Assessing respiratory virus co-infections using an identifiable model: the case of influenza and SARS-CoV-2 in Italy

This study investigates the dynamics of co-infections during an epidemic, particularly in the absence of official data on co-infected individuals. The research has two primary objectives: first, to assess the robustness of the two-pathogen co-infection model proposed by Fahlena et al. (Chaos Sol. Fract., 2022) in terms of structural and practical identifiability; and second, to evaluate the time variation of co-infection percentages in Italy during the winter of 2023-2024. The identifiability analysis is based on official data regarding influenza and SARS-CoV-2 cases, complemented by estimated co-infection data under two scenarios (high and low levels of co-infection). The study finds that when both weekly infection and co-infection data are available, the model's parameters are structurally identifiable. However, if only incidence data for each virus are available, five parameters must be fixed to achieve both structural and practical identifiability, with the remaining parameters being identifiable. Additionally, the model suggests that a unimodal time profile of co-infection percentages could have occurred in Italy during the study period. These results emphasize the importance of comprehensive data for model identification and co-infection estimation during epidemics.