Modelling the COVID-19 Pandemic: Asymptomatic Patients, Lockdown and Herd Immunity

The SARS-Cov-2 is a type of coronavirus that has caused the COVID-19 pandemic. In traditional epidemiological models such as SEIR (Susceptible, Exposed, Infected, Removed), the exposed group E does not infect the susceptible group S. A distinguishing feature of COVID-19 is that, unlike with previous viruses, there is a distinct "asymptomatic" group A, who do not show any symptoms, but can nevertheless infect others, at the same rate as infected patients. This situation is captured in a model known as SAIR (Susceptible, Asymptomatic, Infected, Removed), introduced in Robinson and Stilianakis (2013). The dynamical behavior of the SAIR model is quite different from that of the SEIR model. In this paper, we use Lyapunov theory to establish the global asymptotic stabiilty of the SAIR model. Next, we present methods for estimating the parameters in the SAIR model. We apply these estimation methods to data from several countries including India, and show that the predicted trajectories of the disease closely match actual data.