There exist a number of complex and often nonlinear phenomena in physical and biophysical systems that can be efficiently approached by systems of differential equations. Even though the determin- istic character of the solutions is typically not adequate to describe the actual behaviour of given systems, this approach is very well suited to describe the influence of the well-defined factors on the evolution of the systems described by properly chosen dynamical models. For example, a compartmen- tal model with three groups of people (susceptible, infected, and recovered) is able to capture some of the general principles related to the dynamics of a pandemic in a biophysical system such as the human population. Here, motivated by the ongoing COVID-19 pandemic, with the help of a proper generalisation of the simple model, we analyse influence and efficacy of commonly invoked counter- pandemic actions — lockdowns and mandatory face masks — in reducing the number of fatalities. To reach this goal, our model takes into account the number of hospitalised persons and the frac- tion of those hospitalised who need special treatment in intensive care units. We show that even if there is an optimal time for introduced lockdowns to be effective, it is impossible to reach in practice due to the limited capacity of the health system. The calculations indicate that wearing face masks decreases the number of hospitalised people and the total death toll. Half of the population appro- priately wearing masks, even the home-made ones (with an efficacy of only about 60%), would halve the peak value of those needing intensive medical treatment. Our study indicates a slightly greater effectiveness of masks worn by healthy people, which is related to the fact that ill people do not protect themselves.