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

Abstract

The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number R o . The work here shows that there is global convergence (i.e. across many nations) to an uncontrolled R o = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of R o = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. Implications for evaluating potential control strategies from this uncontrolled R o are briefly discussed in the context of the maximum possible infected fraction of the population (needed for assessing health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in R o > 2.7 within 49 days after first infection, intervention is unlikely to be effective in general for COVID-19. Current optimistic projections place mortality figures in the USA in the range of 100,000 fatalities. For fatalities to be confined to 100,000 requires a reduction in R o from 4.5 to 2.7 within 17 days of first infection assuming a mortality rate of 3.4%. : medRxiv preprint in epidemiology. This dispute moved inoculation from the domain of philosophy, 4 religion, and disjointed trials plagued by high uncertainty into a debate about 5 mathematical models -put forth by Daniel Bernoulli (in 1766) and Jean-Baptiste le 6 Rond D'Alembert (in 1761), both dealing with competing risks of death and 7 interpretation of trials [1]. Since then, the mathematical description of infectious 8 diseases continues to draw significant attention from researchers and practitioners in 9 governments and health agencies alike. Even news agencies are now seeking out 10 explanations to models so as to offer advice and clarity to their audiences during the 11 (near-continuous) coverage of the spread of COVID-19 [2]. The prospect of using 12 mathematical models in conjunction with data is succinctly summarized by the Nobel 13 laureate Ronald Ross, whose 1916 abstract [3] enlightens the role of mathematics in 14 epidemiology today. A quotation from this abstract below, which foreshadows the 15 requirements and challenges for mathematical models to describe emerging epidemics 16 such as 5], needs no further elaboration: 17

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