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, -practising physical or social distancing protocols; -practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents; -practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals; -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 cost-saving 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.

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In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.

The purpose of this paper is to introduce and analyze the shrinking projection algorithm with errors for a finite set of costerro bounded linear mappings in the setting of uniformly convex smooth Banach spaces. Here, under finite dimensional or compactness restriction or the error term being zero, the strong limit point of the sequence stated in the iterative scheme for these mappings in uniformly convex smooth Banach spaces was studied. This paper extends Ezearn and Prempeh’s result for nonexpansive mappings in real Hilbert spaces.

Despite multiple studies in the past, seeking to assess the determinants of students' achievement in mathematics, less attention has been paid to the simultaneous role of classroom management (CM), mastery-oriented instructions, and teacher pedagogical content knowledge (PCK). This study, therefore, looked at the mediation effects of mastery-oriented instructions and CM in the relationship between teacher PCK and students' mathematics achievement. The study was a survey and quantitative. A simple random sampling approach was used to select 401 senior high school students from five schools in the Kumasi Metropolis. A structural equation model was used in analyzing the effect of the relationship between the variables. It was concluded that teacher PCK had a significant relationship with students' mathematics achievement. It also had a significant effect on masteryoriented instructions and CM. It was revealed that both teacher PCK and CM did not mediate the relationship between teachers' PCK and students' mathematics achievement.