  The goal of this article is to analyze some compartmental models specially
designed to model the spread of a disease whose transmission has the same
features as COVID-19. The major contributions of this article are: (1)
Rigorously find sufficient conditions for the outbreak to only have one peak,
i.e. for no second wave of infection to form; (2) Investigate the formation of
other waves of infection when such conditions are not met; (3) Use numerical
simulations to analyze the different roles asymptomatic carriers can have. We
also argue that dividing the population into non-interacting groups leads to an
effective reduction of the transmission rates. As in any compartmental model,
the goal of this article is to provide qualitative understanding rather than
exact quantitative predictions.
