Positivity and equilibrium in a fractional SIR model with Mittag-Leffler memory

Abstract

We present two slightly different constructions of a SIR model in which both the time taken to remove the individual from the infectious compartment and the infectivity have a memory according to Mittag-Leffler distributions. The second construction clearly points out where the proposed generalizations are acting, starting from the classic SIR model. Using integrodifferential techniques, we state and demonstrate novel analytically results on positivity, monotonicity in limiting case, and equilibrium points. The results are also verified numerically.

Keywords

• Fractional SIR model
• Mittag-Leffler functions
• positivity
• integrodifferential equations
• equilibrium