Non-Markovian SIR epidemic spreading model of COVID-19

Lasko Basnarkov; Igor Tomovski; Trifce Sandev; Ljupco Kocarev

doi:10.1016/j.chaos.2022.112286

Non-Markovian SIR epidemic spreading model of COVID-19

Chaos Solitons Fractals. 2022 Jul:160:112286. doi: 10.1016/j.chaos.2022.112286. Epub 2022 Jun 7.

Authors

Lasko Basnarkov^{1

2}, Igor Tomovski², Trifce Sandev^{2

3

4}, Ljupco Kocarev^{1

2}

Affiliations

¹ SS. Cyril and Methodius University, Faculty of Computer Science and Engineering, Rudzer Boshkovikj 16, P.O. Box 393, 1000 Skopje, Macedonia.
² Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia.
³ Institute of Physics & Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany.
⁴ Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia.

Abstract

We introduce non-Markovian SIR epidemic spreading model inspired by the characteristics of the COVID-19, by considering discrete- and continuous-time versions. The distributions of infection intensity and recovery period may take an arbitrary form. By taking corresponding choice of these functions, it is shown that the model reduces to the classical Markovian case. The epidemic threshold is analytically determined for arbitrary functions of infectivity and recovery and verified numerically. The relevance of the model is shown by modeling the first wave of the epidemic in Italy, Spain and the UK, in the spring, 2020.

Keywords: COVID-19; Epidemic spreading models; Non-Markovian processes; SIR model.