Heterogeneity in susceptibility and connectivity for epidemic models - Mr Tarek Alrefae (International Journal of Infectious Diseases)
Introduction: Mathematical modelling of infectious diseases lies on a complexity spectrum. On one end are agent-based models (ABMs), whose ability to incorporate realistic heterogeneities is theoretically unbounded. On the other end are compartmental SIR-like models, where heterogeneity is sacrificed for analytic tractability. The time pressure associated with modelling an outbreak in real-time currently forces the modeller to forgo ABMs and their heterogeneities, which are known to significantly lower the herd immunity threshold (HIT), attack rate, and other relevant epidemiological metrics of interest (Montalban 2022). We investigate and compare the effect of including population-level heterogeneities in both susceptibility and connectivity across two different model structures (an ODE-based SIR-like model and a network model). Methods: We extend previous work (Gomes 2022) by considering distributions for these two sources of heterogeneity other than gamma, and showcase the relation between the distribution choice and HITs/attack rates. We then construct an age-dependent network model of SARS-CoV-2 spread in England between March-July 2020. This network model leverages the flexibility of its architecture by incorporating age-dependent infectivity profiles based on laboratory investigations of culture probability. Results: We verify that model choice has a direct effect on the HIT and attack rate, even in the context of the same outbreak. The model outputs in either case are very sensitive to the coefficient of variation (CV) of the distribution of the relevant source of heterogeneity, exhibiting statistically significant deviations in behaviour even for relatively low levels of heterogeneity (i.e. for low CV levels). The rate at which susceptibles are consumed (in the case of heterogeneous susceptibility) and the rate at which connections are made and lost (in the heterogeneous connectivity case) are also explored as key factors in determining the outcome of an outbreak. Discussion: We demonstrate that even very low levels of population heterogeneity (0 < CV < 1) produce strikingly different epidemic trajectories across two sources of heterogeneity and two common model structures. The role of CV in characterising the magnitude of this disparity is interesting and ripe for further analytical investigation. Our empirical investigation via our heterogeneous network model, when calibrated to real-world activity and contact structure validates our approach. Our results could be enhanced by considering other population structures (in particular, with different age structures) and extending our framework to account for the undeniable effects of viral variants and vaccination. Conclusion: We quantify the role that heterogeneity plays in two important dimensions (susceptibility and connectivity) in both ODE and network models and show that even low heterogeneity levels produce significantly different epidemic trajectories. These results suggest that the predictive power of epidemic models could be greatly improved, eventually helping scientists, public health experts, and governments make more informed decisions regarding interventions and epidemic prevention strategies.