This paper proposes and estimates a new Two-Sector One-Agent model that features large shocks. The resulting medium-scale New Keynesian model includes the standard real and nominal frictions used in the empirical literature and allows for heterogeneous COVID-19 pandemic exposure across sectors. We solve the model nonlinearly and we propose a new nonlinear, non-Gaussian filter designed to handle large pandemic shocks to make inference feasible. Monte Carlo experiments show that it correctly identifies the source and time location of shocks with a massively reduced running time, making the estimation of macro-models with disaster shocks feasible. The estimation is carried out using the Sequential Monte Carlo sampler recently proposed by Herbst and Schorfheide (2014). Our empirical results show that the pandemic-induced economic downturn can be reconciled with a combination of large demand and supply shocks. More precisely, starting from the second quarter of 2020, the model detects the occurrence of a large negative demand shock in consuming all kinds of goods, together with a large negative demand shock in consuming contact-intensive products. On the supply side, our proposed method detects a large labor supply shock to the general sector and a large labor productivity shock in the pandemic-sensitive sector.