Tiered social distancing policies have been adopted by many governments to mitigate the harmful consequences of COVID-19. Such policies have a number of well-established features i.e., they are short-term, adaptive (to the changing epidemiological conditions), and based on a multiplicity of indicators of the prevailing epidemic activity. Here, we use ideas from Behavioural Epidemiology to represent tiered policies in an SEIRS model by using a composite information index including multiple indicators of current and past epidemic activity mimicking those used by governments during the COVID-19 pandemic, such as transmission intensity, infection incidence and hospitals' occupancy. In its turn, the dynamics of the information index is assumed to endogenously inform the governmental social distancing interventions. The resulting model is described by a hereditary system showing a noteworthy property i.e., a dependency of the endemic levels of epidemiological variables from initial conditions. This is a consequence of the need to normalise the different indicators to pool them into a single index. Simulations suggest a rich spectrum of possible results. These include policy suggestions and identify pitfalls and undesired outcomes, such as a worsening of epidemic control, that can arise following such types of approaches to epidemic responses.