COVID-19 in Nigeria(Alexandria Engineering Journal, 2023-08-16) Akinwande, N. I.; Somma, Samuel Abu; Olayiwola, R. O.; Ashezua, T. T.; Gweryina, R. I.; Oguntolu, F. A.Corona virus disease (COVID-19) is a lethal disease that poses public health challenge in both developed and developing countries of the world. Owing to the recent ongoing clinical use of COVID-19 vaccines and noncompliance to COVID-19 health protocols, this study presents a deterministic model with an optimal control problem for assessing the community-level impact of media campaign and double-dose vaccination on the transmission and control of COVID-19. Detailed analysis of the model shows that, using the Lyapunov function theory and the theory of centre manifold, the dynamics of the model is determined essentially by the control reproduction number (𝑅𝑚𝑣). Consequently, the model undergoes the phenomenon of forward bifurcation in the absence of the double dose vaccination effects, where the global disease-free equilibrium is obtained whenever 𝑅𝑚𝑣 ≤ 1. Numerical simulations of the model using data relevant to the transmission dynamics of the disease in Nigeria, show that, certain values of the basic reproduction number ((𝑅0 ≥ 7)) may not prevent the spread of the pandemic even if 100% media compliance is achieved. Nevertheless, with assumed 75% (at 𝑅0 = 4)) media efficacy of double dose vaccination, the community herd immunity to the disease can be attained. Furthermore, Pontryagin’s maximum principle was used for the analysis of the optimized model by which necessary conditions for optimal controls were obtained. In addition, the optimal simulation results reveal that, for situations where the cost of implementing the controls (media campaign and double dose vaccination) considered in this study is low, allocating resources to media campaign-only strategy is more effective than allocating them to a firstdose vaccination strategy. More so, as expected, the combined media campaign-double dose vaccination strategy yields a higher population-level impact than the media campaign-only strategy, double-dose vaccination strategy or media campaign-first dose vaccination strategy.Item A 3-Person Non-Zero-Sum Game for Sachet Water Companies(Asian Research Journal of Mathematics, 2022-06-24) Nyor, N.; Muazu, M. I.; Somma Samuel AbuThe business of Sachet water (popularly called pure water) in Nigeria is often competitive due to the high demand for Sachet water by the populace. This is so because sachet water is the most affordable form of pure drinking water in Nigeria. As such, Sachet Water Firms that want to succeed in an ever increasing competitive market need to have the knowledge of Game Theory to identify which strategy will yield better profit independent of the strategy adopted by other competitors. This paper is aimed to investigate and determine the equilibrium point for three Sachet Water Firms using the Nash Equilibrium Method as it provides a systematic approach for deciding the best strategy in competitive situation. The result showed two Nash Equilibriums (promo, promo) and (stay-put, stay-put) with their respective payoffs of (82; 82; 82) and (147; 147; 147).Item Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination(2022-12-10) Akinwande, N. I; Ashezua, T. T.; Gweryina, R. I.; Somma, Samuel Abu; Oguntolu, F. A.; A. UsmanCOVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ωis suspended (Ω =0)is globally asymptotically stable when the effective reproduction number 𝑅0𝑐<1and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment (Ω >0), the endemic equilibrium using the centremanifold theory is shown to be stable globally whenever 𝑅0𝑐>1. The model is extended into optimal control system and analyzed analytically using Pontryagin’s Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70%of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.Item THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM(Federal University Dutsin MA Journal of Sciences (FJS), 2020-06) Muhammad RIn this paper, we examine in details how to obtain the order, error constant, consistency and convergence of a Runge-Kutta Type method (RKTM) when the step number 𝑘 = 2. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation.