The Euler characteristic as a topological marker for outbreaks in vector-borne disease

Epidemic outbreaks represent a significant concern for the current state of global health, particularly in Brazil, the epicentre of several vector-borne disease outbreaks and where epidemic control is still a challenge for the scientific community. Data science techniques applied to epidemics are usually made via standard statistical and modelling approaches, which do not always lead to reliable predictions, especially when the data lacks a piece of reliable surveillance information needed for precise parameter estimation. In particular, dengue outbreaks reported over the past years raise concerns for global health care, and thus novel data-driven methods are necessary to predict the emergence of outbreaks. In this work, we propose a parameter-free approach based on geometric and topological techniques, which extracts geometrical and topological invariants as opposed to statistical summaries used in established methods. Specifically, our procedure generates a time-varying network from a time-series of new epidemic cases based on synthetic time-series and real dengue data across several districts of Recife, the fourth-largest urban area in Brazil. Subsequently, we use the Euler characteristic (EC) to extract key topological invariant of the epidemic time-varying network and we finally compared the results with the effective reproduction number (R t ) for each data set. Our results unveil a strong correlation between epidemic outbreaks and the EC. In fact, sudden changes in the EC curve preceding and/or during an epidemic period emerge as a warning sign for an outbreak in the synthetic data, the EC transitions occur close to the periods of epidemic transitions, which is also corroborated. In the real dengue data, where data is intrinsically noise, the EC seems to show a better sign-to-noise ratio once compared to R t . In analogy with later studies on noisy data by using EC in positron emission tomography scans, the EC estimates the number of regions with high connectivity in the epidemic network and thus has potential to be a signature of the emergence of an epidemic state. Our results open the door to the development of alternative/complementary topological and geometrical data-driven methods to characterise vector-borne disease outbreaks, specially when the conventional epidemic surveillance methods are not effective in a scenario of extreme noise and lack of robustness in the data.