swash (version 1.2.1)

swash-package: 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

Author

Thomas Wieland

Details

The Swash-Backwash Model 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 package also contains additional helper functions.

References

Swash-Backwash Model:

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

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. 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. tools:::Rd_expr_doi("https://doi.org/10.1017/S0950268822001285").

Basics of epidemiological modeling:

Bonifazi G et al. (2021) A simplified estimate of the effective reproduction number Rt using its relation with the doubling time and application to Italian COVID-19 data. The European Physical Journal Plus 136, 386. tools:::Rd_expr_doi("https://doi.org/10.1140/epjp/s13360-021-01339-6")

Li, MY (2018) An Introduction to Mathematical Modeling of Infectious Diseases. 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. 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. tools:::Rd_expr_doi("https://doi.org/10.1016/j.epidem.2016.11.002")

Spatio-temporal analysis and modeling of infectious diseases:

Bourdin S, Jeanne L, Nadou F, Noiret G (2021) Does lockdown work? A spatial analysis of the spread and concentration of Covid-19 in Italy. Regional Studies, 55, 1182–1193. tools:::Rd_expr_doi("https://doi.org/10.1080/00343404.2021.1887471")

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. tools:::Rd_expr_doi("https://doi.org/10.1371/currents.outbreaks.8b55f4bad99ac5c5db3663e916803261")

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. 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. 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. tools:::Rd_expr_doi("https://doi.org/10.1016/j.ssci.2020.104924")

Panel data:

Greene, WH (2012) Econometric Analysis. Ch. 11.

Wooldridge, JM (2012) Introductory Econometrics. A Modern Approach. Ch. 13.

Bootstrapping und bootstrap confidence intervals:

Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap.

Ramachandran KM, Tsokos CP (2021) Mathematical Statistics with Applications in R (Third Edition). Ch. 13.3.1 (Bootstrap confidence intervals). tools:::Rd_expr_doi("https://doi.org/10.1016/B978-0-12-817815-7.00013-0")

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