[Mathematical model for assessing the level of cross-immunity between strains of influenza virus subtype H₃N₂]

The WHO regularly updates influenza vaccine recommendations to maximize their match with circulating strains. Nevertheless, the effectiveness of the influenza A vaccine, specifically its H3N2 component, has been low for several seasons. The aim of the study is to develop a mathematical model of cross-immunity based on the array of published WHO hemagglutination inhibition assay (HAI) data.

In this study, a mathematical model was proposed, based on finding, using regression analysis, the dependence of HAI titers on substitutions in antigenic sites of sequences. The computer program we developed can process data (GISAID, NCBI, etc.) and create real-time databases according to the set tasks.

Based on our research, an additional antigenic site F was identified. The difference in 1.6 times the adjusted R2, on subsets of viruses grown in cell culture and grown in chicken embryos, demonstrates the validity of our decision to divide the original data array by passage histories. We have introduced the concept of a degree of homology between two arbitrary strains, which takes the value of a function depending on the Hamming distance, and it has been shown that the regression results significantly depend on the choice of function. The provided analysis showed that the most significant antigenic sites are A, B, and E. The obtained results on predicted HAI titers showed a good enough result, comparable to similar work by our colleagues.

The proposed method could serve as a useful tool for future forecasts, with further study to confirm its sustainability.