# Stability, cost-effectiveness, and global sensitivity analysis of COVID-19 model incorporating non-pharmaceutical interventions and indirect transmission

## Authors

• Darmawati Department of Mathematics, Universitas Sulawesi Barat, 91414 Majene, Indonesia
• W. Nur Department of Mathematics, Universitas Sulawesi Barat, 91414 Majene, Indonesia

## Keywords:

Stability analysis, Optimal control, Cost-effectiveness, Global sensitivity, Covid-19

## Abstract

Covid-19 is an ongoing pandemic caused by SARS-CoV-2. Some interventions are implemented to control the spread of the disease. In Indonesia, there is a campaign related to non-pharmaceutical approach called 3M. This campaign is carried out so that people use masks, wash their hands, and keep their distance. In this paper, we propose a mathematical model considering non-pharmaceutical interventions and indirect transmission. The non-pharmaceutical interventions studied are the implementation of mask-wearing, handwashing, and social distancing. The model is presented as a system of first-order differential equations. The basic reproduction number is determined. The system has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The local stability condition of the disease-free equilibrium point is proved using the Lienard-Chipart criterion. Center manifold theory is used to prove the local stability condition of the endemic equilibrium point. We also study the optimal control strategy related to mask-wearing, handwashing, and social distancing. Furthermore, cost-effectiveness analysis of intervention strategies is also conducted by studying the average cost-effectiveness ratio of each intervention strategy. Our results show that the most effective strategy to control covid-19 spread is the combination of mask-wearing, handwashing, and social distancing. Moreover, the most cost-effective strategy is mask-wearing intervention. Global sensitivity analysis is performed by studying the partial rank correlation coefficient. The results show that mask-wearing intervention is the most influential intervention on basic reproduction number compared to social distancing and handwashing