Estimating the Final Epidemic Size for COVID-19 Outbreak using Improved Epidemiological Models

Rajesh Ranjan

where β is the transmission rate, and γ is the average recovery rate. Note that here constant N is not the population of the country but population composed of susceptibles (S), infected (I) and recovered (R). In the present model, at any time the total population N = S + I + R remains constant as dS(t) dt + dI(t) dt + dR(t) dt = 0 Initially, N is approximately equal to S as I is very small. In an outbreak, typically N will increase every day because more people may get affected due to local outbreaks. However, with quarantine and isolation, this number will slowly become constant. Hence, this SIR model, where N is assumed constant, is valid provided measures are taken to ensure N does not increase much with time. In the present situation, most of the countries have taken extensive measures to impose rigorous social distancing and thus increase in N may not be significant. This model assumes equally likely recovery of everyone affected and hence does not consider factors like age, morbidity etc.