Development, study, and comparison of models of cross-immunity to the influenza virus using statistical methods and machine learning.

INTRODUCTION: The World Health Organization considers the values of antibody titers in the hemagglutination inhibition assay as one of the most important criteria for assessing successful vaccination. Mathematical modeling of cross-immunity allows for identification on a real-time basis of new antigenic variants, which is of paramount importance for human health. MATERIALS AND METHODS: This study uses statistical methods and machine learning techniques from simple to complex: logistic regression model, random forest method, and gradient boosting. The calculations used the AAindex matrices in parallel to the Hamming distance. The calculations were carried out with different types and values of antigenic escape thresholds, on four data sets. The results were compared using common binary classification metrics. RESULTS: Significant differentiation is shown depending on the data sets used. The best results were demonstrated by all three models for the forecast autumn season of 2022, which were preliminary trained on the February season of the same year (Auroc 0.934; 0.958; 0.956, respectively). The lowest results were obtained for the entire forecast year 2023, they were set up on data from two seasons of 2022 (Aucroc 0.614; 0.658; 0.775). The dependence of the results on the types of thresholds used and their values turned out to be insignificant. The additional use of AAindex matrices did not significantly improve the results of the models without introducing significant deterioration. CONCLUSION: More complex models show better results. When developing cross-immunity models, testing on a variety of data sets is important to make strong claims about their prognostic robustness.

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

INTRODUCTION: 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. MATERIALS AND METHODS: 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. RESULTS: 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. CONCLUSION: The proposed method could serve as a useful tool for future forecasts, with further study to confirm its sustainability.