In this work, we analyse mobile phone variation before and after the 2016 Central Italy earthquake in the affected areas, using Twitter and public reconstruction works data. We create three models and show that Twitter data and the related sentiment on the earthquake, as well as the distribution emergency houses, can contribute to explaining population variations. Our final Poisson regression model explains more than 80% of the variance of the population's variation based on the percentage of negative polarity tweets, the number of emergency houses, the number of negative tweets on the earthquake weighted by the number of residents, number of tweets posted on the earthquake anniversary, the distance from the epicentre and several variables related to public reconstruction works (e.g., school, public housing, hydrological disruption, viability). We found that sentiment on the emergency house can be a proxy for population variation because people who live there did not displace from the crater area. The number of tweets posted during the anniversary day can, instead, indicate negative population variation because the higher the number of tweets, the more people can feel nostalgic after having relocated.