On the Estimation of Contact Matrices for Age-Structured Models at the Onset of Epidemic Spread

Estimation of transmission and contact rate parameters among individuals in different age groups is a key point in the mathematical modeling of infectious disease transmission. Several approaches exist for this task, but given the complexity of the problem, it is not always clear which is the most appropriate in each case. Our goal is to contribute to this task in the event of an emerging disease. We propose a methodology to estimate the contact rate parameters from the fraction of the incidence reported in each age group at the beginning of the epidemic spread. Working with an age-structured SIR model, we obtain an equation that relates the contact parameters to various epidemiological quantities potentially available through different sources. We first explore, using an individual-based model, the appropriateness and limitations of our approach when strong restrictions on social activities are in place. We then apply the method to obtain information about the contact structure by age during the COVID-19 epidemic spread in Greater Buenos Aires (Argentina) in 2020. As we have the fractions of reported incidence by age but only rough estimations of other quantities involved in the method, we define several epidemiological scenarios based on various hypotheses. Using the different sets of contact parameters obtained, we evaluate control strategies and analyze the dependence of the results on our assumptions. Our method may also provide a useful framework for assessing how well contact matrices reproduce different aspects of the transmission process through comparison with individual-based model simulations of synthetic contact structures.