Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies

Abstract

The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new LSHSEAIHR COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, LS, and high-risk susceptible populations, HS. The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model’s most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended LSHSEAIHR model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin’s maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity.