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Pattern of tick aggregation on mice: larger than expected distribution tail enhances the spread of tick-borne pathogens.

Ferreri L, Giacobini M, Bajardi P, Bertolotti L, Bolzoni L, Tagliapietra V, Rizzoli A, Rosà R - PLoS Comput. Biol. (2014)

Bottom Line: Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance.Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution.Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

View Article: PubMed Central - PubMed

Affiliation: Computational Epidemiology Group, Department of Veterinary Sciences, University of Torino, Torino, Italy; Applied Research on Computational Complex Systems Group, Department of Computer Science, University of Torino, Torino, Italy.

ABSTRACT
The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

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Estimated parameters of different distributions (NB on left and PL on right) obtained inside (blue) and outside (red) of the mice peak abundance time window.Time windows are defined by  (from left to right for each subsets). Vertical bars indicate best model fits (central horizontal lines) with their uncertainties that are  confidence interval for NB models while standard deviations for PL models.
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pcbi-1003931-g005: Estimated parameters of different distributions (NB on left and PL on right) obtained inside (blue) and outside (red) of the mice peak abundance time window.Time windows are defined by (from left to right for each subsets). Vertical bars indicate best model fits (central horizontal lines) with their uncertainties that are confidence interval for NB models while standard deviations for PL models.

Mentions: On the data sets classified as inside (IN) and outside (OUT) the time window of mice abundance peak, we fitted for different time-window lengths () the parameters and for NB distribution (Figure 5, left panels) and and for PL distribution (Figure 5, right panels). We observed a larger PL scaling parameter inside the mice abundance peak than outside (two-sample t-test output: for t-statistic = , df, ) indicating a larger heterogeneity in tick burden outside the abundance peak time. Moreover the GOF test indicated a rejection of the NB fit in both sets (IN and OUT) with . On the other hand, the GOF test with showed that the PL model cannot be ruled out in both sets (p-value>0.1) and the LLR test indicated that the PL fitting outperforms the NB model (p-value<0.05) in the estimates both inside and outside the peak time window.


Pattern of tick aggregation on mice: larger than expected distribution tail enhances the spread of tick-borne pathogens.

Ferreri L, Giacobini M, Bajardi P, Bertolotti L, Bolzoni L, Tagliapietra V, Rizzoli A, Rosà R - PLoS Comput. Biol. (2014)

Estimated parameters of different distributions (NB on left and PL on right) obtained inside (blue) and outside (red) of the mice peak abundance time window.Time windows are defined by  (from left to right for each subsets). Vertical bars indicate best model fits (central horizontal lines) with their uncertainties that are  confidence interval for NB models while standard deviations for PL models.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230730&req=5

pcbi-1003931-g005: Estimated parameters of different distributions (NB on left and PL on right) obtained inside (blue) and outside (red) of the mice peak abundance time window.Time windows are defined by (from left to right for each subsets). Vertical bars indicate best model fits (central horizontal lines) with their uncertainties that are confidence interval for NB models while standard deviations for PL models.
Mentions: On the data sets classified as inside (IN) and outside (OUT) the time window of mice abundance peak, we fitted for different time-window lengths () the parameters and for NB distribution (Figure 5, left panels) and and for PL distribution (Figure 5, right panels). We observed a larger PL scaling parameter inside the mice abundance peak than outside (two-sample t-test output: for t-statistic = , df, ) indicating a larger heterogeneity in tick burden outside the abundance peak time. Moreover the GOF test indicated a rejection of the NB fit in both sets (IN and OUT) with . On the other hand, the GOF test with showed that the PL model cannot be ruled out in both sets (p-value>0.1) and the LLR test indicated that the PL fitting outperforms the NB model (p-value<0.05) in the estimates both inside and outside the peak time window.

Bottom Line: Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance.Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution.Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

View Article: PubMed Central - PubMed

Affiliation: Computational Epidemiology Group, Department of Veterinary Sciences, University of Torino, Torino, Italy; Applied Research on Computational Complex Systems Group, Department of Computer Science, University of Torino, Torino, Italy.

ABSTRACT
The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

Show MeSH
Related in: MedlinePlus