Objectives: The main objective of this research is to demonstrate the effectiveness of non-pharmaceutical interventions (social isolation and quarantine) and of vaccination. Methods: The SIR epidemiological numerical model has been revised to obtain a new model (SAIRDQ), which involves additional variables: the population that died due to the disease (D), the isolated (A), quarantined population (Q) and the effect of vaccination. We have obtained the epidemiological parameters from the data, which are not constant during the evolution of the pandemic, using an iterative approximation method. Results: Analysis of the data of infected and deceased suggest that the evolution of the coronavirus epidemic in Peru has arrived at the end of the second wave (around October 2021). We have simulated the effect of quarantine and vaccination, which are effective measures to reduce the impact of the pandemic. For a variable infection and isolation rate, due to the end of the quarantine, the death toll would be around 200 thousand; if the isolation and quarantine were relaxed since March 01, 2021, there could be more than 280 thousand deaths. Conclusions: Without non-pharmaceutical interventions and vaccination, the number of deaths would be much higher than 280 thousand.