A spatio-temporal individual-based network framework for West Nile virus in the USA: Spreading pattern of West Nile virus

Abstract

West Nile virus (WNV)-a mosquito-borne arbovirus-entered the USA through New York City in 1999 and spread to the contiguous USA within three years while transitioning from epidemic outbreaks to endemic transmission. The virus is transmitted by vector competent mosquitoes and maintained in the avian populations. WNV spatial distribution is mainly determined by the movement of residential and migratory avian populations. We developed an individual-level heterogeneous network framework across the USA with the goal of understanding the long-range spatial distribution of WNV. To this end, we proposed three distance dispersal kernels model: 1) exponential-short-range dispersal, 2) power-law-long-range dispersal in all directions, and 3) power-law biased by flyway direction -long-range dispersal only along established migratory routes. To select the appropriate dispersal kernel we used the human case data and adopted a model selection framework based on approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC). From estimated parameters, we find that the power-law biased by flyway direction kernel is the best kernel to fit WNV human case data, supporting the hypothesis of long-range WNV transmission is mainly along the migratory bird flyways. Through extensive simulation from 2014 to 2016, we proposed and tested hypothetical mitigation strategies and found that mosquito population reduction in the infected states and neighboring states is potentially cost-effective.

Fig 1. A simple caricature of the actual contact network for the avian population.

Here, A, B, C are three sub-networks. Solid lines represent intra-links in a sub-network and dashed lines represent inter-sub-network links.

Fig 2. Inter-links among sub-networks.

a) for exponential distance kernel, b) for power-law distance kernel, and c) for power-law distance kernel biased by flyway. Gray links represent undirected links and orange links represent directed links (for spring migration –northbound; for late summer/fall migration –southbound). Intra-links are not visible here. These are one realization of the stochastic networks, which are rescaled by 0.1 for better visualization.

Fig 3. Population of the marginal posterior distribution of the three models for the year 2015.

Model-1 represents exponential kernel, model-2 represents power-law kernel, and model-3 represents power-law influenced by flyway kernel. Here, Population-8 is the approximation of the final marginal posterior distribution of model parameter m and population 1-7 are intermediate distributions. Population-0 is the discrete uniform prior distribution, which is not shown here.

Fig 4. Histograms of the approximated posteriors distribution of parameters for power-law influenced by flyway kernel for the year 2015.

a) Network Parameter K; b) constant for transmission rate β₀; c) transition rate from exposed to infectious node λ, and d) human spillover η.

Fig 5. Absolute errors of the simulated human cases of 49 states by weeks with the observed data for the year 2015.

Mean of 1000 realizations has used as the simulated data. On the blue boxes, the red horizontal lines show the median and the bottom and top edges of the boxes indicate 25^th and 75^th percentile respectively. The whiskers show the ranges of data points not considered outliers and outliers are showing by red + symbol. Californian outliers are marked by black circles.

Fig 6. WNV human incidence by states for the year 2015 from power-law influenced by flyway kernel model (for K_pl = 2.3147, β₀ = 0.0059day^-1, λ = 0.0721day^-1, η = 0.4558day^-1), generated from 1000 simulation and observed data are indicated by blue colored star points.

States name are given in the short form. Simulated results are represented with a box plot in which the red horizontal lines show the median and the bottom and top edges of the boxes indicate 25^th and 75^th percentile respectively, The whiskers show the ranges of data points not considered outliers and outliers are showing by red + symbol. Broken scale is used for sake of visualization.

Fig 7. Disease prevalence map for WNV human incidence for the year 2015.

The darker regions imposed greater prevalence. States are divided into four groups by incidence number; group-1: more than 99, group-2: 50-99. group-3: 25-49, and group-4: less than 25 incidences. a) States are divided by the median of the output of 1000 simulations, b) states are divided by observed data.

Fig 8. Infected states for two types of mitigation strategies.

a) Dynamic infected places tracing; case-1: control measures are applied only in the infected states, case-2: control measures are applied in the infected states plus in their first neighboring states, case-3: control measures are applied in the infected places plus in their first and second neighboring states, and b) static ranked based strategy –states are ranked by; 1) temperature (Temp.), 2) avian population size (Pop.), 3) both(Temp & Pop.), then control measures are applied in the top 30% states. Log scale has used in x-axis for better visualization.

Fig 9. Number of states where control measures are applied for the infected places tracing mitigation strategy.

Log scale has used in x-axis for better visualization.