Estimating age-stratified transmission and reproduction numbers during the early exponential phase of an epidemic: A case study with COVID-19 data

In a pending pandemic, early knowledge of age-specific disease parameters, e.g., susceptibility, infectivity, and the clinical fraction (the fraction of infections coming to clinical attention), supports targeted public health responses like school closures or sequestration of the elderly. The earlier the knowledge, the more useful it is, so the present article examines an early phase of many epidemics, exponential growth. Using age-stratified COVID-19 case counts collected in Canada, China, Israel, Italy, the Netherlands, and the United Kingdom before April 23, 2020, we present a linear analysis of the exponential phase that attempts to estimate the age-specific disease parameters given above. Some combinations of the parameters can be estimated by requiring that they change smoothly with age. The estimation yielded: (1) the case susceptibility, defined for each age-group as the product of susceptibility to infection and the clinical fraction; (2) the mean number of transmissions of infection per contact within each age-group; and (3) the reproduction number of infection within each age-group, i.e., the diagonal of the age-stratified next-generation matrix. Our restriction to data from the exponential phase indicates the combinations of epidemic parameters that are intrinsically easiest to estimate with early age-stratified case counts. For example, conclusions concerning the age-dependence of case susceptibility appeared more robust than corresponding conclusions about infectivity. Generally, the analysis produced some results consistent with conclusions confirmed much later in the COVID-19 pandemic. Notably, our analysis showed that in some countries, the reproduction number of infection within the half-decade 70–75 was unusually large compared to other half-decades. Our analysis therefore could have anticipated that without countermeasures, COVID-19 would spread rapidly once seeded in homes for the elderly.