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Analysis of a Model for Coronavirus Spread

Author

Listed:
  • 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
    Member of the INdAM research group GNCS.)

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.

Suggested Citation

  • Youcef Belgaid & Mohamed Helal & Ezio Venturino, 2020. "Analysis of a Model for Coronavirus Spread," Mathematics, MDPI, vol. 8(5), pages 1-30, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:820-:d:359894
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