A fractional order SIR epidemic model for dengue transmission

In the present work, we study the fractional order differential equation of the dengue epidemic system based on the susceptible-infected-recuperated (SIR) model. The threshold quantity value R0 similar to the basic reproduction number is obtained using the next-generation matrix approach. The local stability of the disease-free equilibrium (DFE) point and endemic equilibrium point is presented. Using the linearization theorem, we achieved that DFE is locally asymptotically stable when R0 < 1 and is unstable when R0 > 1. When R0 > 1, the endemic equilibrium is locally asymptotically stable. Numerical simulations are given for different parameter setting of the order of derivative α. The proposed model is validated using published weekly dengue cases in Malaysia which were recorded in 2016. It is observed that the proposed model provides a more realistic way to understand the dynamic of dengue disease.