West Nile virus transmission and human infection risk in Veneto (Italy): a modelling analysis

An intensified and continuous West Nile virus (WNV) spread across northern Italy has been observed since 2008, which caused more than one hundred reported human infections until 2016. Veneto is one of the Italian regions where WNV is considered endemic, and the greatest intensity of circulation was observed during 2013 and 2016. By using entomological data collected across the region in those years, we calibrated a temperature-driven mathematical model through a Bayesian approach that simulates the WNV infection in an avian population with seasonal demography. We considered two alternative routes of life cycle re-activation of the virus at the beginning of each vector breeding season: in the first one the virus is maintained by infected birds, in the other by diapausing mosquitoes previously infected. Afterwards, we computed seasonal risk curves for human infection and quantified how they translate into reported symptomatic cases. According to our results, WNV is more likely to be re-activated each year via previously infected mosquitoes. The highest probability of human infection is expected to occur in August, consistently with observations. Our epidemiological estimates can be of particular interest for public health authorities, to support decisions in term of designing efficient surveillance plans and preventive measures.


Supplementary Figure S2. Interpolated mosquito abundance (M(t)) for an average trapped area
A of the considered cluster (in red in Figure 1 in the main text). Red lines: interpolated mosquito abundance. Black dots: observed average weekly captures rescaled by the capture rate α.

Additional methods
In this section, we provide additional details on the model and its temperature-dependent functions.

Model equations
The model flow depicted in Figure 2 in the main text is a visual description of the following set of equations: Where BT is the total avian population and Ba is the number of adult birds. All parameters are described in Table 1 in the main text.

Mosquito death rate (μM)
The mortality rate of adult female mosquitoes has been taken as the function of temperature suggested in [2], multiplied by the average increase factor found in [3].

Probability of WNV transmission from bird to vector (pBM)
In [4] the authors compute this rate for three different temperatures, namely 18, 23 and 28°C. We modeled this probability as a function of temperature following the approach presented in [3]. As shown in Figure S3, our proposed function fits well the observed values.
Supplementary Figure S3. Probability of WNV transmission from bird to vector (pBM). Orange dots: observed laboratory data [4].

Predicted seroprevalence
From Figure S4

Human fit without model
For each week w, there are pw positive pools out of nw analyzed, with an average size (number of mosquitoes per pool) mw. By dividing pw/nw/mw we can obtain an average WNV prevalence δW in the mosquito population for week w, together with 95%CI by performing a binomial test. Similarly to the procedure presented in the main text, we predicted the number of reported WNV human infections Nw from a Poisson(R•ρ•δW•M(w)), where R is the ratio between the cluster area and trapped area A, M(w) is the average interpolated weekly mosquito abundance, δW is the mosquito prevalence drawn from the distributions computed as explained previously and ρ is a free rescaling parameter, estimated with a MCMC approach applied to the Poisson likelihood of observing the recorded infections, given the model predictions, by modelling simultaneously the two considered years. In this case, we can interpret ρ as a product of the mosquito biting rate on humans, the probability of virus transmission to humans per infectious bite, the probability of symptoms development and the reporting rate.
As shown in Figure S5, this simpler modelling approach fits very poorly the observed data. In particular, it overestimates the number of infections at the beginning of the season. Its associated DIC value is 93.7, which is much higher than the ones shown in Table 3.
Supplementary Figure S5 ) where ̅ is the parameter average value as reported in Table 1 in the main text. For instance, to assess if different pMB values might affect our results, we run 100 samplings from N(0.94, 0.094 2 ) and, for each extracted parameter value, we fitted the observed data with models B and M by MCMC, as explained in the main text, and subsequently rerun the simulations to investigate whether such parameter perturbations affected substantially the predicted avian and vector prevalences.
As shown in Figures S6-S8, changes in the parameters in Ω do not substantially alter the estimated prevalence for both populations. In particular, we can note that the temporal dynamics is not varied whereas the magnitude might change slightly. Overall, such plots are comparable to the ones presented in the main text ( Figure 3). For instance, the median of the 5% credible interval of the 2013 mosquito population is, at its peak, between 2.7 and 3.5•10 -3 when the bird susceptibility pMB is changed (first line and column of Figure S7), similarly to what is reported in panel C in Figure 3 in the main text (lower boundary of the shaded area). From Tables S2 and S3 we can note that the estimated distributions of the free model parameters are usually uncorrelated with the perturbed parameters, except for few cases when, although significant (p-value<0.05), the correlation coefficient is often lower than 0.3. The biting rate is more sensitive to changes in the parameters in Ω: for instance, higher avian fertility rates are associated to higher average estimated biting rates.
Overall, from Figures S9 and S10 it is clear that changes in the parameters in Ω do not produce substantial differences in the average estimated parameters with respect to the values presented in Table 2 in the main text. In addition, from Figure S10 we can note that model M usually fits worse than model B (empty dots) when the estimated average initial avian densities (B0(2013), B0(2016)) and biting rate (b) lie out of the cluster that includes the most frequent parameter estimations.
Finally, we can conclude that changes in the model constant parameters produce very small variations in model simulations. Moreover, such variations do not alter substantially the estimated values for the free parameters.
Model M usually outscores model B and we can remark that, when assuming WNV is re-activated with infectious birds (blue lines of the last two columns in Figures S6-S8), the highest avian prevalence is always predicted to occur in spring, contrary to observation.  Supplementary Table S3