Self-affinity and dengue fever

Dengue is a complex public health problem common in tropical and subtropical regions. This disease has risen substantially in the last three decades and the physical means depicts the self-affine behavior of the occurrences of reported cases of dengue in the state of Bahia-Brazil. This study uses Detrended Fluctuation Analysis (DFA) to verify the scale behavior in time series of cases of dengue and to evaluate the long-range correlations characterized by the power-law $\alpha $ exponent for different cities of the state of Bahia-Brazil. The scaling exponent ($\alpha $) presents different long-range correlations, i.e., uncorrelated, anti-persistent, persistent and diffusive behaviors. The long-range correlations highlighted a complex behavior of the time series of this disease. The findings show that there are two distinct kinds of scale behavior. The first one, the time series presents a persistent $\alpha$ exponent for a period of one month. Nevertheless, for large periods, the time series signal approaches of the subdiffusive behavior. The hypothesis of the long-range correlations in the time series of the occurrences of reported cases of dengue was validated. The observed self-affinity can be useful as forecasting tool in future periods through an extrapolation of the $\alpha $ exponent behavior. This complex system has a higher predictability in relatively short time (about one month) and it suggests a new tool in epidemiological control strategy. However, predictions for large periods using DFA are hidden by the subdiffusive behavior.