Recently, global epidemic models that use climatological factors have been proposed to explain influenza activities for both temperate and tropical regions. In this paper, these global models were extended by including interactions of climatological factors. This study was aimed to estimate the relative benefits of such interactions in explaining the global influenza epidemics. The effects of four climatological factors on laboratory-confirmed influenza cases were investigated, i.e., weekly temperature, precipitation, absolute humidity and relative humidity. It was found that countries in Europe and Australia have higher forecast skill, indicating the stronger relationship of influenza with climatological factors, than regions in other continents. The influenza activities of 47 (83%) countries can be explained with a closer match using multi-factor interactions along with original factors than only using the original factors. The temperate countries are characterized by the interaction of factors of temperature and absolute/relative humidity. In contrast, the interaction of factors of precipitation and absolute/relative humidity are dominant in tropical countries.