Modelling Semi-Random Human Mixing: A Modified Force of Infection in Population-level Epidemic Modelling

Mathematical modelling can help inform public health policies; however, the assumptions about mixing impact results. Classical models typically assume everyone has an equal likelihood of interacting with everyone else, whereas in reality, people more frequently interact within smaller clusters, such as households, schools, or workplaces. In this study, we propose the Semi-Random Mixing (SeRaMix) approach based on network connectivity, where individuals have localised interactions with sparse external links. We derive an equation-based SeRaMix model (SeRaMix-EBM) with a modified force-of-infection function that preserves mathematical tractability while capturing more realistic mixing patterns. We derive its basic reproduction number ( ℛ ₀ ) and, using numerical simulation, examine how cluster size and external connections shape outbreak dynamics compared to the classical approach. We validated the results of our SeRaMix-EBM against the stochastic, individual-based model (IBM) simulations. The results show that the SeRaMix-EBM is a good approximation for the IBM, but with much less computational complexity. Model simulations show that the predicted impact of interventions can be different between the classical and SeRaMix-EBM, depending on what type of intervention is considered. These findings indicate that semi-random mixing should be considered when creating models to inform policy, particularly for predicting outbreaks and the impact of non-pharmaceutical interventions.