Quantifying infectious disease epidemic risks: A practical approach for seasonal pathogens
Authors: Kaye AR , Guzzetta G , Tildesley MJ , Thompson RN 
Published: August 2024

For many infectious diseases, the risk of outbreaks varies seasonally. If a pathogen is usually absent from a host population, a key public health policy question is whether the pathogen’s arrival will initiate local transmission, which depends on the season in which arrival occurs. This question can be addressed by estimating the “probability of a major outbreak” (the probability that introduced cases will initiate sustained local transmission). A standard approach for inferring this probability exists for seasonal pathogens (involving calculating the Case Epidemic Risk; CER) based on the mathematical theory of branching processes. Under that theory, the probability of pathogen extinction is estimated, neglecting depletion of susceptible individuals. The CER is then one minus the extinction probability. However, as we show, if transmission cannot occur for long periods of the year (e.g., over winter or over summer), the pathogen will inevitably go extinct, leading to a CER of zero even if seasonal outbreaks can occur. This renders the CER uninformative in those scenarios. We therefore devise an alternative approach for inferring outbreak risks for seasonal pathogens (involving calculating the Threshold Epidemic Risk; TER). Estimation of the TER involves calculating the probability that introduced cases will initiate a local outbreak in which a threshold number of infections is exceeded before outbreak extinction. For simple seasonal epidemic models, such as the stochastic Susceptible-Infectious-Removed model, the TER can be calculated numerically (without model simulations). For more complex models, such as stochastic host-vector models, the TER can be estimated using model simulations. We demonstrate the application of our approach by considering Chikungunya virus in northern Italy as a case study. In that context, transmission is most likely in summer, when environmental conditions promote vector abundance. We show that the TER provides more useful assessments of outbreak risks than the CER, enabling practically relevant risk quantification for seasonal pathogens.

Author Summary

Invasive pathogens pose a challenge to human health, particularly as outbreak risks for some infectious diseases are being exacerbated by climate change. For example, the occurrence of seasonal vector-borne disease outbreaks in mainland Europe is increasing, even though pathogens like the Chikungunya and dengue viruses are not normally present there. In this changing landscape, assessing the risk posed by invasive pathogens requires computational methods for estimating the probability that introduced cases will lead to a local outbreak, as opposed to the first few cases fading out without causing a local outbreak. In this article, we therefore provide a computational framework for estimating the risk that introduced cases will lead to a local outbreak in which a pre-specified, context specific threshold number of cases is exceeded (we term this risk the “Threshold Epidemic Risk”, or TER). Since even small seasonal outbreaks can have negative impacts on local populations, we demonstrate that calculation of the TER provides more appropriate estimates of local outbreak risks than those inferred using standard methods. Going forwards, our computational modelling framework can be used to assess outbreak risks for a wide range of seasonal diseases.