Regular physical activity contributes to higher levels of well-being, healthy aging and prevention of several chronic diseases such as depression. To establish or change behaviours concerning physical activity, social contagion may play a role. The aim of this study was to model the contagion of physical activity based on empirical Twitter data and to assess the role of homophily within this contagion. To model the contagion of physical activity, an adaptive temporal-causal network model was designed, and accordingly, the parameters of the model were tuned using empirical data obtained from Twitter. Two variants of the adaptive temporal-causal network model were created, in which one calculated the weights of the connections between the nodes based on follow relations on Twitter, while in the other the connection weights were modulated by the homophily principle. The results indicate that within the considered social network of already active persons homophily does not play an important role in the physical activity behaviour.