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.