Fractional differential model of the spread of COVID-19

Abstract

This paper studies a mathematical model of the spread of the COVID-19 pandemic based on ordinary differential equations with a time-fractional derivative. The model takes into account the susceptibility of the population to infection, the incubation period, the number of contacts between healthy and sick people, number of infected, recovered and deceased people in a certain period. To test the model a comparison was made with models obtained with a time derivative of integer orders, with known data for the Italian region of Lombardy. The results suggest that the use of a mathematical model based on a time-fractional derivative with the help of data such as susceptibility of the population to infection, incubation period, number of infected, recovered and deceased people in a certain period, ultimately can help health authorities to develop effective measures against the pandemic. This is especially possible if we expand the model and consider partial differential equations describing the convection-diffusion process, taking into account the prediction of the geographical distribution of the most important medical resources.