Abstract: We propose a mathematical model of COVID-19 pandemic preserving an optimal balance between the adequate description of a pandemic by SIR model and simplicity of practical estimates. As base model equations, we derive two-parameter nonlinear first-order ordinary differential equations with retarded time argument, applicable to any community (country, city, etc.).The presented examples of modeling the pandemic development depending on two parameters: the time of possible dissemination of infection by one virus carrier and the probability of contamination of a healthy population member in a contact with an infected one per unit time, e.g., a day, is in qualitative agreement with the dynamics of COVID-19 pandemic. The proposed model is compared with the SIR model.