A Caputo-Based Fractional Order Modelling of COVID-19 in Nigeria (Journal of Nonlinear Modeling and Analysis, 2025)
Our focus in this work is the proposition of a fractional ordermodel based on Caputo fractional derivatives for the understanding of howcoronavirus disease is transmitted in a community, using Nigeria as a casestudy. By using Laplace transform, we show that the state variables of themodel are non-negative at all times and show the existence and uniqueness ofsolutions for the model. Thorough analysis of the model shows that the modelis Ulam-Hyers-Rassias stable and that its disease-free equilibrium is locallyand globally asymptotically stable whenever the reproduction number of thedisease 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 toour model. By adopting these parameter estimates, using MATLAB, we perform the numerical simulation of the model with a view to validating resultsfrom qualitative analysis of the model. Numerical results show that plots forthe model at different fractional orders have major determining influence onvarious compartments of the model as it varies. Various distinct results wereobserved for each of the compartments in different fractional orders, highlighting the importance of consideration of the fractional order in modelling thehighly contagious COVID-19 disease. This work highlights the advantage offractional order model over the classical integer order model in the sense thatthe solution obtained for the fractional order model possesses a higher degreeof freedom that enables variation of the system so as to obtain as many preferable responses of the different classes as desired since variation of fractionalorder $ξ$ can be done at any preferable fractional rate 0.7, 0.4, 0.2 etc.