O'Dea, E. B. | bioRxiv Science

bioRxiv2018

Estimating the distance to an epidemic threshold

The epidemic threshold of the susceptible-infected-recovered (SIR) model is a boundary separating parameters that can permit epidemics from those that cannot. This threshold corresponds to points where the stability of the systems equilibrium reaches zero. Consequently, we use the average rate at which deviations from the equilibrium shrink to define a distance to this threshold. However, the vital dynamics of the host population may occur slowly even when transmission is far from threshold levels. Here we show analytically how such slow dynamics can prevent estimation of the distance to the threshold for some individual variables of the model. Although these results are exact only in the limit of long-term observation of a large system, we find that they still provide useful insight into the behaviour of estimates from simulations with a range of population sizes, environmental noise, and observation schemes. Having established some guidelines about when estimates are accurate, we then illustrate how multiple distance estimates can be used to estimate the rate of approach to the threshold. The estimation approach is general and may be applicable to zoonotic pathogens such as MERS-CoV as well as vaccine-preventable diseases such as measles.

epidemiology↗

bioRxiv2017

Disentangling reporting and disease transmission using second order statistics

Second order statistics such as the variance and autocorrelation can be useful indicators of the stability of randomly perturbed systems, in some cases providing early warning of an impending, dramatic change in the systems dynamics. One specific application area of interest is the surveillance of infectious diseases. In the context of disease (re-)emergence, a goal could be to have an indicator that is informative of whether the system is approaching the epidemic threshold, a point beyond which a major outbreak becomes possible. Prior work in this area has provided some proof of this principle but has not analytically treated the effect of imperfect observation on the behavior of indicators. This work provides expected values for several moments of the number of reported cases, where reported cases follow a binomial or negative binomial distribution with a mean based on the number of deaths in a birth-death-immigration process over some reporting interval. The normalized second factorial moment and the decay time of the number of case reports are two indicators that are insensitive to the reporting probability. Simulation is used to show how this insensitivity could be used to distinguish a trend of increased reporting from a trend of increased transmission. The simulation study also illustrates both the high variance of estimates and the possibility of reducing the variance by avE. ODea eraging over an ensemble of estimates from multiple time series.

epidemiology↗