H2H2-boundedness of the pullback attractor for the non-autonomous SIR equations with diffusion

We prove some regularity results for the pullback attractor of a non-autonomous SIR model with diffusion in a bounded domain ΩΩ of RdRd where d≥1d≥1. We show a regularity result for the unique solution of the problem. We establish a general result about H2(Ω)3H2(Ω)3-boundedness of invariant sets for the associate evolution process. Then, as a consequence, we deduce that the pullback attractor of the non-autonomous system of SIR equations with diffusion is bounded in H2(Ω)3H2(Ω)3.