Mathematical modeling of pine wilt disease with Caputo fractional operator

Abstract

In this work, we investigate the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative. Moreover, with the use of fixed point theorem, the existence and uniqueness of the pine wilt disease model are obtained under Caputo operator. Using forward normalized sensitivity index, we determine the most sensitive parameters essential for the control of the infection and the results show that, decreasing the values of contact rate of a susceptible vector with infected pine trees and progression rate play a significant role in controlling the spread of pine wilt disease infection. On the other hand, we obtain different numerical simulations results of the model using the appropriate parameter values. Hence, from the graphs, it can be concluded that Caputo fractional operator gives more biologically observable behavior of the proposed disease model thanks to the changed fractional order. Compared to the previously built integer order model, the non-integer order derivative provided more efficient and flexible information about the complexity of the model's dynamics. © 2020