Who Acquires Infection from Whom? A Sensitivity Analysis of Transmission Dynamics During the Early Phase of the Covid-19 Pandemic in Belgium

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. The study of the corresponding linearised system can be related to that of a linear operator. In the context of a discrete-time model, this equates to a square matrix referred to 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 and show how to quantify its impact via user-friendly indices. We analyze 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, following the first lockdown period. Our results support the hypothesis that transmission is only influenced to a small extent by children in the age band [0,18) and by adults over 60 years of age during the early phases of the pandemic up to the end of July 2020.