Mathematical Modeling and Stability Analysis of the COVID-19 Spread by Considering Quarantine and Hospitalize

Abstract

A virus that attacks the human respiratory system that first appeared in the province of Wuhan, China is known as COVID-19 (SARS COV2 n-corona virus). In order to anticipate the increasing of the cases, a strategy is needed to inhibit its growth and spread. Seeing the projection of future situations becomes very important, so we can anticipate with a selection of policy scenarios. The dynamical system model approach is very important for predicting future situations as well as selectable scenarios based on simulation results. In this study, we develop a COVID-19 transmission model which can be used to predict the epidemiological outcome and simultaneously to evaluate the effect of quarantine and hospitalization to COVID-19 spread. The mathematical model of the transmission of COVID-19 was developed in the form of the non-linear differential equation system, with seven variables, namely susceptible, exposed, infected, quarantined-1 (exposed individuals who were quarantined), quarantined-2 (infected individuals who were quarantined), hospitalized and recovered. The proposed model has a non-endemic and endemic equilibrium point. Local stability analysis of the non-endemic equilibrium point was investigated using the Routh-Hurwitz criterion, while global stability of the endemic equilibrium point was analyzed by using the Lyapunov method. If the basic reproduction number is less than one, then non-endemic equilibrium point is stable. On the other hand, if the basic reproduction number is greater than one, then endemic equilibrium point is stable. Verification of the developed model was carried out through numerical simulations using data from Central Java Province, Indonesia. We have investigated that parameter related to quarantine and hospitalize affect the number of new infections COVID-19 and the basic reproduction number. From the simulation results, it was found that strict quarantine and hospitalize have the potential to succeed in reducing and inhibiting the transmission of the COVID-19. It can be used by the government in making policies to increase the implementation of quarantine and hospitalize in the community.