Fractional vector-borne disease model with lifelong immunity under Caputo operator

Abstract

This study provides a comprehensive analysis of the vector-borne disease model with lifelong immunity by means of the Caputo fractional differential operator. We present the existence and uniqueness of the solution of the suggested fractional disease model by utilizing the fixed-point theorem. Some basic properties of the non-integer order model such as invariant region, the positiveness of the solution are given under the Caputo derivative. Moreover, analysis of the model shows that disease-free equilibrium is locally asymptotically stable. On the other hand, numerical results with various graphs are presented by taking advantage of different values of non-integer order alpha. Also, for the disease model under consideration, more detailed results are obtained thanks to the fractional-order derivative as can be seen from the solution curves in the graphs.