A deterministic model for homologous antibody dependant enhancement on influenza infection

Antibody dependant enhancement refers that viral infectivity was unexpectedly enhanced at low antibody concentration compared to when antibodies were absent, such as Dengue, Zika and influenza virus. To mathematically describe switch from enhancement to neutralisation with increase of antibody concentration, one hyperbolic tangent variant is used as switching function in existed models. However, switching function with hyperbolic tangent contains four parameters, and does not always increase with antibody concentration. To address this problem, we proposed a monotonically increasing Logistical function variant as switching function, which only contains position parameter and magnitude parameter. Analysing influenza viral titre estimated from 21 focus reduction assay (FRA) datasets from neutralisation group (viral titre lower than negative control on all serial dilutions) and 20 FRA dataset from enhancement group (viral titre higher than negative control on high serial dilution), switching function with Logistic function performs better than existed model independent of both groups and exhibited different behaviour/character; specifically, magnitude parameter estimated from enhancement group is lower, but position parameter estimated from enhancement group is higher. A lower magnitude parameter refers that enhancement group more rapidly switches from enhancement to neutralisation with increase of antibody concentration, and a higher position parameter indicates that enhancement group provides a larger antibody concentration interval corresponding to enhancement. Integrating estimated neutralisation kinetics with viral replication, we demonstrated that antibody-induced bistable influenza kinetics exist independent of both groups. However, comparing with neutralisation group, enhancement group provides higher threshold value of antibody concentration corresponding to influenza infectivity. This explains the observed phenomenon that antibody dependent enhancement enhances susceptibility, severity, and mortality to influenza infection. On population level, antibody dependant enhancement can promote H1N1 and H3N2 influenza virus cooperate to sustain long-term circulation on human populations according to antigenic seniority theory.