Analysis of an age structured SIR epidemic model with fractional Caputo derivative

In this paper, we consider a mathematical model with fractional derivatives in the sense of Caputo with respect to time. It describes the spread of an infectious disease that is directly transmitted in an age-structured population and whose transmission coefficient varies with age. We formulate the basic model as an abstract fractional Cauchy problem on a Banach space to prove the existence, and uniqueness of a local mild solution and ensure the global existence of a solution. Moreover, the results for the existence and uniqueness of non-trivial steady states are also demonstrated under the appropriate conditions.