Persistent Laplacian projected Omicron BA.4 and BA.5 to become new dominating variants.

Due to its high transmissibility, Omicron BA.1 ousted the Delta variant to become a dominating variant in late 2021 and was replaced by more transmissible Omicron BA.2 in March 2022. An important question is which new variants will dominate in the future. Topology-based deep learning models have had tremendous success in forecasting emerging variants in the past. However, topology is insensitive to homotopic shape evolution in virus-human protein-protein binding, which is crucial to viral evolution and transmission. This challenge is tackled with persistent Laplacian, which is able to capture both the topological change and homotopic shape evolution of data. Persistent Laplacian-based deep learning models are developed to systematically evaluate variant infectivity. Our comparative analysis of Alpha, Beta, Gamma, Delta, Lambda, Mu, and Omicron BA.1, BA.1.1, BA.2, BA.2.11, BA.2.12.1, BA.3, BA.4, and BA.5 unveils that Omicron BA.2.11, BA.2.12.1, BA.3, BA.4, and BA.5 are more contagious than BA.2. In particular, BA.4 and BA.5 are about 36% more infectious than BA.2 and are projected to become new dominant variants by natural selection. Moreover, the proposed models outperform the state-of-the-art methods on three major benchmark datasets for mutation-induced protein-protein binding free energy changes. Our key projection about BA4 and BA.5's dominance made on May 1, 2022 (see arXiv:2205.00532) became a reality in late June 2022.