Browsing by Author "Gordon, Joseph Frank"

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    Approximation methods for common fixed points of non-expansive mappings in Hilbert spaces
    (October 11, 2016) Gordon, Joseph Frank
    This thesis is an extensive exposition and review of the paper "Approximation methods of common fixed point of non-expansive mappings in a Hilbert space" in which the author, Paul- Emile Mainge proposed two numerical approaches to solving this problem by implicit and explicit viscosity like-methods. The study as obtain in the thesis was the strong convergence results of the implicit anchor-like algorithm and the explicit procedure for approximating the common fixed point of countable infinite family of non-expansive self-mappings. This thesis basically details the proofs of the main theorem of Paul’s paper as well as detailed exposition of the mathematics involved in it. Detailed proofs of subsidiary results leading up to the proof of the main theorem of Paul’s paper are also discussed. Finally, the main theorem of the paper is also demonstrated in a series of lemmas.
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    Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets
    (2022-06) Addai, Emmanuel; Zhang, Lingling; Ackora-Prah, Joseph; Gordon, Joseph Frank; Asamoah, Joshua Kiddy K.; Essel, John Fiifi; 0000-0002-7066-246X
    Fractional order and fractal order are mathematical tools that can be used to model realworld problems. In order to demonstrate the usefulness of these operators, we develop a new fractal-fractional model for the propagation of the Zika virus. This model includes insecticide-treated nets and the generalized fractal-fractional Mittag-Leffler kernel. The existence, uniqueness, and Ulam–Hyres stability conditions for the given system are determined. Using the Newton polynomial, the numerical scheme is described. From the numerical simulations, we notice that a change in the fractal-fractional order directly affects the dynamics of the Zika virus. We also notice that the use of fractal order only converges to faster than the use of fractional order only. Testing the inherent potency of insecticide-treated nets when the fractal-fractional order is 0.99 indicates that increased use of insecticide-treated nets increases the number of healthy humans. The fractalfractional analysis captures the geometric pattern of the Zika virus that is repeated at every scale, which cannot be captured by classical geometry. This backs up the idea that the best way to control the disease is to know enough about how it spread in the past.
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    Optimal control and comprehensive cost-effectiveness analysis for COVID-19
    (Elsevier, 2022-01) Asamoah, Joshua Kiddy K.; Okyere, Eric; Abidemi, Afeez; Moore, Stephen E.; Sun, Gui-Quan; Jin, Zhen; Acheampong, Edward; Gordon, Joseph Frank; 0000-0002-7066-246X
    Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin’s maximum principle. The optimal control model captures four time-dependent control functions, thus, 𝑢1-practising physical or social distancing protocols; 𝑢2-practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents; 𝑢3-practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals; 𝑢4-fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most costsaving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.