Mathematical modeling of Influenza H1N1 over vaccine influence based on real data

We build a mathematical model applied to influenza H1N1. The model structure consists of splitting the human population according to susceptible, infected by the disease, and recovered which includes the vaccinated population. We develop stability analysis and calculate equilibrium point and basic reproduction number. We analyze model parameters and their role over the representation of São Paulo's real data, provided by SINAN (a serious notifications system), which helps to estimate the disease transmission rate, as well as population mortality and birth rates, through the least-squares method. We take into account the numerical method accuracy related to the infected curve fitting and the real data from 2013. In an attempt to study the vaccination influence over the number of cases, and to identify risks and forecasting outbreaks, we carry out numerical simulations by varying the vaccination rate parameter. Spite of vaccination reaches a small group of the population each year (around 20% based on 2010-2018 data), we conclude it is a key parameter that plays a role over the possibility of reducing cases through the curve flattening. We encourage public policies as an effective measure, to provide significant stimulus and adherence to vaccination programs, and a decrease of infected cases number.