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 (R0) 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.

The authors have declared no competing interest.

MLS was funded by the Institute for Global Pandemic Planning (IGPP), Warwick Medical School, University of Warwick, UK.

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

Yes

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

Yes

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

Yes

I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

Yes