Help for package swash

Type:

Package

Title:

Swash-Backwash Model for the Single Epidemic Wave

Version:

1.2.2

Date:

2025-07-03

Author:

Thomas Wieland

[aut, cre]

Maintainer:

Thomas Wieland <geowieland@googlemail.com>

Depends:

R (≥ 3.5.0), lubridate, sf, spdep

Description:

The Swash-Backwash Model for the Single Epidemic Wave was developed by Cliff and Haggett (2006) <doi:10.1007/s10109-006-0027-8> to model the velocity of spread of infectious diseases across space. This package enables the calculation of the Swash-Backwash Model for user-supplied panel data on regional infections. The package also provides additional functions for bootstrap confidence intervals, country comparison, visualization of results, and data management.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Imports:

methods

NeedsCompilation:

Packaged:

2025-07-07 05:21:55 UTC; thoma

Repository:

CRAN

Date/Publication:

2025-07-07 07:00:02 UTC

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 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 other functions for spatio-temporal analysis and modeling of infectious diseases, such as fitting logistic growth models (growth(sbm), logistic_growth()) and exponential growth models for the initial phase of a spread (growth_initial(sbm), exponential_growth()), as well as for spatial statistics.

Author(s)

Thomas Wieland

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. doi: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. doi: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. doi: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. doi:10.1140/epjp/s13360-021-01339-6

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. doi:10.1371/currents.outbreaks.b4690859d91684da963dc40e00f3da81

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

Wieland T (2020) A phenomenological approach to assessing the effectiveness of COVID-19 related nonpharmaceutical interventions in Germany. Safety Science 131, 104924. doi:10.1016/j.ssci.2020.104924

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. doi: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. doi: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. doi: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. doi:10.18335/region.v7i2.324

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. doi:10.48088/ejg.t.wie.13.4.018.033

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). doi: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

Switzerland Daily COVID-19 cases by region

Description

A dataset containing COVID-19 cases by region (NUTS 3 = cantons) and time periods (days) for Switzerland (Source: Federal Office of Public Health FOPH).

Usage

data(COVID19Cases_geoRegion)

Format

A data.frame with multiple columns:

geoRegion: (character) Region for which the data was collected.
datum: (Date) Date of record.
entries: (integer) Number of reported cases on this date.
sumTotal: (integer) Cumulative case numbers.
timeframe_14d: (logical) Indicates whether the time period covers the last 14 days.
timeframe_all: (logical) Indicates whether the time period covers all previous data.
offset_last7d: (integer) Offset of the last 7 days.
sumTotal_last7d: (integer) Cumulative case numbers of the last 7 days.
offset_last14d: (integer) Offset of the last 14 days.
sumTotal_last14d: (integer) Cumulative case numbers of the last 14 days.
offset_last28d: (integer) Offset of the last 28 days.
sumTotal_last28d: (integer) Cumulative case numbers of the last 28 days.
sum7d: (numeric) Sum of the last 7 days.
sum14d: (numeric) Sum of the last 14 days.
mean7d: (numeric) Average of the last 7 days.
mean14d: (numeric) Average of the last 14 days.
entries_diff_last_age: (integer) Difference from the last age group.
pop: (integer) Population of the region.
inz_entries: (numeric) Incidence of the entries.
inzsumTotal: (numeric) Incidence of cumulative cases.
inzmean7d: (numeric) Incidence of the 7-day average.
inzmean14d: (numeric) Incidence of the 14-day average.
inzsumTotal_last7d: (numeric) Incidence of cumulative cases in the last 7 days.
inzsumTotal_last14d: (numeric) Incidence of cumulative cases in the last 14 days.
inzsumTotal_last28d: (numeric) Incidence of cumulative cases in the last 28 days.
inzsum7d: (numeric) Incidence of the last 7 days.
inzsum14d: (numeric) Incidence of the last 14 days.
sumdelta7d: (numeric) Difference in sums of the last 7 days.
inzdelta7d: (numeric) Difference in incidence of the last 7 days.
type: (character) Type of recorded data (e.g., COVID-19 cases).
type_variant: (character) Variant of the data type.
version: (character) Version of the data collection.
datum_unit: (character) Unit of date specification (e.g., day).
entries_letzter_stand: (integer) Last known count of entries.
entries_neu_gemeldet: (integer) Newly reported entries.
entries_diff_last: (integer) Difference in last entries.

