Generalising epidemic dynamics: Deriving a fractional SIR model

Abstract: 

This talk will show the derivation for the governing equations that describe the evolution of an SIR model for the spread of a disease in which the probability of recovering from the disease is a function of the time since infection. The derivation is based on a stochastic process, a continuous time random walk, describing the motion of individuals through SIR compartments. If the probability of recovering is power law distributed then the governing equations involve fractional-order derivatives. I will show that the fractional order recovery model is consistent with the general age-structured Kermack-McKendrick SIR model.