Math. Model. Nat. Phenom.
Volume 16, 2021
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||15|
|Published online||02 June 2021|
SIARD model and effect of lockdown on the dynamics of COVID-19 disease with non total immunity
Le Havre, France.
2 ULH, LMAH, 76600 Le Havre. France
3 FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France.
4 Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire BP 133, Kenitra, Morocco.
* Corresponding author: firstname.lastname@example.org
Accepted: 26 April 2021
We propose a new compartmental mathematical model describing the transmission and the spreading of COVID-19 epidemic with a special focus on the non-total immunity. The model (called SIARD) is given by a system of differential equations which model the interactions between five populations “susceptible”, “reported infectious”, “unreported infectious”, “recovered with/without non total immunity” and “death”. Depending on the basic reproduction number, we prove that the total immunity induces local stability-instability of equilibria and the epidemic may disappear after a first epidemic wave and more epidemic waves may appear in the case of non-total immunity. Using the sensitivity analysis we identify the most sensitive parameters. Numerical simulations are carried out to illustrate our theoretical results. As an application, we found that our model fits well the Moroccan epidemic wave, and predicts more than one wave for French case.
Mathematics Subject Classification: 34D05 / 65L08 / 92B05
Key words: Covid19 / SIARD model / ODE, basic reproduction number / stability
© The authors. Published by EDP Sciences, 2021
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