  We develop an agent-based model to assess the cumulative number of deaths
during hypothetical Covid-19-like epidemics for various non-pharmaceutical
intervention strategies. We consider local and non-local modes of disease
transmission. The first simulates transmission through social contacts in the
vicinity of the place of residence while the second through social contacts in
public places: schools, hospitals, airports, etc., where many people meet, who
live in remote geographic locations. Epidemic spreading is modeled as a
discrete-time stochastic process on random geometric networks. We use the
Monte-Carlo method in the simulations. The~following assumptions are made. The
basic reproduction number is 2.5 and the infectious period lasts approximately
ten days. Infections lead to SARS in about one percent of cases, which are
likely to lead to respiratory default and death, unless the patient receives an
appropriate medical treatment. The~healthcare system capacity is simulated by
the availability of respiratory ventilators or intensive care beds. Some
parameters of the model, like mortality rates or the number of respiratory
ventilators per 100000 inhabitants, are chosen to simulate the real values for
the USA and Poland. In the simulations we compare `do-nothing' strategy with
mitigation strategies based on social distancing and reducing social mixing. We
study epidemics in the pre-vaccine era, where immunity is obtained only by
infection. The model applies only to epidemics for which reinfections are rare
and can be neglected. The results of the simulations show that strategies that
slow the development of an epidemic too much in the early stages do not
significantly reduce the overall number of deaths in the long term, but
increase the duration of the epidemic. In particular, a~hybrid strategy where
lockdown is held for some time and is then completely released, is inefficient.
