  The short-term economic consequences of the critical measures employed to
curb the transmission of Covid-19 are all too familiar, but the consequences of
isolation and loneliness resulting from those measures on the mental well-being
of the population and their ensuing long-term economic effects are largely
unknown. Here we offer a stochastic agent-based model to investigate social
restriction measures in a community where the feelings of loneliness of the
agents dwindle when they are socializing and grow when they are alone. In
addition, the intensity of those feelings, which are measured by a real
variable that we term degree of loneliness, determines whether the agent will
seek social contact or not. We find that decrease of the number, quality or
duration of social contacts lead the community to enter a regime of burnout in
which the degree of loneliness diverges, although the number of lonely agents
at a given moment amounts to only a fraction of the total population. This
regime of mental breakdown is separated from the healthy regime, where the
degree of loneliness is finite, by a continuous phase transition. We show that
the community dynamics is described extremely well by a simple mean-field
theory so our conclusions can be easily verified for different scenarios and
parameter settings. The appearance of the burnout regime illustrates neatly the
side effects of social distancing, which give to many of us the choice between
physical infection and mental breakdown.
