Fractional dynamics of a Chikungunya transmission model

Abstract

In this paper, we introduce a Caputo-sense fractional derivative to an existing model for the Chikungunya transmission dynamics, replacing integer derivative. After reviewing previous work on the integer order model, we suggest a change whereby the integer derivative is replaced by the Caputo derivative operator, and then we obtain results about the asymptotic stability of equilibrium points in this new fractional model. We prove the existence and uniqueness of the solution as well as the global stability of the fractional system. We then construct a numerical scheme for the fractional model, and use parameter values from the Chikungunya epidemic in Chad to perform numerical simulations. This allows us to validate our theoretical results and compare the dynamics behaviour of both models. We find from numerical simulations, that for the fractional-order parameter η in the range (0.85;1), daily detected cases are closer to those the model predict. Thus in the case of Chikungunya epidemic in Chad, the model with fractional derivative produces better results than which with integer derivative.