Assessment of climate change impact on the malaria vector Anopheles hyrcanus, West Nile disease, and incidence of melanoma in the Vojvodina Province (Serbia) using data from a regional climate model

the highest value of the KC spectrum (KCM)], and sample entropy (SE) [31] were used to quantify the regularity and complexity of air temperature and precipitation time series, obtained by the EBU-POM model, representing both deterministic chaos and stochastic pro- cesses. We considered the complexity of the EBU-POM model using the observed and mod- elled time series of temperature and precipitation. We computed the KC spectrum, KC, KCM and SE values for temperature and precipitation. The calculations were performed for the entire time interval 1961–1990: (i) on a daily basis with a size of n = 10,958 samples for temper- ature and (ii) on a monthly basis with a size n = 360 for the precipitation. The simulated time series of temperature and precipitation were obtained by the EBU-POM model for the given period. The observed time series of temperature and precipitations for two stations: Sombor (SO) (88 m.a.s.l.) and Novi Sad (NS) (84 m.a.s.l.) in the considered area, were taken from daily meteorological reports of the Republic Hydrometeorological Service of Serbia. For both sites, the modelled complexity is lower than the observed one, but with the reliability which is in the interval values allowed by the information measures (KC, KCM, and SE) [32,33,34]. The term model reliability we have used in the following context. The Lyapunov exponent (LLE) relates to the predictability of measured time series, which includes deterministic chaos as an inherent component. Model predictability is here understood as the degree to which a correct predic-

tion of a system’s state can be made either qualitatively or quantitatively. In a stochastic analy- sis, a random process is considered predictable if it is possible to infer the next state from previous observations. In many models, however, randomness is a phenomenon which “spoils” predictability [35]. Deterministic chaos does not mechanically denote total predict- ability but means that at least it improves the prognostic power. In contrast, stochastic trajecto- ries cannot be projected into the future. If LLE>1 then time series is not chaotic, but is rather stochastic, and predictions cannot be based on chaos theory. However, if 0<LLE<1 it indicates the existence of chaos in time series. In that case, one can compute the approximate time [often called Lyapunov time (LT)] limit for which accurate prediction for a chaotic system is a function of LLE. It designates a period when a specific process (physical, mechanical, hydro- logical, quantum, or even biological) moves beyond the bounds of precise (or probabilistic) predictability and enters a chaotic mode. According to Frison and Abarbanel [36] that time can be calculated as LLE Δtlyap = 1/LLE. If LLE!0, implying that Δtlyap!1, then long-term accurate predictions are possible. However, many climate time series are highly complex. Therefore, Δtlyap can be corrected for randomness in the following way. Similar to Δtlyap we can introduce a randomness time Δtrand = 1/KC (in time units, second, hour or day). Hence- forth, we shall denote this quantity Kolmogorov time (KT), as it quantifies the period beyond

which randomness significantly influences predictability. Then, the Lyapunov time corrected for randomness is defined as [0,Δtlyap]\[0,Δtrand]. It can be stated that the KT designates the size of the time window within time series where complexity remains nearly unchanged. These findings mean that the models with a KC (and KCM) complexity lower than the measured time series complexity cannot always reconstruct some of the structures contained in the observed data. However, it does not mean that outputs from EBU-POM model do not cor- rectly simulate climate elements since both sites’ values indicate the absence of stochastic influ- ences, providing reliable projections of the climate elements [37]. Therefore, the EBU-POM model can be considered as a model having high performances and reliability in projection of temperature and precipitation, two of the most important elements used in different climate research. For An. hyrcanus, the temperature trend was evaluated by the Mann-Kendall test using the R statistical package [38]. Field observed values on species distribution and density for the period 1985–2015 and forecasts of the numbers of sites invaded and specimens sampled for the period 2016–2030 based on linear trends were obtained by the Eviews 9.5 software [39]. Impact of climate change on malaria vector, West Nile disease, and incidence of melanoma PLOS ONE | https://doi.org/10.1371/journal.pone.0227679 January 15, 2020 7 / 17