A renewal equation model for disease transmission dynamics with contact tracing

Contact tracing is one of the most cost-effective and widely adopted non-pharmaceutical interventions to counteract the spread of infectious diseases in the absence of effective treatments and vaccines. We propose a deterministic model for disease transmission dynamics, structured by time since infection, that includes diagnosis of symptomatic individuals and contact tracing. A mechanistic formulation of the processes at the individual level leads to an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. Using parameters from SARS-CoV-2, we show how the model can give information on the parameter combinations for diagnosis of symptomatic infections and contact tracing that allow to attain control, and by means of numerical simulations we investigate the effect of a temporary interruption of contact tracing in the presence of limited tracing resources.

Joint work [1] with Lorenzo Pellis (U. Manchester, UK), Nicholas H. Ogden (Public Health Agency of Canada) and Jianhong Wu (York U., Toronto, Canada).

This seminar is part of the UMI-MSE Online Seminars on Advances in Socio-Epidemic Mathematical Modelling (more information).