Global Analysis and Optimal Control Model of COVID-19.

Sacrifice Nana-Kyere,Anthony Donkor,Paddy Jonathan,Glory Kofi Hoggar,Francis Agyei Boateng,Isaac Kwasi Adu,Banon Desmond Titus,Andrei Korobeinikov,Daniel Kwarteng

doi:10.1155/2022/9491847

Abstract

COVID-19 remains the concern of the globe as governments struggle to defeat the pandemic. Understanding the dynamics of the epidemic is as important as detecting and treatment of infected individuals. Mathematical models play a crucial role in exploring the dynamics of the outbreak by deducing strategies paramount for curtailing the disease. The research extensively studies the SEQIAHR compartmental model of COVID-19 to provide insight into the dynamics of the disease by underlying tailored strategies designed to minimize the pandemic. We first studied the noncontrol model's dynamic behaviour by calculating the reproduction number and examining the two nonnegative equilibria' existence. The model utilizes the Castillo-Chavez method and Lyapunov function to investigate the global stability of the disease at the disease-free and endemic equilibrium. Sensitivity analysis was carried on to determine the impact of some parameters on R0. We further examined the COVID model to determine the type of bifurcation that it exhibits. To help contain the spread of the disease, we formulated a new SEQIAHR compartmental optimal control model with time-dependent controls: personal protection and vaccination of the susceptible individuals. We solved it by utilizing Pontryagin's maximum principle after studying the dynamical behaviour of the noncontrol model. We solved the model numerically by considering different simulation controls' pairing and examined their effectiveness.

Highlights

The unusual, life-threatening pneumonia condition affecting humanity remains the globe’s concern as governments struggle to defeat the pandemic
This section formulates a compartmental SEQIAHR transmission model for COVID-19 disease to understand the dynamical behaviour of the disease and the strategy needed in curtailing it
Global stability analyses for the two equilibria were carried out by employing the Castillo-Chavez method and Lyapunov function to investigate the global stability of the disease at the disease-free and endemic equilibrium

Summary

Introduction

The unusual, life-threatening pneumonia condition affecting humanity remains the globe’s concern as governments struggle to defeat the pandemic. Hellewell et al [25] assessed the effectiveness of a stochastic transmission model to control the new SARS-CoV-2 disease by utilizing the preventive measures of isolation and contact tracing. Asamoah et al [57] applied an optimal control theory to nonlinear ordinary differential equations of SEAIRV compartmental model of coronavirus transmission that analyzed the cost-effective strategy of all the proposed methods. The authors in [61] applied an optimal control analysis to a mathematical model of SARS-CoV-19 to help deduce many possible strategies for the control of the disease. The study is motivated by the available COVID-19 works and formulating a new SEQIAHR compartmental optimal control model that would add to the existing knowledge and help improve public health decision-making by providing scientific strategies to prevent the disease.

The Model Formulation

Analysis of Model

COVID-19 Optimal Control Model

Model Application with Numerical Examples