A Caputo-Based Fractional Order Modelling of COVID-19 in Nigeria

Abstract

Our focus in this work is the proposition of a fractional order model based on Caputo fractional derivatives for the understanding of how coronavirus disease is transmitted in a community, using Nigeria as a case study. By using Laplace transform, we show that the state variables of the model are non-negative at all times and show the existence and uniqueness of solutions for the model. Thorough analysis of the model shows that the model is Ulam-Hyers-Rassias stable and that its disease-free equilibrium is locally and globally asymptotically stable whenever the reproduction number of the disease is less than unity. By gathering real-life data about the disease in Nigeria from accredited authority, Nigerian Centre for Disease Control (NCDC), we estimate parameters driving the spread of the disease by fitting this data to our model. By adopting these parameter estimates, using MATLAB, we perform the numerical simulation of the model with a view to validating results from qualitative analysis of the model. Numerical results show that plots for the model at different fractional orders have major determining influence on various compartments of the model as it varies. Various distinct results were observed for each of the compartments in different fractional orders, highlighting the importance of consideration of the fractional order in modelling the highly contagious COVID-19 disease. This work highlights the advantage of fractional order model over the classical integer order model in the sense that the solution obtained for the fractional order model possesses a higher degree of freedom that enables variation of the system so as to obtain as many preferable responses of the different classes as desired since variation of fractional order $ξ$ can be done at any preferable fractional rate 0.7, 0.4, 0.2 etc.