Mathematical modeling, analysis and numerical simulation of the COVID-19 transmission with mitigation of control strategies used in Cameroon

Seraphin Djaoue; Gabriel Guilsou Kolaye; Hamadjam Abboubakar; Ado Adamou Abba Ari; Irepran Damakoa

doi:10.1016/j.chaos.2020.110281

Mathematical modeling, analysis and numerical simulation of the COVID-19 transmission with mitigation of control strategies used in Cameroon

Chaos Solitons Fractals. 2020 Oct:139:110281. doi: 10.1016/j.chaos.2020.110281. Epub 2020 Sep 18.

Authors

Seraphin Djaoue¹, Gabriel Guilsou Kolaye¹, Hamadjam Abboubakar², Ado Adamou Abba Ari^{3

4}, Irepran Damakoa²

Affiliations

¹ Department of Mathematics and Computer Science, University of Maroua, P.O. Box 814, Maroua, Cameroon.
² LASE Lab, University of Ngaoundere, P.O. Box 455 Ngaoundere, Cameroon.
³ LaRI Lab, University of Maroua, P.O. Box 814 Maroua, Cameroon.
⁴ LI-PaRAD Lab, Université Paris Saclay, University of Versailles Saint-Quentin-en-Yvelines, 45 Avenue États-Unis Versailles cedex 78035, France.

Abstract

In this paper, we formulated a general model of COVID-19model transmission using biological features of the disease and control strategies based on the isolation of exposed people, confinement (lock-downs) of the human population, testing people living risks area, wearing of masks and respect of hygienic rules. We provide a theoretical study of the model. We derive the basic reproduction number $R_{0}$ which determines the extinction and the persistence of the infection. It is shown that the model exhibits a backward bifurcation at $R_{0} = 1$ . The sensitivity analysis of the model has been performed to determine the impact of related parameters on outbreak severity. It is observed that the asymptomatic infectious group of individuals may play a major role in the spreading of transmission. Moreover, various mitigation strategies are investigated using the proposed model. A numerical evaluation of control strategies has been performed. We found that isolation has a real impact on COVID-19 transmission. When efforts are made through the tracing to isolate 80% of exposed people the disease disappears about 100 days. Although partial confinement does not eradicate the disease it is observed that, during partial confinement, when at least 10% of the partially confined population is totally confined, COVID-19 spread stops after 150 days. The strategy of massif testing has also a real impact on the disease. In that model, we found that when more than 95% of moderate and symptomatic infected people are identified and isolated, the disease is also really controlled after 90 days. The wearing of masks and respecting hygiene rules are fundamental conditions to control the COVID-19.

Keywords: Backward; Basic reproduction number; Extinction; Masks; Persistence; Quarantine; Testing.