Details

The data is included as it was published in by the Swiss Federal Office of Public Health (Bundesamt fuer Gesundheit, BAG). Note that the reporting date equals the date of SARS-CoV-2 testing.

Source

Federal Office of Public Health FOPH (2023) COVID-19 Dashboard Source Data. https://www.covid19.admin.ch/api/data/documentation (retrieved 2023-06-28)

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

COVID19Cases_geoRegion_balanced <- 
  is_balanced(
  data = COVID19Cases_geoRegion,
  col_cases = "entries",
  col_date = "datum",
  col_region = "geoRegion"
)
# Test whether "COVID19Cases_geoRegion" is balanced panel data 

COVID19Cases_geoRegion_balanced$data_balanced
# Balanced? TRUE or FALSE

Austria Daily COVID-19 cases by region 2020-02-26 to 2020-05-31

Description

A dataset containing COVID-19 cases by region (NUTS 3) and time periods (days) for Austria (Source: BMSGPK).

Usage

data(Oesterreich_Faelle)

Format

A data.frame with multiple columns:

NUTS3: (character) Region for which the data was collected.
Datum: (Date) Date of record.
Faelle: (integer) Number of reported cases on this date.

Details

The original data was originally published by BMSGPK at a smaller spatial scale level (political districts, "Politische Bezirke"). The data was linked to a corresponding shapefile from Statistik Austria (2022), joined to the NUTS3 level via a spatial join, and summed over the Austrian NUTS3 regions. The spatial join is based on polygon centroids of the political districts level; in cases where the centroid was outside the polygon, it was placed inside the polygon manually.

Source

BMSGPK, Oesterreichisches COVID-19 Open Data Informationsportal (2022) COVID-19: Zeitliche Darstellung von Daten zu Covid19-Faellen je Bezirk. https://www.data.gv.at/katalog/dataset/4b71eb3d-7d55-4967-b80d-91a3f220b60c (retrieved 2022-06-23)

Statistik Austria (2022) Politische Bezirke. https://www.data.gv.at/katalog/dataset/stat_gliederung-osterreichs-in-politische-bezirke131e2 (retrieved 2022-06-27)

Wieland T (2022) C19dNUTS: Dataset of Regional COVID-19 Deaths per 100,000 Pop (NUTS). R package v1.0.1. doi:10.32614/CRAN.package.C19dNUTS

Examples

data(Oesterreich_Faelle)
# Get Austrian COVID19 cases at NUTS 3 level
# (first wave, same final date as in Swiss data: 2020-05-31)

AT_covidwave1 <- 
  swash (
    data = Oesterreich_Faelle,
    col_cases = "Faelle",
    col_date = "Datum",
    col_region = "NUTS3"
  )
# Swash-Backwash Model for Austrian COVID19 cases
# Spatial aggregate: NUTS 3

summary(AT_covidwave1)
# Summary of model results

German Counties with COVID-19 Cases

Description

A dataset containing German counties (NUTS 3) with COVID-19 cases (Source: Robert Koch Institute).

Usage

data(RKI_Corona_counties)

Format

A data.frame with multiple columns:

OBJECTID: unknown/not necessary
ADE: (unknown/not necessary
GF: unknown/not necessary
BSG: unknown/not necessary
RS: (character) County code 1
AGS: (character) County code 2
SDV_RS: (character) County code 3
GEN: (character) County name
BEZ: (character) County type
IBZ: unknown/not necessary
BEM: unknown/not necessary
NBD: unknown/not necessary
SN_L: unknown/not necessary
SN_R: unknown/not necessary
SN_K: unknown/not necessary
SN_V1: unknown/not necessary
SN_V2: unknown/not necessary
SN_G: unknown/not necessary
FK_S3: unknown/not necessary
NUTS: (character) NUTS 3 code
RS_0: unknown/not necessary
AGS_0: unknown/not necessary
WSK: unknown/not necessary
EWZ: (numeric) Population
KFL: (numeric) Area in sq. km
DEBKG_ID: unknown/not necessary
Shape__Are: unknown/not necessary
Shape__Len: unknown/not necessary
death_rate
cases: (numeric) COVID-19 cases
deaths: (numeric) COVID-19 associated deaths
cases_per_: (numeric) COVID-19 cases per 100,000 inhabitants
cases_pe_1: unknown/not necessary
BL: (character) Federal state
BL_ID: (integer) Federal state ID
county: (character) County name
last_updat: Date of last update
geometry: Geometry

Details

The data is included as it was published in by the Robert Koch Institute (Robert Koch-Institut, RKI) but extended by the geometry column (Original data: shapefile).

