A deterministic compartmental model for investigating the impact of escapees on the transmission dynamics of COVID-19

The recent outbreak of the novel coronavirus (COVID-19) pandemic has devastated many parts of the globe. Non-pharmaceutical interventions are the widely available measures to combat and control the COVID-19 pandemic. There is great concern over the rampant unaccounted cases of individuals skipping the border during this critical period in time. We develop a deterministic compartmental model to investigate the impact of escapees (individuals who evade mandatory quarantine) on the transmission dynamics of COVID-19. A suitable Lyapunov function has shown that the disease-free equilibrium is globally asymptotically stable, provided $R_0<1$. We performed a global sensitivity analysis using the Latin-hyper cube sampling method and partial rank correlation coefficients to determine the most influential model parameters on the short and long-term dynamics of the pandemic to minimize uncertainties associated with our variables and parameters. Results confirm a positive correlation between the number of escapees and the reported COVID-19 cases. It is shown that escapees are primarily responsible for the rapid increase in local transmissions. Also, the results from sensitivity analysis show that an increase in governmental role actions and a reduction in the illegal immigration rate will help to control and contain the disease spread.