Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain.

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations. Mathematically, its dynamics is governed by a nonlinear system of ordinary differential equations, where the non-linearity arises from the effective contacts between susceptible and infected individuals. Two key aspects of this study is that we use a vaccine distribution over time that is based on real data specific to the elderly people in the Valencian Community and the calibration process takes into account that over one influenza season a specific proportion of the population becomes infected with influenza. To consider the effectiveness of the vaccine, the model incorporates a parameter, the vaccine attenuation factor, which is related with the vaccine efficacy against the influenza virus. With this framework, in order to calibrate the model parameters and to obtain an influenza vaccine efficacy estimation, we considered the 2016-2017 influenza season in the Valencian Community, Spain, using the influenza reported cases of vaccinated and unvaccinated. In order to ensure the model identifiability, we choose to deterministically calibrate the parameters for different scenarios and we find the one with the minimum error in order to determine the vaccine efficacy. The calibration results suggest that the influenza vaccine developed for 2016-2017 influenza season has an efficacy of approximately 76.7%, and that the risk of becoming infected is five times higher for an unvaccinated individual in comparison with a vaccinated one. This estimation partially agrees with some previous studies related to the influenza vaccine. This study presents a new integrated mathematical approach to study the influenza vaccine efficacy and gives further insight into this important public health topic.