Who acquires infection from whom? A sensitivity analysis of transmission dynamics during the early phase of the COVID-19 pandemic in Belgium

Abstract

Age-related heterogeneity in a host population, whether due to how individuals mix and contact each other, the nature of host-pathogen interactions defining epidemiological parameters, or demographics, is crucial in studying infectious disease dynamics. Compartmental models represent a popular approach to address the problem, dividing the population of interest into a discrete and finite number of states depending on, for example, individuals' age and stage of infection. We study the corresponding linearised system whose operator, in the context of a discrete-time model, equates to a square matrix known as the next generation matrix. Performing formal perturbation analysis of the entries of the aforementioned matrix, we derive indices to quantify the age-specific variation of its dominant eigenvalue (i.e., the reproduction number) and explore the relevant epidemiological information we can derive from the eigenstructure of the matrix. The resulting method enables the assessment of the impact of age-related population heterogeneity on virus transmission. In particular, starting from an age-structured SEIR model, we demonstrate the use of this approach for COVID-19 dynamics in Belgium. We analyse the early stages of the SARS-CoV-2 spread, with particular attention to the pre-pandemic framework and the lockdown lifting phase initiated as of May 2020. Our results, influenced by our assumption on age-specific susceptibility and infectiousness, support the hypothesis that transmission was only influenced to a small extent by children in the age group [0,18) and adults over 60 years of age during the early phases of the pandemic and up to the end of July 2020.

Keywords: Age-structured models; Basic reproduction number; COVID-19; Next generation operator; Sensitivity.