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

Abstract

A dengue epidemic model with fractional order derivative is formulated to an-alyze the effect of temperature on the spread of the vector-host transmitteddengue disease. The model is composed of a system of fractional order differ-ential equations formulated within Caputo fractional operator. The stabilityof the equilibrium points of the considered dengue model is studied. The cor-responding basic reproduction number R 0 is derived and it is proved that ifR 0 < 1, the disease-free equilibrium (DFE) is locally asymptotically stable. L1method is applied to solve the dengue model numerically. Finally, numericalsimulations are also presented to illustrate the analytical results showing thein uence of the temperature on the dynamics of the vector-host interaction indengue epidemics.