In this paper, we propose an epidemiological infective-hospitalized (IH) model and adopt a heuristic algorithm to predict the transition of infective individuals, which optimizes, at the metapopulation level, the IH model's approximation to the surveillance reports of (cumulative) laboratory confirmed cases. Applying to the data of the 2009 outbreak of a new strain of influenza A (H1N1) in the United States, we obtain the invasion tree along which the virus spreads from the source state reporting the first confirmed case to infect other states. Basically, the surveillance-data-based inference of invasion tree agrees with real epidemic pathways observed in outbreaks of influenza A (H1N1), which verifies the validity of our heuristic inference algorithm.