Risk mapping for COVID-19 outbreaks in Australia using mobility data.

COVID-19 is highly transmissible and containing outbreaks requires a rapid and effective response. Because infection may be spread by people who are pre-symptomatic or asymptomatic, substantial undetected transmission is likely to occur before clinical cases are diagnosed. Thus, when outbreaks occur there is a need to anticipate which populations and locations are at heightened risk of exposure. In this work, we evaluate the utility of aggregate human mobility data for estimating the geographical distribution of transmission risk. We present a simple procedure for producing spatial transmission risk assessments from near-real-time population mobility data. We validate our estimates against three well-documented COVID-19 outbreaks in Australia. Two of these were well-defined transmission clusters and one was a community transmission scenario. Our results indicate that mobility data can be a good predictor of geographical patterns of exposure risk from transmission centres, particularly in outbreaks involving workplaces or other environments associated with habitual travel patterns. For community transmission scenarios, our results demonstrate that mobility data add the most value to risk predictions when case counts are low and spatially clustered. Our method could assist health systems in the allocation of testing resources, and potentially guide the implementation of geographically targeted restrictions on movement and social interaction.

The distribution of the time taken for an epidemic to spread between two communities.

Assessing the risk of disease spread between communities is important in our highly connected modern world. However, the impact of disease- and population-specific factors on the time taken for an epidemic to spread between communities, as well as the impact of stochastic disease dynamics on this spreading time, are not well understood. In this study, we model the spread of an acute infection between two communities ('patches') using a susceptible-infectious-removed (SIR) metapopulation model. We develop approximations to efficiently evaluate the probability of a major outbreak in a second patch given disease introduction in a source patch, and the distribution of the time taken for this to occur. We use these approximations to assess how interventions, which either control disease spread within a patch or decrease the travel rate between patches, change the spreading probability and median spreading time. We find that decreasing the basic reproduction number in the source patch is the most effective way of both decreasing the spreading probability, and delaying epidemic spread to the second patch should this occur. Moreover, we show that the qualitative effects of interventions are the same regardless of the approximations used to evaluate the spreading time distribution, but for some regions in parameter space, quantitative findings depend upon the approximations used. Importantly, if we neglect the possibility that an intervention prevents a large outbreak in the source patch altogether, then intervention effectiveness is not estimated accurately.

Estimating the basic reproductive number during the early stages of an emerging epidemic.

A novel outbreak will generally not be detected until such a time that it has become established. When such an outbreak is detected, public health officials must determine the potential of the outbreak, for which the basic reproductive numberR0 is an important factor. However, it is often the case that the resulting estimate of R0 is positively-biased for a number of reasons. One commonly overlooked reason is that the outbreak was not detected until such a time that it had become established, and therefore did not experience initial fade out. We propose a method which accounts for this bias by conditioning the underlying epidemic model on becoming established and demonstrate that this approach leads to a less-biased estimate of R0 during the early stages of an outbreak. We also present a computationally-efficient approximation scheme which is suitable for large data sets in which the number of notified cases is large. This methodology is applied to an outbreak of pandemic influenza in Western Australia, recorded in 2009.

Hybrid Markov chain models of S-I-R disease dynamics.

Deterministic epidemic models are attractive due to their compact nature, allowing substantial complexity with computational efficiency. This partly explains their dominance in epidemic modelling. However, the small numbers of infectious individuals at early and late stages of an epidemic, in combination with the stochastic nature of transmission and recovery events, are critically important to understanding disease dynamics. This motivates the use of a stochastic model, with continuous-time Markov chains being a popular choice. Unfortunately, even the simplest Markovian S-I-R model-the so-called general stochastic epidemic-has a state space of order [Formula: see text], where N is the number of individuals in the population, and hence computational limits are quickly reached. Here we introduce a hybrid Markov chain epidemic model, which maintains the stochastic and discrete dynamics of the Markov chain in regions of the state space where they are of most importance, and uses an approximate model-namely a deterministic or a diffusion model-in the remainder of the state space. We discuss the evaluation, efficiency and accuracy of this hybrid model when approximating the distribution of the duration of the epidemic and the distribution of the final size of the epidemic. We demonstrate that the computational complexity is [Formula: see text] and that under suitable conditions our approximations are highly accurate.