The spread of highly pathogenic avian influenza (HPAI) H5N1 remains a threat for both wild and domestic bird populations, while low pathogenic avian influenza (LPAI) strains have been reported to induce partial immunity to HPAI in poultry and some wild birds inoculated with both HPAI and LPAI strains. Here, based on the reported data and experiments, we develop a two-strain avian influenza model to examine the extent to which this partial immunity observed at the individual level can affect the outcome of the outbreaks among migratory birds in the wild at the population level during different seasons. We find a distinct mitigating effect of LPAI on the death toll induced by HPAI strain, and this effect is particularly important for populations previously exposed to and recovered from LPAI. We further investigate the effect of the dominant mode of transmission of an HPAI strain on the outcome of the epidemic. Four combinations of contact based direct transmission and indirect fecal-to-oral (or environmental) routes are examined. For a given infection peak of HPAI, indirect fecal-to-oral transmission of HPAI can lead to a higher death toll than that associated with direct transmission. The mitigating effect of LPAI can, in turn, be dependent on the route of infection of HPAI.