Legionnaires disease is a severe respiratory illness caused by Legionella bacteria, typically occurring sporadically with unidentified sources of infection. Researchers developed a mathematical model combining spatial variations, meteorological influences, and extended time lags to predict disease risk. The model uses data on temperature, air humidity, precipitation, and cloud cover to create a daily vulnerability index. During 2000-2019, the model improved outbreak detection in 15 of 20 years compared to the standard approach, with an average improvement of 6.0 percent and a maximum improvement of 14.4 percent in 2013. The model also clarified the two-stage dynamics of Legionnaires disease, distinguishing bacterial growth in the environment from the shorter infection period. This approach provides a robust platform for targeted epidemiological surveillance and predictive modelling of Legionnaires disease.