Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

Gabriel G. Katul; Assaad Mrad; Sara Bonetti; Gabriele Manoli; Anthony J. Parolari

The R o may be determined by regressing log(i) against t, and the slope of this 133 regression determines R o when γ can be separately estimated. More sophisticated 134 fitting procedures can also be conducted on sampled I(t) versus t. A major limitation to 135 this exercise is that I(t) at early times, often determined from reported confirmed cases, 136 is uncertain and depends on testing frequency that may vary in time as I increases. An 137 alternative is to regress di/dt upon i at early times to detect the highest slope, which 138 can then be used to infer R o . This approach is also featured in Figure 1 , which 139 illustrates that the SIR dynamics exhibit rapid deviations from a linear di/dt with i set 140 by early times thereby underestimating R o (for a given γ). Evidently, inference of R o 141 requires estimates of early time slope, which cannot be easily detected in practice.