The pattern of increasing public interest in an issue after media coverage followed by waning media attention and public interest after government attention ot the issue is known as the

I think the answer is Agenda building process. This is used by media to show the development of an issue while getting the interest of the public. Media sees that public involvement on an issue is meaningful. The idea of mass involvement can be seen in social media which gives a sense of direction on an issue. There are also some researchers that proved blogging, and internet proliferation of issues can attract people and politicians.