An SEIR epidemic model of fractional order to analyze the evolution of the COVID-19 epidemic in Argentina

Santos, Juan; Carcione, Jos'e; Savioli, Gabriela; Sciences, Patricia Gauzellino School of Earth; Engineering,; University, Hohai; Nanjing,; China,; Aires, Universidad de Buenos; Ingenier'ia, Facultad de; Petr'oleo, Instituto del Gas y del; Aires, Buenos; Argentina,; Mathematics, Departmet of; University, Purdue; States, United; Oceanography, National Institute of; Geophysics, Applied; OGS,; Trieste,; Italy,; Geof'isicas, Facultad de Ciencias Astron'omicas y; Plata, Universidad Nacional de La

A pandemic caused by a new coronavirus (COVID-19) has spread worldwide, inducing an epidemic still active in Argentina. In this chapter, we present a case study using an SEIR (Susceptible-Exposed-Infected-Recovered) diffusion model of fractional order in time to analyze the evolution of the epidemic in Buenos Aires and neighboring areas (Regi\'on Metropolitana de Buenos Aires, (RMBA)) comprising about 15 million inhabitants. In the SEIR model, individuals are divided into four classes, namely, susceptible (S), exposed (E), infected (I) and recovered (R). The SEIR model of fractional order allows for the incorporation of memory, with hereditary properties of the system, being a generalization of the classic SEIR first-order system, where such effects are ignored. Furthermore, the fractional model provides one additional parameter to obtain a better fit of the data. The parameters of the model are calibrated by using as data the number of casualties officially reported. Since infinite solutions honour the data, we show a set of cases with different values of the lockdown parameters, fatality rate, and incubation and infectious periods. The different reproduction ratios R0 and infection fatality rates (IFR) so obtained indicate the results may differ from recent reported values, constituting possible alternative solutions. A comparison with results obtained with the classic SEIR model is also included. The analysis allows us to study how isolation and social distancing measures affect the time evolution of the epidemic.