Source

RKI (2020) RKI Corona Landkreise. Robert Koch-Institut (RKI), dl-de/by-2-0. Attribution: Robert Koch-Institut, Bundesamt für Kartographie und Geodäsie. https://npgeo-corona-npgeo-de.hub.arcgis.com/datasets/917fc37a7095 (retrieved 2020-03-30)

Examples

data(RKI_Corona_counties)
# German counties (Source: Robert Koch Institute)

Corona_nbstat <- 
  nbstat (
    RKI_Corona_counties, 
    ID_col="AGS",
    link_data = RKI_Corona_counties, 
    data_ID_col = "AGS", 
    data_col = "EWZ", 
    func = "sum"
  )
Corona_nbstat$nbmat_data_aggregate
# Sum of population (EWZ) of neighbouring counties

Effective Reproduction Number for Epidemic Data

Description

Calculation of the effective reproduction number for infection/surveillance data

Usage

R_t(
  infections, 
  GP = 4,
  correction = FALSE
  )

Arguments

infections

numeric vector with infection data

GP

Generation period, in days

correction

Correction of values equal to zero? (Recommended)

Details

The function calculates the effective reproduction number (=growth factor), R_t, of an infections time series.

Value

list with two entries:

R_t:

Object of class "numeric" R_t values

infections_data:

Object of class "data.frame" Dataset with infections data and R_t

Author(s)

Thomas Wieland

References

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

COVID19Cases_BS <-
  COVID19Cases_geoRegion[(COVID19Cases_geoRegion$geoRegion == "ZH")
                         & (COVID19Cases_geoRegion$sumTotal > 0),]
# COVID cases for Zurich

Rt_BS <- R_t(infections = COVID19Cases_BS$entries)
# Effective reproduction number

Rt_BS

Correction of Non-balanced Panel Dataset with Regional Infection Data

Description

This function corrects non-balanced input panel data by replacing missing entries with a user-given constant (e.g., 0).

Usage

as_balanced(
  data, 
  col_cases, 
  col_date, 
  col_region, 
  fill_missing = 0
  )

Arguments

data

data.frame with regional infection data

col_cases

Column containing the cases (numeric)

col_date

Column containing the time points (e.g., days)

col_region

Column containing the unique identifier of the regions (e.g., name, NUTS 3 code)

fill_missing

Constant to fill missing values (default and recommended: 0)

Details

The Swash-Backwash Model for the Single Epidemic Wave does not necessarily require balanced panel data in order for the calculations to be carried out. However, for a correct estimation it is implicitly assumed that the input data is balanced. The function corrects non-balanced panel data. It is executed automatically whithin the swash() function (when using the function is_balanced()), but can also be used separately.

Value

data

Corrected input dataset (data.frame)

Author(s)

Thomas Wieland

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. doi:10.1007/s10109-006-0027-8

Smallman-Raynor MR, Cliff AD, Stickler PJ (2022) Meningococcal Meningitis and Coal Mining in Provincial England: Geographical Perspectives on a Major Epidemic, 1929–33. Geographical Analysis 54, 197–216. doi:10.1111/gean.12272

Smallman-Raynor MR, Cliff AD, The COVID-19 Genomics UK (COG-UK) Consortium (2022) Spatial growth rate of emerging SARS-CoV-2 lineages in England, September 2020–December 2021. Epidemiology and Infection 150, e145. doi:10.1017/S0950268822001285.

Panel data:

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

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

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

COVID19Cases_geoRegion_balanced <- 
  is_balanced(
  data = COVID19Cases_geoRegion,
  col_cases = "entries",
  col_date = "datum",
  col_region = "geoRegion"
)
# Test whether "COVID19Cases_geoRegion" is balanced panel data 

COVID19Cases_geoRegion_balanced$data_balanced
# Balanced? TRUE or FALSE

if (COVID19Cases_geoRegion_balanced$data_balanced == FALSE) {
  COVID19Cases_geoRegion <- 
    as_balanced(
    COVID19Cases_geoRegion,
    col_cases = "entries",
    col_date = "datum",
    col_region = "geoRegion"
  )
}
# Correction of dataset "COVID19Cases_geoRegion"
# not necessary as parameter balance of is_balanced is set TRUE by default

Two-country Comparison of Swash-Backwash Model Parameters

Description

This function enables bootstrap estimates for the mean difference of Swash-Backwash Model parameters of two countries to be compared.

