A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative

Abstract

This paper considers and analyzes a fractional order model for COVID-19 and tuberculosis co-infection, using the Atangana-Baleanu derivative. The existence and uniqueness of the model solutions are established by applying the fixed point theorem. It is shown that the model is locally asymptotically stable when the reproduction number is less than one. The global stability analysis of the disease free equilibrium points is also carried out. The model was simulated using data relevant to both diseases in New Delhi, India. Fitting the model to the cumulative confirmed COVID-19 cases for New Delhi from March 1, 2021 to June 26, 2021, COVID-19 and TB contact rates and some other important parameters of the model are estimated. The numerical method used combines the two-step Lagrange polynomial and the fundamental theorem of fractional calculus and has been shown to be highly accurate and efficient, user-friendly and converges quickly to the exact solution even with a large step of discretization. Simulations of the Fractional order model revealed that reducing the risk of COVID-19 infection by latently-infected TB individuals will not only bring down the burden of COVID-19, but will also reduce the co-infection of both diseases in the population. Also, the conditions for the co-existence or elimination of both diseases from the population are established.

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