Geodesic
Investigating the impact of isolation, self-isolation and environmental transmission on the spread of COVID-19: Case study in Rwanda
Mathematica Applicanda, Tome 51 (2023) no. 2, pp. 239-271.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this work, we propose a ten-compartmental COVID-19 model with human to human and environment to human transmissions. A notational feature of this model is the consideration of the infected who escape from the self–isolation and later spread the disease. The model is rigorously analysed both theoretically and numerically. From the mathematical point of view, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R is less than one, that is the disease dies out. When R is greater than one, we prove that the model admits a unique endemic equilibrium, locally asymptotically stable, meaning that the disease would persist, at least inside the basin of attraction of the endemic equilibrium. The sensitivity analysis of the model highlights that the environmental transmission is the most influent parameter, which leads in an increasing number of infected individuals whenever it increases. The model is calibrated using the daily cumulative asymptomatic cases in Rwanda reported from the 1 April 2022 to the 14 June 2022. We found that the basic reproduction number is equal to 0.6479 and most infected people in Rwanda during this period of time are asymptomatic. We investigate the impact of isolation and self-isolation to reduce the disease burden, and both sensitivity analysis and numerical analysis show that the isolation has more effect on the dynamics of the infected than the self-isolation. We also prove that, the individuals who escape from the self-isolation, contribute, but weakly to the increasing of the number of infected individuals.
DOI : 10.14708/ma.v51i2.7212
Classification : 62J05, : 92D20
Mots-clés : COVID-19, Isolation, Environmental transmission, Stability of equilibria, Sensitivity 
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Jean Lubuma; Arsene Jaures Ouemba Tassa; Francis Signing; Berge Tsanou. Investigating the impact of isolation, self-isolation and environmental transmission on the spread of COVID-19: Case study in Rwanda. Mathematica Applicanda, Tome 51 (2023) no. 2, pp.  239-271. doi : 10.14708/ma.v51i2.7212. http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i2.7212/

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