A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point

Isra Al-Shbeil, Noureddine Djenina (), Ali Jaradat, Abdallah Al-Husban, Adel Ouannas and Giuseppe Grassi
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Isra Al-Shbeil: Department of Mathematics, Faculty of Sciences, University of Jordan, Amman 11942, Jordan
Noureddine Djenina: Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Ali Jaradat: Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan
Abdallah Al-Husban: Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan
Adel Ouannas: Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: Owing to the COVID-19 pandemic, which broke out in December 2019 and is still disrupting human life across the world, attention has been recently focused on the study of epidemic mathematical models able to describe the spread of the disease. The number of people who have received vaccinations is a new state variable in the COVID-19 model that this paper introduces to further the discussion of the subject. The study demonstrates that the proposed compartment model, which is described by differential equations of integer order, has two fixed points, a disease-free fixed point and an endemic fixed point. The global stability of the disease-free fixed point is guaranteed by a new theorem that is proven. This implies the disappearance of the pandemic, provided that an inequality involving the vaccination rate is satisfied. Finally, simulation results are carried out, with the aim of highlighting the usefulness of the conceived COVID-19 compartment model.

Keywords: dynamical systems; epidemics; stability; disease; bio mathematics modeling; COVID 19 model; basic reproduction number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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