Optimal control and comprehensive cost-effectiveness analysis for COVID-19

TL;DR

This study develops an optimal control model for COVID-19 in Saudi Arabia, analyzing cost-effectiveness of various interventions and identifying the most efficient strategies without vaccination.

Contribution

It formulates a novel non-autonomous nonlinear epidemic model with four control functions and performs comprehensive cost-effectiveness analysis using Pontryagin's maximum principle.

Findings

Physical distancing is the most cost-effective strategy.

Strategies 6, 11, 12, and 14 are equally effective in infection control.

Numerical simulations validate the optimal control strategies.

Abstract

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.