Epidemic dynamics with time-varying transmission risk reveal the role of disease stage-dependent infectiousness

Abstract

A key characteristic of acute communicable diseases is the infectiousness that varies over time as the infection dynamics evolve within a host, which influences the risk of transmission in different stages of the disease. Despite the evidence of time-varying transmission risk, most dynamic models of epidemics assume a constant transmission rate during the infectious period. Recent work has shown the difference in epidemic dynamics when this assumption is relaxed and different transmission rates are used by discretizing the infectious period into multiple sub-periods. Here, we develop an age-structured model to integrate a continuous time-varying transmission risk, based on an established correlation between the viral dynamics and infectiousness profile. Taking into account the natural history and parameter estimates of COVID-19 caused by the original strain of SARS-CoV-2, we demonstrate the difference in temporal epidemic dynamics when a continuous time-varying transmission probability is used as compared to multiple constant transmission probabilities. Our results show a significant difference between the incidence curves in terms of the magnitude and peak time, even when the reproduction number and total number of infections are the same for continuous and discrete transmission probabilities. Finally, we demonstrate the spurious outcome of preventing an epidemic through the isolation of infectious individuals when constant transmission probabilities are used, highlighting the importance of integrating a continuous time-dependent transmission parameter in dynamic models. These findings suggest a more cautious interpretation of model outcomes, especially those that are intended to evaluate the effectiveness of interventions and inform policy decisions for disease mitigation strategies.

Keywords: Disease modelling; Infectiousness; Transmissibility; Viral dynamics.