The Influenza virus spreads globally every year and, until before the coronavirus pandemic in 2019, infected from 10% to 20% of the world's population, causing approximately 500.000 deaths annually. A way of keeping up with the progress of Influenza in Brazil is through the number of reported cases on the INFOgripe, which surveys Acute Respiratory Distress Syndrome (ARDS) in the country. However, due to high subnotification levels, these data represent only a partial picture of the disease's dynamic.

In order to study the dynamic of the virus, we extracted the time series of positive cases reported for Influenza A and treated it as a partially observed Markov process. To draw inference on the parameters that determine the dynamic of the disease, we employed the SIRS (Susceptible - Infected - Recovered - Susceptible) model, that splits the population into compartments, providing a framework for studying the transmission of the virus between individuals.

The main objective of this study is to estimate the parameters that determine the flow of individuals between SIRS model compartments using the iterated filtering method. From these estimates, values for the average infection period, average loss of immunity period and the basic reproductive number of the disease were evaluated. The parameter representing the disease's report rate was also estimated, and an alternative parametrization for the model was proposed with the aim of increasing efficiency in the estimating algorithm. The pomp package, implemented in the R software, was used for all computations.

Our findings indicate that the alternative parameterization yields parameter values close to a global maximum for the likelihood function. Our study reveals that when the magnitude of the disease's report rate is about 0.0001, the resulting set of parameters are compatible with reference values found in the literature. The present study should be understood as an intermediate step in modeling influenza A virus. Future work may consider fitting more complex models to the data, with the introduction, for example, of covariates for the parameters of interest.