  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. The
optimal control model captures four time-dependent control functions, thus,
$u_1$-practising physical or social distancing protocols; $u_2$-practising
personal hygiene by cleaning contaminated surfaces with alcohol-based
detergents; $u_3$-practising proper and safety measures by exposed,
asymptomatic and symptomatic infected individuals; $u_4$-fumigating schools in
all levels of education, sports facilities, commercial areas and religious
worship centres. We 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. 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.
