A Predictive Spatial Model to Quantify the Risk of Air-Travel-Associated Dengue Importation into the United States and Europe

Table 1

Problem Notation.

𝑁𝑈	Subset of susceptible nodes in the United States
𝑁𝐸	Subset of susceptible nodes in Europe
𝑁	Complete set of susceptible nodes (𝑁𝑈⋃𝑁𝐸)
𝐺	Set of nodes in the endemic region
𝐼𝑖	Number of reported infections at node 𝑖
𝑃𝑖	Total number of predicted infections at node 𝑖
𝑃𝑗𝑖	Number of predicted infections at node 𝑖 attributed to node 𝑗
𝜆	Vector of parameter to be optimized
𝑥𝑗	Vector of characteristics of infecting node 𝑗
𝑦𝑖	Vector of characteristics of susceptible node 𝑖
𝑧𝑗𝑖	Vector if parameters specific to link (𝑗,𝑖)
𝑉^𝑗𝑖	Normalized passenger air travel volume between nodes 𝑗 and 𝑖, ranging from 0 to 1
𝑆𝑖	Climate suitability of node 𝑖, ranging from 0 to 1
𝐼^𝑖	Normalized reported infections at node 𝑖
𝐷^𝑗𝑖	Normalized distance between nodes 𝑗 and 𝑖, ranging from 0 to 1
𝐴(𝑖)	Set of endemic nodes adjacent to susceptible node 𝑖
𝛼,𝑏	Parameters to be optimize