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Before the current pandemic, influenza and respiratory syncytial virus (RSV)were the leading etiological agents of seasonal acute respiratory infections(ARI) around the world. In this setting, medical doctors typically based thediagnosis of ARI on patients' symptoms alone and did not routinely conductvirological tests necessary to identify individual viruses, limiting theability to study the interaction between multiple pathogens and to make publichealth recommendations. We consider a stochastic kinetic model (SKM) for twointeracting ARI pathogens circulating in a large population and anempirically-motivated background process for infections with other pathogenscausing similar symptoms. An extended marginal sampling approach, based on thelinear noise approximation to the SKM, integrates multiple data sources andadditional model components. We infer the parameters defining the pathogens'dynamics and interaction within a Bayesian model and explore the posteriortrajectories of infections for each illness based on aggregate infectionreports from six epidemic seasons collected by the state health department anda subset of virological tests from a sentinel program at a general hospital inSan Luis Potos\'{i}, M\'{e}xico. We interpret the results and makerecommendations for future data collection strategies.

Inference for stochastic kinetic models from multiple data sources for  joint estimation of infection dynamics from aggregate reports and virological  data