An epidemiological model for COVID-19 was developed and implemented in MATLAB/GNU Octave for use by public health practitioners, policy makers, and the general public. The model distinguishes four stages in the disease: infected, sick, seriously sick, and better. The model was preliminarily parameterized based on observations of the spread of the disease. The model assumes a case mortality rate of 1.5%. Preliminary simulations with the model indicate that concepts such as “herd immunity” and containment (“flattening the curve”) are highly misleading in the context of this virus. Public policies based on these concepts are inadequate to protect the population. Only reducing the R 0 of the virus below 1 is an effective strategy for maintaining the death burden of COVID-19 within the normal range of seasonal flu. The model is illustrated with the cases of Italy, France, and Iran and is able to describe the number of deaths as a function of time in all these cases although future projections tend to slightly overestimate the number of deaths when the analysis is made early on. The model can also be used to describe reopenings of the economy after a lockdown. The case mortality rate is still prone to large uncertainty, but modeling combined with an investigation of blood donations in The Netherlands imposes a lower limit of 1%. Electronic supplementary material The online version of this article (10.1007/s11071-020-05861-7) contains supplementary material, which is available to authorized users.