Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study

Abstract

Life style of people almost in every country has been changed with arrival of corona virus. Under the drastic influence of the virus, mathematicians, statisticians, epidemiologists, microbiologists, environmentalists, health providers, and government officials started searching for strategies including mathematical modeling, lock-down, face masks, isolation, quarantine, and social distancing. With quarantine and isolation being the most effective tools, we have formulated a new nonlinear deterministic model based upon ordinary differential equations containing six compartments (susceptible $S\left(t\right),$ exposed $E\left(t\right),$ quarantined $Q\left(t\right),$ infected $I\left(t\right),$ isolated $J\left(t\right)$ and recovered $R\left(t\right)$ ). The model is found to have positively invariant region whereas equilibrium points of the model are investigated for their local stability with respect to the basic reproductive number $R_0$ . The computed value of $R_0=1.31$ proves endemic level of the epidemic. Using nonlinear least-squares method and real prevalence of COVID-19 cases in Pakistan, best parameters are obtained and their sensitivity is analyzed. Various simulations are presented to appreciate quarantined and isolated strategies if applied sensibly.

Keywords: COVID-19; Computer simulation; Deterministic model; Parameter estimation; Sensitivity analysis; Stability.