Usage

compare_countries(
  sbm1, 
  sbm2, 
  country_names = c("Country 1", "Country 2"), 
  indicator = "R_0A", 
  iterations = 20, 
  samples_ratio = 0.8, 
  alpha = 0.05, 
  replace = TRUE
  )

Arguments

sbm1

A sbm object for country 1

sbm2

A sbm object for country 2

country_names

list with user-given country names (two entries)

indicator

character, indicator to be analyzed ("S_A", "I_A", "R_A", "t_LE", "t_LE", or "R_0A" (default and recommended: "R_0A"))

iterations

Number of iterations for resampling (default: 100)

samples_ratio

Proportion of regions included in each sample (default: 0.8)

alpha

Significance level \alpha for the confidence intervals (default: 0.05)

replace

Resampling with replacement (TRUE or FALSE, default: TRUE = bootstrap resampling)

Details

The combination of the Swash-Backwash Model and bootstrap resampling 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. Since the initial data in the Swash-Backwash Model should be balanced, entity-based bootstrap sampling is carried out in the compare_countries() function. This means that not, for example, 80% of all observations are included in each sample at a sample ratio equal to p = 0.8, but rather all observations for 80% of the regions. For both countries, B bootstrap samples (default: 100) are drawn for which the Swash-Backwash Model is calculated. Based on the distribution of indicators, confidence intervals are calculated at the user-specified significance level \alpha. The compare_countries() function calculates the differences of the user's desired indicator between the two samples, D, and also calculates \alpha confidence intervals for this.

Value

object of class countries, see countries-class

Author(s)

Thomas Wieland

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. doi:10.1007/s10109-006-0027-8

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). doi:10.1016/B978-0-12-817815-7.00013-0

Examples

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

data(Oesterreich_Faelle)
# Get Austrian COVID19 cases at NUTS 3 level
# (first wave, same final date as in Swiss data: 2020-05-31)

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)

AT_covidwave1 <- 
  swash (
    data = Oesterreich_Faelle,
    col_cases = "Faelle",
    col_date = "Datum",
    col_region = "NUTS3"
  )
# Swash-Backwash Model for Austrian COVID19 cases
# Spatial aggregate: NUTS 3

AT_vs_CH <- 
  compare_countries(
    CH_covidwave1, 
    AT_covidwave1,
    country_names = c("Switzerland", "Austria"))
# Country comparison Switzerland vs. Austria
# default config: 20 iterations, alpha = 0.05, sample ratio = 80%,
# indicator: R_0A

summary(AT_vs_CH)
# Summary of country comparison

plot(AT_vs_CH)
# Plot of country comparison

Methods for Function `confint`

Description

Methods for function confint

Methods

signature(object = "sbm", iterations = 100, samples_ratio = 0.8, alpha = 0.05, replace = TRUE): Creates bootstrap confidence intervals for sbm objects. The argument iterations indicates the number of bootstrap samples which are drawn. Since the initial data in the Swash-Backwash Model should be balanced, entity-based bootstrap sampling is carried out. This means that not, for example, 80% of all observations are included in each sample at a sample ratio equal to p = 0.8 (samples_ratio = 0.8), but rather all observations for 80% of the regions. The significance level for the confidence intervals \alpha is set by the argument alpha (default: 0.05, which corresponds to a 95% confidence level).

Author(s)

Thomas Wieland

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. doi:10.1007/s10109-006-0027-8

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). doi:10.1016/B978-0-12-817815-7.00013-0

Class `"countries"`

Description

The class "countries" contains the results of a two-country comparison analysis using the Swash-Backwash Model, including two "sbm_ci" classes for each country. Use summary(countries) and plot(countries) for results summary and plotting, respectively.

Objects from the Class

Objects can be created by calls of the form new("countries", ...). Objects can be created by the function compare_countries(sbm1, sbm2).

