Pathway model report"
In qPRAentry: Quantitative Pest Risk Assessment at the Entry Step

knitr::opts_chunk$set(echo=FALSE, warning=FALSE, message=FALSE,
                      fig.pos = 'h',
                      fig.align = 'center',
                      fig.height = 3,
                      fig.width = 7)

nuts_yr <- params$nuts_yr # NUTS classification year
ntrade <- params$ntrade # Ntrade data
model_def <- params$model_def # model equation
param_names <- params$param_names # parameter names
n_iter <- params$n_iter # number of iterations
par_settings <- params$par_settings # Parameter distributions
dist_result <- params$dist_result # random values generated from the distributions
Ninf <- params$Ninf # Ninf results
Ninf_EU <- params$Ninf_EU # Ninf results total EU
NUTS_lev <- params$nuts_level #selected NUTS (depending on the Excel Ntrade file chosen)

# function to print the model equation on multiple lines
split_equation <- function(eq, width = 70) {
  parts <- strsplit(eq, "(?<=\\*|\\/|\\+|\\-)", perl = TRUE)[[1]]
  output <- ""
  line_length <- 0
  for (part in parts) {
    line_length <- line_length + nchar(part)
     if (grepl("\\*", part)) {
      part <- gsub("\\*", " \\\\cdot ", part)
    }
    if (line_length > width) {
      output <- paste0(output, part, " \\\\ ")
      line_length <- nchar(part)
    } else {
      output <- paste0(output, part, " ")
    }
  }
  return(output)
}

# width: width of the line
model_def_split <- split_equation(model_def, width=100)

Introduction

This report details the results of the pathway model analysis conducted using the Pathway model app of the \texttt{qPRAentry} package. It provides an estimation of the number of potential founder populations $(\mathit{NPFP})$ of a pest in different regions, using $N_{trade}$ data combined with additional user-defined parameters. The pathway model complexity can vary based on factors such as the specific pest under consideration and the availability of detailed data. As the approach used is based on the work of the European Food Safety Authority (EFSA), additional information can be found in the EFSA Guidance on quantitative pest risk assessment [@efsa2018guidance].

Pathway model

The defined pathway model and its corresponding parameters are presented below:

\begin{gather} r model_def_split \end{gather}

A total of r n_iter iterations were performed to randomly generate parameter values based on the specified distribution.

Parameter distributions:

tex_to_expr <- function(tex_str) {
  tex_str <- gsub("\\$", "", tex_str) 
  tex_str <- gsub("_\\{([^}]+)\\}", "[\\1]", tex_str) 
  tex_str <- gsub("_([[:alnum:]])", "[\\1]", tex_str)
  tex_str <- gsub("\\^\\{([^}]+)\\}", "^\\1", tex_str)
  tex_str <- gsub("\\^([[:alnum:]])", "^\\1", tex_str)

  parse(text = tex_str)[[1]]
}

par(mfrow = c(1, 2), mar = c(4, 3, 2, 1))

for (i in seq_along(param_names)) {
  par_name <- tex_to_expr(param_names[i])
  # Histogram
  hist(dist_result[[i]], 
       main = bquote(atop(.(par_name), .(par_settings[i]))),
       xlab = "",
       probability = TRUE, 
       breaks = "fd", 
       col = "lightblue",
       cex.main = 0.8,
       cex.lab = 0.8) 
  # Add a density line
  lines(density(dist_result[[i]]), col = "blue", lwd = 2)
}

$\mathit{NPFP}$ results

As a result of the pathway model the $\mathit{NPFP}$ is estimated for each NUTS r NUTS_lev level. The summary of the overall results for all the selected NUTS are shown below.

# Display the table
knitr::kable(Ninf_EU, 
             caption = "Table 1: Number of potential founder populations (NPFP) results for 
             all the selected NUTS", 
             digits = 4)

Based on the median NPFP, there would be 1 entry event in the whole territory every r round(1/Ninf_EU["Median"]) years (90% interval: r round(1/Ninf_EU["Q0.05"]) - r round(1/Ninf_EU["Q0.95"]) years).

The map below shows the median $\mathit{NPFP}$ values by NUTSr NUTS_lev.

plot_nuts(Ninf, "NUTS_ID", "Median", 
          nuts_level = NUTS_lev, nuts_year = nuts_yr,
          title = "NPFP Median", legend_title = "NPFP") +
   xlim(-20, 40) + ylim(35,70) +
   theme_bw()+
  theme(
     plot.title = element_text(size = 14),
     legend.title = element_text(size = 12)
   )