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arXiv · 2101.00517

Advanced and comprehensive research on the dynamics of COVID-19 under mass communication outlets intervention and quarantine strategy: a deterministic and probabilistic approach

Driss Kiouach·Salim El Azami El-idrissi·Yassine Sabbar
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Abstract

The ongoing Coronavirus disease 2019 (COVID-19) is a major crisis that has significantly affected the healthcare sector and global economies, which made it the main subject of various fields in scientific and technical research. To properly understand and control this new epidemic, mathematical modelling is presented as a very effective tool that can illustrate the mechanisms of its propagation. In this regard, the use of compartmental models is the most prominent approach adopted in the literature to describe the dynamics of COVID-19. Along the same line, we aim during this study to generalize and ameliorate many existing works that consecrated to analyse the behaviour of this epidemic. Precisely, we propose an SQEAIHR epidemic system for Coronavirus. Our constructed model is enriched by taking into account the media intervention and vital dynamics. By the use of the next-generation matrix method, the theoretical basic reproductive number $R_0$ is obtained for COVID-19. Based on some nonstandard and generalized analytical techniques, the local and global stability of the disease-free equilibrium are proven when $R_0 < 1$. Moreover, in the case of $R_0 > 1$, the uniform persistence of COVID-19 model is also shown. In order to better adapt our epidemic model to reality, the randomness factor is taken into account by considering a proportional white noises, which leads to a well-posed stochastic model. Under appropriate conditions, interesting asymptotic properties are proved, namely: extinction and persistence in the mean. The theoretical results show that the dynamics of the perturbed COVID-19 model are determined by parameters that are closely related to the magnitude of the stochastic noise. Finally, we present some numerical illustrations to confirm our theoretical results and to show the impact of media intervention and quarantine strategies.

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Driss Kiouach, Salim El Azami El-idrissi, Yassine Sabbar. 2021-01-02. Advanced and comprehensive research on the dynamics of COVID-19 under mass communication outlets intervention and quarantine strategy: a deterministic and probabilistic approach. https://arxiv.org/abs/2101.00517

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