A non-integer order dengue internal transmission model

Abstract

A non-linear mathematical model with non-integer order γ, 0 < γ≤ 1 , is used to analyze the dengue virus transmission in the human body. Both disease-free F0 and endemic F∗ equilibria are calculated. Their stability is also described using the stability theorem of non-integer order. The threshold parameter R0 demonstrates an important behavior in the stability of a considerable model. For R0< 1 , the disease-free equilibrium (DFE) F0 is an attractor. For R0> 1 , F0 is not stable, the endemic equilibrium (EE) F∗ exists, and it is an attractor. Numerical examples of the proposed model are also proven to study the behavior of the system.