Dynamics and Analysis of Dengue Epidemics: A Fractional Order SIR Model with Next-Generation Matrix Methodology

One of the major infectious diseases in the world is dengue. Dengue fever, a mosquito-borne viral infection, continues to pose a significant public health threat in tropical and subtropical countries. In this article, we analyze the susceptible-infected-recuperated (SIR) model-based fractional order differential equation of the dengue epidemic system and we analyze of fractional model for the dengue transmission utilizing the new term Human hospitalized. The next-generation matrix methodology is used to obtain the threshold quantity value $R_{0}$, which is comparable to the essential reproduction value. In the case of constant controls, we evaluate the presence and consistency of the disease-free and infectious equilibrium simulation alternatives. The disease-free equilibrium (DFE) point and the endemic equilibrium point's local stability are discussed. We were able to determine that DFE is locally asymptotically stable when $R_{0}<1$ and unstable when $R_{0}>1$ by applying the linearization theorem. Numerical simulations are conducted to validate the proposed model against real-world dengue data. For various parameter values of the derivative $\alpha$ order, numerical simulations are provided. The proposed model is validated using published every year (390 millions) dengue cases are reported in world wide. The presented model, it is noted, offers a more accurate means of analyzing the dynamics of the disease dengue. 2010 MSC: 26A33, 34K37.