On the Construction of Some Deterministic and Stochastic Non-Local SIR Models

Giacomo Ascione
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Giacomo Ascione: Dipartimento di Matematica e Applicazioni Renato Caccioppoli, Università degli Studi di Napoli Federico II, I-80126 Naples, Italy

Mathematics, 2020, vol. 8, issue 12, 1-28

Abstract: Fractional-order epidemic models have become widely studied in the literature. Here, we consider the generalization of a simple S I R model in the context of generalized fractional calculus and we study the main features of such model. Moreover, we construct semi-Markov stochastic epidemic models by using time changed continuous time Markov chains, where the parent process is the stochastic analog of a simple S I R epidemic. In particular, we show that, differently from what happens in the classic case, the deterministic model does not coincide with the large population limit of the stochastic one. This loss of fluid limit is then stressed in terms of numerical examples.

Keywords: epidemic model; Bernstein function; semi-Markov process; subordinator; fluid limit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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