Slots

sbm_ci1:: Object of class "sbm_ci" Results of "confint(sbm1)" for country 1
sbm_ci2:: Object of class "sbm_ci" Results of "confint(sbm1)" for country 2
D:: Object of class "numeric" Results: Difference D between the samples with respect to the chosen indicator
D_ci:: Object of class "numeric" Results: \alpha confidence intervals of D
config:: Object of class "list" Configuration details for bootstrap sampling
country_names:: Object of class "character" User-stated country names
indicator:: Object of class "character" User-stated indicator to be tested

Methods

plot: signature(x = "countries"): Plots the results of a two-country comparison with the Swash-Backwash Model
show: signature(object = "countries"): Prints an countries object; use summary(sbm_ci) for results
summary: signature(object = "countries"): Prints a summary of a countries object (results of the two-country comparison)

Author(s)

Thomas Wieland

Examples

showClass("countries")

Exponential Growth Model for Epidemic Data

Description

Estimation of exponential growth models from daily infections data

Usage

exponential_growth(
  y, 
  t, 
  GI = 4
  )

Arguments

y

numeric vector with cumulative infections data over time

t

vector of class numeric or Date with time points or dates

GI

Generation interval for computing R_0

Details

This function allows the estimation of an exponential growth model. The user must specify the dependent variable (daily infections) and the time variable (time counter or date values). The estimation is performed using a linearized model as an OLS estimator. The results are the exponential growth rate r, basic reproduction number R_0, and the doubling rate.

Value

list with four entries:

exp_gr:

numeric value of exponential growth rate

R0:

numeric value of basic reproduction number

doubling:

numeric value of doubling rate

model_data:

lm object of regression model

Author(s)

Thomas Wieland

References

Pell B, Kuang Y, Viboud C, Chowell G (2018) Using phenomenological models for forecasting the 2015 ebola challenge. Epidemics 22, 62–70. doi:10.1016/j.epidem.2016.11.002

Examples

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

COVID19Cases_ZH <-
  COVID19Cases_geoRegion[(COVID19Cases_geoRegion$geoRegion == "ZH")
                         & (COVID19Cases_geoRegion$sumTotal > 0),]
# COVID cases for Zurich

expgrowth_BS <- exponential_growth (
  y = COVID19Cases_ZH$sumTotal[1:28], 
  t = COVID19Cases_ZH$datum[1:28] 
)
# Exponential growth model for the first 4 weeks

expgrowth_BS$doubling
# Doubling rate

Logistic Growth Models for Regional Infections

Description

Estimates N logistic growth models for N regions.

Usage

growth(
  object, 
  S_iterations = 10, 
  S_start_est_method = "bisect", 
  seq_by = 10, 
  nls = TRUE
  )

Arguments

object

object of class sbm

S_iterations

Number of iterations for saturation value search

S_start_est_method

Method for saturation value search, either "bisect" or "trial_and_error"

seq_by

No of segments for the "trial_and_error" estimation of the saturation value

nls

Nonlinear estimation? TRUE or FALSE

Details

The function estimates logistic growth models for regional infections based on a sbm object. See logistic_growth for further details.

Value

list with two entries:

results:

Object of class "data.frame" Results of the logistic growth models (coefficients and derivates)

logistic_growth_models:

Object of class "list" List with N entries for N growth models resp. loggrowth objects

Author(s)

Thomas Wieland

References

Pell B, Kuang Y, Viboud C, Chowell G (2018) Using phenomenological models for forecasting the 2015 ebola challenge. Epidemics 22, 62–70. doi:10.1016/j.epidem.2016.11.002

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

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)

CH_covidwave1_growth <- growth(CH_covidwave1)
CH_covidwave1_growth
# Logistic growth models for sbm object CH_covidwave1

Methods for Function `growth`

Description

Methods for function growth

Methods

signature(object = "sbm", S_iterations = 10, S_start_est_method = "bisect", seq_by = 10, nls = TRUE): Estimation of N logistic growth models for N regions. Both OLS and NLS estimation are estimated by default (set nls = FALSE to skip NLS estimation). Parameters S_iterations, S_start_est_method, and seq_by are used to control the saturation value estimation (see logistic_growth).

Author(s)

Thomas Wieland

Exponential Growth Models for Regional Infections

Description

Estimates N exponential growth models for a given time period in N regions.

