A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals

A Othman Almatroud; Noureddine Djenina; Adel Ouannas; Giuseppe Grassi; M Mossa Al-sawalha; A Othman Almatroud; Noureddine Djenina; Adel Ouannas; Giuseppe Grassi; M Mossa Al-sawalha

doi:10.3934/mbe.2022578

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12387-12404. doi: 10.3934/mbe.2022578

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A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals

1.
Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
2.
Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El-Bouaghi, Algeria
3.
Dipartimento Ingegneria Innovazione, Universita Del Salento, Lecce 73100, Italy

Received: 13 May 2022 Revised: 14 July 2022 Accepted: 17 July 2022 Published: 25 August 2022

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.
- Discrete-time systems,
- forward difference systems,
- backward difference systems,
- Covid-19 model,
- epidemic model,
- stability
Citation: A Othman Almatroud, Noureddine Djenina, Adel Ouannas, Giuseppe Grassi, M Mossa Al-sawalha. A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12387-12404. doi: 10.3934/mbe.2022578

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Abstract

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.

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