Calibration and comparison of SIR, SEIR/SLIR and SLAIR models for influenza dynamics: insights from the 2016-2017 season in the Valencian Community, Spain

Influenza and influenza-like illnesses pose significant challenges to healthcare systems globally. Mathematical models play a crucial role in understanding their dynamics, calibrating them to specific scenarios and making projections about their evolution over time. This study proposes a calibration process for three different but well-known compartmental models-SIR, SEIR/SLIR and SLAIR-using influenza data from the 2016-2017 season in the Valencian Community, Spain. The calibration process involves indirect calibration for the SIR and SLIR models, requiring post-processing to compare model output with data, while the SLAIR model is directly calibrated through direct comparison. Our calibration results demonstrate remarkable consistency between the SIR and SLIR models, with slight variations observed in the SLAIR model due to its unique design and calibration strategy. Importantly, all models align with existing evidence and intuitions found in the medical literature. Our findings suggest that at the onset of the epidemiological season, a significant proportion of the population (ranging from 29.08% to 43.75% of the total population) may have already entered the recovered state, likely due to immunization from the previous season. Additionally, we estimate that the percentage of infected individuals seeking healthcare services ranges from 5.7% to 12.2%. Through a well-founded and calibrated modeling approach, our study contributes to supporting, settling and quantifying current medical issues despite the inherent uncertainties involved in influenza dynamics. The full Mathematica code can be downloaded from https://munqu.webs.upv.es/software.html.