Risk assessment of travel-related spread of disease with epiflows

By Paula Moraga | September 10, 2018

In this post I show how to use the R package epiflows for risk assessment of travel-related spread of disease. Infectious diseases can spread beyond national borders. Residents of an infectious location can travel abroad and infect people living there. Also, travelers can acquire a disease while staying in a foreign country, and then seed new outbreaks in their home country after their return. The amount of disease spread will depend on factors such as the number of infected cases, population flows between locations, lengths of stay, and disease incubation and infectious periods. The epiflows package uses the mathematical model developed by Dorigatti et al. (2017) to integrate all these factors and calculate the mean number of infections that could be spread to other locations together with uncertainty measures. Here, I explain how to use epiflows to estimate the spread of yellow fever from Espirito Santo, Brazil, to other countries in the period December 2016 to May 2017. Details of the underlying model and other options of the package can be seen in Moraga et al. (2018).

Data

We use the data of yellow fever in Brazil that is contained in the epiflows package as data("Brazil_epiflows"). This data contains an object of class epiflows which has, for each location, the population, the number of disease cases, dates, and lengths of stay. Brazil_epiflows also contains the population flows between the Brazil states and other countries.

library(epiflows)
data("Brazil_epiflows")
Brazil_epiflows
## 
## /// Epidemiological Flows //
## 
##   // class: epiflows, epicontacts
##   // 15 locations; 100 flows; directed
##   // optional variables: pop_size, duration_stay, num_cases, first_date, last_date 
## 
##   // locations
## 
## # A tibble: 15 x 6
##    id               location_populati~ num_cases_time_wi~ first_date_cases
##  * <chr>                         <dbl>              <dbl> <fct>           
##  1 Espirito Santo             3973697.              2600. 2017-01-04      
##  2 Minas Gerais              20997560.              4870. 2016-12-19      
##  3 Rio de Janeiro            16635996.               170. 2017-02-19      
##  4 Sao Paulo                 44749699.               200. 2016-12-17      
##  5 Southeast Brazil          86356952.              7840. 2016-12-17      
##  6 Argentina                       NA                 NA  <NA>            
##  7 Chile                           NA                 NA  <NA>            
##  8 Germany                         NA                 NA  <NA>            
##  9 Italy                           NA                 NA  <NA>            
## 10 Paraguay                        NA                 NA  <NA>            
## 11 Portugal                        NA                 NA  <NA>            
## 12 Spain                           NA                 NA  <NA>            
## 13 United Kingdom                  NA                 NA  <NA>            
## 14 United States o~                NA                 NA  <NA>            
## 15 Uruguay                         NA                 NA  <NA>            
## # ... with 2 more variables: last_date_cases <fct>, length_of_stay <dbl>
## 
##   // flows
## 
## # A tibble: 100 x 3
##    from             to         n
##    <chr>            <chr>  <dbl>
##  1 Espirito Santo   Italy  2828.
##  2 Minas Gerais     Italy 15714.
##  3 Rio de Janeiro   Italy  8164.
##  4 Sao Paulo        Italy 34039.
##  5 Southeast Brazil Italy 76282.
##  6 Espirito Santo   Spain  3270.
##  7 Minas Gerais     Spain 18176.
##  8 Rio de Janeiro   Spain  9443.
##  9 Sao Paulo        Spain 39371.
## 10 Southeast Brazil Spain 88231.
## # ... with 90 more rows

Call estimate_risk_spread()

We can use the function estimate_risk_spread() to calculate the mean number of cases spread from the state Espirito Santo to other locations and the 95% confidence intervals. To call this function we need to specify the epiflows object (Brazil_epiflows), the code of the location ("Espirito Santo"), the functions of the disease incubation and infectious distributions, and the number of simulations.

set.seed(2018-07-25)
res <- estimate_risk_spread(Brazil_epiflows, 
                            location_code = "Espirito Santo",
                            r_incubation = function(n) rlnorm(n, 1.46, 0.35),
                            r_infectious = function(n) rnorm(n, 4.5, 1.5/1.96),
                            n_sim = 100000
                           )
res
##                          mean_cases lower_limit_95CI upper_limit_95CI
## Italy                     0.2233656        0.1520966        0.3078136
## Spain                     0.2255171        0.1537452        0.3126801
## Portugal                  0.2317019        0.1565528        0.3383112
## Germany                   0.1864162        0.1259548        0.2721890
## United Kingdom            0.1613418        0.1195261        0.2089475
## United States of America  0.9253419        0.6252207        1.3511047
## Argentina                 1.1283506        0.7623865        1.6475205
## Chile                     0.2648277        0.1789370        0.3866836
## Uruguay                   0.2408942        0.1627681        0.3517426
## Paraguay                  0.1619724        0.1213114        0.1926966

Results

The results object is a data frame containing the mean number of cases spread to each country and the lower and upper limits of the 95% confidence intervals. We can plot the results with the function ggplot() of the ggplot2 package as follows.

library(ggplot2)
res$location <- rownames(res)
ggplot(res, aes(x = mean_cases, y = location)) +
  geom_point(size = 2) +
  geom_errorbarh(aes(xmin = lower_limit_95CI, xmax = upper_limit_95CI), height = .25) +
  theme_bw(base_size = 12, base_family = "Helvetica") +
  ggtitle("Yellow Fever Spread from Espirito Santo, Brazil") +
  xlab("Number of cases") +
  xlim(c(0, NA))

Visualization of population flows

epiflows also incorporates functions to plot population flows between locations. There are three types of plots that can be produced:

  • Interactive map. This type of plot requires Brazil_epiflows to contain the coordinates of the locations. In this example the coordinates are in data frame YF_coordinates and can be added to Brazil_epiflows with the add_coordinates() function of epiflows.
data("YF_coordinates")
Brazil_epiflows <- add_coordinates(Brazil_epiflows, coordinates = YF_coordinates[, -1])

plot(Brazil_epiflows, type = "map")


  • Dynamic network with locations shown as nodes and connections between them representing population flows.
plot(Brazil_epiflows, type = "network")
  • Grid with population flows shown as points.
plot(Brazil_epiflows, type = "grid")

Conclusion

The epiflows package allows the identification of locations where diseases are most likely to spread. This information can help public health officials to limit the global spread of local outbreaks.

epiflows has been developed by several members of the R Epidemics Consortium (RECON). You can see the development version here. Please get in touch via GitHub issues if you have any comment, question or would like to contribute!

References

Moraga P, Dorigatti I, Kamvar ZN, Piatkowski P, Toikkanen SE, Nagraj VP, Donnelly CA and Jombart T. (2018), epiflows: an R package for risk assessment of travel-related spread of disease. F1000Research, 7:1374.

Dorigatti I, Hamlet A, Aguas R, Cattarino L, Cori A, Donnelly CA, Garske T, Imai N and Ferguson NM (2017), International risk of yellow fever spread from the ongoing outbreak in Brazil, December 2016 to May 2017. Euro Surveill. 22(28):pii=30572.



comments powered by Disqus