Usage

growth_initial(
  object, 
  time_units = 10,
  GI = 4
  )

Arguments

object

object of class sbm

time_units

numeric value for the analysis time (time units from start)

GI

Generation interval for computing R_0

Details

The function estimates exponential growth models for regional infections based on a sbm object. Such models are design for the analysis of the initial phase of an epidemic spread. The user must state how much time units (from start) are included. See exponential_growth for further details of the estimation.

Value

list with two entries:

results:

Object of class "data.frame" Results of the exponential growth models (growth rate, basic reproduction number, doubling rate) for each region

exponential_growth_models:

Object of class "list" List with N entries for N exponential models

Author(s)

Thomas Wieland

References

Pell B, Kuang Y, Viboud C, Chowell G (2018) Using phenomenological models for forecasting the 2015 ebola challenge. Epidemics 22, 62–70. doi:10.1016/j.epidem.2016.11.002

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)

CH_covidwave1_initialgrowth_3weeks <- 
  growth_initial(
    CH_covidwave1,
    time_units = 21
    )
CH_covidwave1_initialgrowth_3weeks$results
# Exponential models for sbm object CH_covidwave1 
# initial growth in the first 3 weeks

Methods for Function `growth_initial`

Description

Methods for function growth_initial

Methods

signature(object = "sbm", time_units = 10, GI = 4): Estimation of N exponential growth models for the initial phase of an epidemic spread for N regions. Set argument GI for the calculation of the basic reproduction number(see exponential_growth).

Author(s)

Thomas Wieland

Creating Histograms with Confidence Intervals

Description

Plot of a histogram of a given vector x and the related confidence intervals (lower, upper).

Usage

hist_ci(
  x, 
  alpha = 0.05,
  col_bars = "grey", 
  col_ci = "red",
  ...
  )

Arguments

x

A numeric vector

alpha

Significance level \alpha for 1-\alpha*100 confidence intervals

col_bars

Color of bars in histogram

col_ci

Color of lines for confidence interval

...

Additional arguments passed to barplot()

Details

Helper function for plot(sbm_ci), but may be used separately.

Value

Histogram plot, no returned value

Author(s)

Thomas Wieland

Examples

numeric_vector <- c(1,9,5,6,3,10,20,6,9,14,3,5,8,6,11)
# any numeric vector

hist_ci(numeric_vector)

Test whether Panel Dataset with Regional Infection Data is Balanced

Description

The function tests whether the input panel data with regional infections is balanced.

Usage

is_balanced(
  data, 
  col_cases, 
  col_date, 
  col_region, 
  as_balanced = TRUE, 
  fill_missing = 0
  )

Arguments

data

data.frame with regional infection data

col_cases

Column containing the cases (numeric)

col_date

Column containing the time points (e.g., days)

col_region

Column containing the unique identifier of the regions (e.g., name, NUTS 3 code)

as_balanced

Boolean argument which indicates whether non-balanced panel data shall be balanced (default: TRUE)

fill_missing

Constant to fill missing values (default and recommended: 0)

Details

The Swash-Backwash Model for the Single Epidemic Wave does not necessarily require balanced panel data in order for the calculations to be carried out. However, for a correct estimation it is implicitly assumed that the input data is balanced. The function tests whether the panel data is balanced. It is executed automatically whithin the swash() function (using automatic correction with as_balanced = TRUE), but can also be used separately.

Value

List with two entries:

data_balanced

Result of test (TRUE or FALSE)

data

Input dataset (data.frame)

Author(s)

Thomas Wieland

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. doi:10.1007/s10109-006-0027-8

Panel data:

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

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

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

COVID19Cases_geoRegion_balanced <- 
  is_balanced(
  data = COVID19Cases_geoRegion,
  col_cases = "entries",
  col_date = "datum",
  col_region = "geoRegion"
)
# Test whether "COVID19Cases_geoRegion" is balanced panel data 

COVID19Cases_geoRegion_balanced$data_balanced
# Balanced? TRUE or FALSE

if (COVID19Cases_geoRegion_balanced$data_balanced == FALSE) {
  COVID19Cases_geoRegion <- 
    as_balanced(
    COVID19Cases_geoRegion,
    col_cases = "entries",
    col_date = "datum",
    col_region = "geoRegion"
  )
}
# Correction of dataset "COVID19Cases_geoRegion"
# not necessary as parameter balance of is_balanced is set TRUE by default

Class `"loggrowth"`

Description

The class "loggrowth" contains the results of the logistic_growth() function. Use summary(sbm) and plot(sbm) for results summary and plotting, respectively.

