Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective

Semu M Kassa; John B H Njagarah; Yibeltal A Terefe

doi:10.1016/j.chaos.2020.109968

Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective

Chaos Solitons Fractals. 2020 Sep:138:109968. doi: 10.1016/j.chaos.2020.109968. Epub 2020 Jun 5.

Authors

Semu M Kassa¹, John B H Njagarah¹, Yibeltal A Terefe²

Affiliations

¹ Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), Private Bag 016, Palapye, Botswana.
² Department of Mathematics and Applied Mathematics, University of Limpopo, South Africa.

Abstract

In this article, a mathematical model for the transmission of COVID-19 disease is formulated and analysed. It is shown that the model exhibits a backward bifurcation at $R_{0} = 1$ when recovered individuals do not develop a permanent immunity for the disease. In the absence of reinfection, it is proved that the model is without backward bifurcation and the disease free equilibrium is globally asymptotically stable for $R_{0} < 1$ . By using available data, the model is validated and parameter values are estimated. The sensitivity of the value of $R_{0}$ to changes in any of the parameter values involved in its formula is analysed. Moreover, various mitigation strategies are investigated using the proposed model and it is observed that the asymptomatic infectious group of individuals may play the major role in the re-emergence of the disease in the future. Therefore, it is recommended that in the absence of vaccination, countries need to develop capacities to detect and isolate at least 30% of the asymptomatic infectious group of individuals while treating in isolation at least 50% of symptomatic patients to control the disease.

Keywords: Backward bifurcation; COVID-19; Disease threshold; Epidemiological model; Mitigation strategy; Self-protection; Sensitivity analysis.