Sparse deep neural networks (DNNs) emerged as the result of search for networks with less storage and lower computational complexity. The sparse DNN inference is the task of using such trained DNN networks to classify a batch of input data. We propose an efficient, hybrid model- and data-parallel DNN inference using hypergraph models and partitioners. We exploit tiling and weak synchronization to increase cache reuse, hide load imbalance, and hide synchronisation costs. Finally, a blocking approach allows application of this new hybrid inference procedure for deep neural networks. We initially experiment using the hybrid tiled inference approach only, using the first five layers of networks from the IEEE HPEC 2019 Graph Challenge, and attain up to 2x speedup versus a data-parallel baseline.