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Mathematical model of Covid-19 pandemic based on retarded differential equation

F.M. Pen'kov, Al-Farabi Kazakh National University, Almaty, Kazakhstan
S.I. Vinitsky, Joint Institute for Nuclear Research, Dubna, Russia; Peoples' Friendship University of Russia, Moscow, Russia
V.L. Derbov, Saratov State University, Saratov, Russia
A.A. Gusev, Joint institute for Nuclear Research, Dubna, Russia
P.M. Krassovitskiy Joint Institute for Nuclear Research, Dubna, Russia; Institute of Nuclear Physics, Almaty, Kazakhstan


We propose a mathematical model of Covid-19 pandemic preserving an optimal balance between the model precision and simplicity for practical estimates. As base equations, we derive two-parameter nonlinear _first-order ordinary differential equations with retarded time argument, applicable to any community (country, city, etc.). Examples of modeling the pandemic development are presented depending on two parameters: the time of possible dissemination of infection by one virus carrier and the probability of contamination of a healthy individual in a contact with an infected one per unit time, e.g, a day. The results show qualitative agreement with the available statistics of Covid-19 pandemic. The proposed model is compared with the conventional SIR model.


Vladimir Derbov
Saratov State University


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