Uniform boundedness of the attractor in H2 of a non-autonomous epidemiological system

In this paper, we prove the uniform boundedness of the pullback attractor of a non-autonomous SIR (susceptible, infected, recovered) model from epidemiology considered in Anguiano and Kloeden [M. Anguiano, P.E. Kloeden, Asymptotic behavior of the nonautonomous SIR equations with diffusion, Communications on Pure and Applied Analysis 13 No. 1 (2014) 157-173]. We prove two uniform boundedness of this pullback attractor, firstly in the norm H1 0, and later, under appropriate additional assumptions, in the norm H2.