A theoretical analysis of a SEAIJR model of Spanish flu with fractional derivative

Abstract

A nonlinear system of ordinary differential equations comprised with six classes depicting the spread of the 1918–1920 Spanish flu has been considered in this work. Specific analysis including the well-poseness of the model, equilibrium points, stability analysis of equilibrium points have been presented. A Lyapunov analysis was presented also. Using the linear growth and the Lipschitz conditions, we established the conditions under which the model has a unique system of solutions. While the model was extended as the time derivative was converted to different fractional differential operators, a numerical scheme based on the Lagrange polynomial interpolation was used to solve numerically the obtained models and numerical simulations were performed for different values of fractional orders.

Keywords

• Fractional derivatives
• Fractional Lyapunov function
• Lagrange polynomial interpolation