Global stability of COVID-19 model involving the quarantine strategy and media coverage effects

Ahmed A Mohsen; Hassan Fadhil AL-Husseiny; Xueyong Zhou; Khalid Hattaf; Ahmed A Mohsen; Hassan Fadhil AL-Husseiny; Xueyong Zhou; Khalid Hattaf

doi:10.3934/publichealth.2020047

AIMS Public Health

2020, Volume 7, Issue 3: 587-605. doi: 10.3934/publichealth.2020047

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Global stability of COVID-19 model involving the quarantine strategy and media coverage effects

1.
Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Iraq
2.
Department of Mathematics, College of Science, University of Baghdad, Iraq
3.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, Henan, P.R. China
4.
Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco
5.
Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P.O Box 7955 Sidi Othman, Casablanca, Morocco

Received: 02 June 2020 Accepted: 29 July 2020 Published: 03 August 2020

In this paper, we build and analyze a mathematical model of COVID-19 transmission considering media coverage effects. Due to transmission characteristics of COVID-19, we can divided the population into five classes. The first class describes the susceptible individuals, the second class is exposed individuals, the third class is infected individuals, the fourth class is quarantine class and the last class is recovered individuals. The existence, uniqueness and boundedness of the solutions of the model are discussed. The basic reproduction number $ℛ_{0}$ is obtained. All possible equilibrium points of the model are investigated and their local stability is discussed under some conditions. The disease-free equilibrium is local asymptotically stable when $ℛ_{0} < 1$ and unstable when $ℛ_{0} > 1$ . The globally asymptotical stability of all point is verified by Lyapunov function. Finally, numerical simulations are carried out to confirm the analytical results and understand the effect of varying the parameters on spread of COVID-19. These findings suggested that media coverage can be considered as an effective way to mitigate the COVID-19 spreading.
- COVID-19,
- media coverage effect,
- quarantine,
- mathematical modeling,
- backward bifurcation
Citation: Ahmed A Mohsen, Hassan Fadhil AL-Husseiny, Xueyong Zhou, Khalid Hattaf. Global stability of COVID-19 model involving the quarantine strategy and media coverage effects[J]. AIMS Public Health, 2020, 7(3): 587-605. doi: 10.3934/publichealth.2020047

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Abstract

In this paper, we build and analyze a mathematical model of COVID-19 transmission considering media coverage effects. Due to transmission characteristics of COVID-19, we can divided the population into five classes. The first class describes the susceptible individuals, the second class is exposed individuals, the third class is infected individuals, the fourth class is quarantine class and the last class is recovered individuals. The existence, uniqueness and boundedness of the solutions of the model are discussed. The basic reproduction number

ℛ_{0}

is obtained. All possible equilibrium points of the model are investigated and their local stability is discussed under some conditions. The disease-free equilibrium is local asymptotically stable when

ℛ_{0} < 1

and unstable when

ℛ_{0} > 1

. The globally asymptotical stability of all point is verified by Lyapunov function. Finally, numerical simulations are carried out to confirm the analytical results and understand the effect of varying the parameters on spread of COVID-19. These findings suggested that media coverage can be considered as an effective way to mitigate the COVID-19 spreading.

Acknowledgments

The authors thankful to acknowledge the reviewers for their valuable suggestions and comments. Which have contributed to the improvement of the authors work.

Conflict of interest

The authors declare no conflicts of interest.

References

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