Modeling the impact of temperature on fractional order dengue model with vertical transmission

A dengue epidemic model with fractional order derivative is formulated to investigate the effect of temperature on the spread of the vector-host transmitted dengue disease. The model consists of system of fractional order differential equations formulated within Caputo fractional operator. The stability of the equilibrium points of the considered dengue model is studied. The corresponding basic reproduction number R_0 is derived and it is proved that if R_0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1 method is applied to solve the dengue model numerically. Finally, numerical simulations are also presented to illustrate the analytical results showing the influence of the temperature on the dynamics of the vector-host interaction in dengue epidemics.