swash-package: Implementation of the Swash-Backwash Model for the Single...

In swash: Swash-Backwash Model for the Single Epidemic Wave

Implementation of the Swash-Backwash Model for the Single Epidemic Wave and additional functions in R

Description

Swash-Backwash Model for the single epidemic wave (Cliff and Haggett 2006) with additional functions for bootstrap confidence intervals and data management; other functions for spatio-temporal analysis and modeling of infectious diseases

Details

The Swash-Backwash Model (SBM) for the Single Epidemic Wave is the spatial equivalent of the classic epidemiological SIR (Susceptible-Infected-Recovered) model. It was developed by Cliff and Haggett (2006) to model the velocity of spread of infectious diseases across space. Current applications can be found, for example, in Smallman-Raynor et al. (2022a,b). This package enables the calculation of the Swash-Backwash Model for user-supplied panel data on regional infections. The core of this is the swash() function, which calculates the model and creates a model object of the sbm class defined in this package. This class can be used to visualize results (summary(), plot()) and calculate bootstrap confidence intervals for the model estimates (confint(sbm)); the latter returns an object of class sbm_ci as defined in this package. Two sbm_ci objects for different countries may be compared with compare_countries(), which allows the estimation of mean differences of a user-specified model parameter (e.g., spatial reproduction number R_{OA}) between two countries. This makes it possible to check whether the spatial spread velocity of a communicable disease is significantly different in one country than in another country; the result is an object of class countries.

The package also contains other functions for spatio-temporal analysis and modeling of infectious diseases, such as fitting logistic growth models and exponential growth models for the initial phase of a spread, all of which can be used both on sbm objects (growth(sbm), growth_initial(sbm)) and stand-alone (logistic_growth()), exponential_growth()). These function return objects of class loggrowth and expgrowth, respectively, both defined in this package. Other functions include spatial statistics (nbstat() for neighborhood statistics), breakpoints analysis for time series models (plot_breakpoints()), and fit metrics (metrics(), binary_metrics(), binary_metrics_glm()). The package includes example data from the SARS-CoV-2/COVID-19 pandemic.

Author(s)

Thomas Wieland

References

Chowell G, Simonsen L, Viboud C, Yang K (2014) Is West Africa Approaching a Catastrophic Phase or is the 2014 Ebola Epidemic Slowing Down? Different Models Yield Different Answers for Liberia. PLoS currents 6. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://dx.doi.org/10.1371/currents.outbreaks.b4690859d91684da963dc40e00f3da81")}

Chowell G, Viboud C, Hyman JM, Simonsen L (2015) The Western Africa ebola virus disease epidemic exhibits both global exponential and local polynomial growth rates. PLOS Currents Outbreaks, ecurrents.outbreaks.8b55f4bad99ac5c5db3663e916803261. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1371/currents.outbreaks.8b55f4bad99ac5c5db3663e916803261")}

Cliff AD, Haggett P (2006) A swash-backwash model of the single epidemic wave. Journal of Geographical Systems 8(3), 227-252. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1007/s10109-006-0027-8")}

Li, MY (2018) An Introduction to Mathematical Modeling of Infectious Diseases. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1007/978-3-319-72122-4")}

Nishiura H, Chowell G (2009) The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends. In Chowell G, Hyman JM, Bettencourt LMA (eds.) Mathematical and statistical estimation approaches in epidemiology, 103–121. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1007/978-90-481-2313-1_5")}

Pell B, Kuang Y, Viboud C, Chowell G (2018) Using phenomenological models for forecasting the 2015 ebola challenge. Epidemics 22, 62–70. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1016/j.epidem.2016.11.002")}

Smallman-Raynor MR, Cliff AD, Stickler PJ (2022a) Meningococcal Meningitis and Coal Mining in Provincial England: Geographical Perspectives on a Major Epidemic, 1929–33. Geographical Analysis 54, 197–216. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1111/gean.12272")}

Smallman-Raynor MR, Cliff AD, The COVID-19 Genomics UK (COG-UK) Consortium (2022b) Spatial growth rate of emerging SARS-CoV-2 lineages in England, September 2020–December 2021. Epidemiology and Infection 150, e145. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1017/S0950268822001285")}.

Viboud C, Bjørnstad ON, Smith DL, Simonsen L, Miller MA, Grenfell BT (2006) Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza. Science 312, 447-451. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1126/science.1125237")}

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.18335/region.v7i2.324")}

Wieland T (2020) A phenomenological approach to assessing the effectiveness of COVID-19 related nonpharmaceutical interventions in Germany. Safety Science 131, 104924. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1016/j.ssci.2020.104924")}

Wieland T (2022) Spatial patterns of excess mortality in the first year of the COVID-19 pandemic in Germany. European Journal of Geography 13(4), 18-33. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.48088/ejg.t.wie.13.4.018.033")}

Wieland T (2025) Assessing the effectiveness of non-pharmaceutical interventions in the SARS-CoV-2 pandemic: results of a natural experiment regarding Baden-Württemberg (Germany) and Switzerland in the second infection wave. Journal of Public Health 33(11), 2497-2511. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1007/s10389-024-02218-x")}

Examples

data(COVID19Cases_geoRegion)
# Get SWISS COVID19 cases at NUTS 3 level

COVID19Cases_geoRegion <- 
  COVID19Cases_geoRegion[!COVID19Cases_geoRegion$geoRegion %in% c("CH", "CHFL"),]
# Exclude CH = Switzerland total and CHFL = Switzerland and Liechtenstein total

COVID19Cases_geoRegion <- 
  COVID19Cases_geoRegion[COVID19Cases_geoRegion$datum <= "2020-05-31",]
# Extract first COVID-19 wave

CH_covidwave1 <- 
  swash (
    data = COVID19Cases_geoRegion, 
    col_cases = "entries", 
    col_date = "datum", 
    col_region = "geoRegion"
    )
# Swash-Backwash Model for Swiss COVID19 cases
# Spatial aggregate: NUTS 3 (cantons)

summary(CH_covidwave1)
# Summary of Swash-Backwash Model

plot(CH_covidwave1)
# Plot of Swash-Backwash Model edges and total epidemic curve

swash documentation built on Feb. 15, 2026, 5:07 p.m.