Social dialogue, the foundation of our democracies, is currently threatened by disinformation and partisanship, with their disrupting role on individual and collective awareness and detrimental effects on decision-making processes. Despite a great deal of attention to the news sphere itself, little is known about the subtle interplay between the offer and the demand for information. Still, a broader perspective on the news ecosystem, including both the producers and the consumers of information, is needed to build new tools to assess the health of the infosphere. Here, we combine in the same framework news supply, as mirrored by a fairly complete Italian news database - partially annotated for fake news, and news demand, as captured through the Google Trends data for Italy. Our investigation focuses on the temporal and semantic interplay of news, fake news, and searches in several domains, including the virus SARS-CoV-2 pandemic. Two main results emerge. First, disinformation is extremely reactive to people's interests and tends to thrive, especially when there is a mismatch between what people are interested in and what news outlets provide. Second, a suitably defined index can assess the level of disinformation only based on the available volumes of news and searches. Although our results mainly concern the Coronavirus subject, we provide hints that the same findings can have more general applications. We contend these results can be a powerful asset in informing campaigns against disinformation and providing news outlets and institutions with potentially relevant strategies.