Analysis of a Model for Coronavirus Spread

Youcef Belgaid, Mohamed Helal and Ezio Venturino
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Youcef Belgaid: Laboratory of Biomathematics, Univ. Sidi Bel Abbes, P.B. 89, Sidi Bel Abbes 22000, Algeria
Mohamed Helal: Laboratory of Biomathematics, Univ. Sidi Bel Abbes, P.B. 89, Sidi Bel Abbes 22000, Algeria
Ezio Venturino: Dipartimento di Matematica “Giuseppe Peano”, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Mathematics, 2020, vol. 8, issue 5, 1-30

Abstract: The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

Keywords: dynamical systems; compartment model; epidemics; basic reproduction number; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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