Objects from the Class

Objects can be created by the function logistic_growth.

Slots

LinModel:: Object of class list Results of the OLS helper model
GrowthModel_OLS:: Object of class list Results of the OLS fit (predicted, parameters, first derivative)
GrowthModel_NLS:: Object of class list Results of the NLS fit (predicted, parameters, first derivative)
t:: Object of class numeric Input time points data
y:: Object of class numeric Input infections data
config:: Object of class list Model fit configurations

Methods

plot: signature(x = "loggrowth"): Plots the results of the logistic growth model (observed, predicted, first derivative)
summary: signature(object = "loggrowth"): Prints a summary of loggrowth objects

Author(s)

Thomas Wieland

References

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

Examples

showClass("loggrowth")

Logistic Growth Model for Epidemic Data

Description

Estimation of logistic growth models from cumulative infections data, linearized OLS and/or NLS

Usage

logistic_growth(
  y, 
  t, 
  S = NULL,
  S_start = NULL, 
  S_end = NULL, 
  S_iterations = 10, 
  S_start_est_method = "bisect", 
  seq_by = 10,
  nls = TRUE
  )

Arguments

y

numeric vector with cumulative infections data over time

t

vector of class numeric or Date with time points or dates

S

Saturation value for the model

S_start

Start value of the saturation value for estimation

S_end

End value of the saturation value for estimation

S_iterations

Number of iterations for saturation value search

S_start_est_method

Method for saturation value search, either "bisect" or "trial_and_error"

seq_by

No of segments for the "trial_and_error" estimation of the saturation value

nls

Nonlinear estimation? TRUE or FALSE

Details

This function allows the estimation of a logistic growth model. The user must specify the dependent variable (cumulative infections) and the time variable (time counter or date values). The estimation is performed using a linearized model as an OLS estimator and as an NLS estimator. For the former, the saturation value can either be specified by the user or found using a search algorithm. The parameters from the OLS fit are used as starting values for the NLS estimation.

Value

object of class loggrowth-class

Author(s)

Thomas Wieland

References

Pell B, Kuang Y, Viboud C, Chowell G (2018) Using phenomenological models for forecasting the 2015 ebola challenge. Epidemics 22, 62–70. doi:10.1016/j.epidem.2016.11.002

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

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

COVID19Cases_BS <-
  COVID19Cases_geoRegion[(COVID19Cases_geoRegion$geoRegion == "ZH")
                         & (COVID19Cases_geoRegion$sumTotal > 0),]
# COVID cases for Zurich

loggrowth_BS <- logistic_growth (
  y = as.numeric(COVID19Cases_BS$sumTotal), 
  t = COVID19Cases_BS$datum, 
  S = 5557,
  S_start = NULL, 
  S_end = NULL, 
  S_iterations = 10, 
  S_start_est_method = "bisect", 
  seq_by = 10,
  nls = TRUE
)
# Logistic growth model with stated saturation value

summary(loggrowth_BS)
# Summary of logistic growth model

plot(loggrowth_BS)
# Plot of logistic growth model

Construct Neighbourhood Matrix from Polygons

Description

Building a neighbourhood matrix based on regions (polygons) with contiguous boundaries and resulting a data frame

Usage

nbmatrix(
  polygon_sf, 
  ID_col,
  row.names = NULL
  )

Arguments

polygon_sf

sf object with polygons

ID_col

Column of polygon_sf with unique ID of each polygon

row.names

row.names for the sf object

Details

The function is based on spdep::poly2nb, which creates neighbours lists. The input is a sf object (spatial data frame) and the results are 1) a nb list (poly2nb result) and 2) a data.frame.

Value

list with two entries:

nb:

Object of class "sb" Neighbours list; see the spdep:poly2nb documentation

nbmat:

Object of class "data.frame" Dataset neighbouring regions

Author(s)

Thomas Wieland

References

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

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. doi:10.48088/ejg.t.wie.13.4.018.033

Examples

data(RKI_Corona_counties)
# German counties (Source: Robert Koch Institute)

Corona_nbmat <- 
  nbmatrix (
    RKI_Corona_counties, 
    ID_col="AGS"
  )
# Creating neighborhood matrix

Calculate Neighbourhood Statistics from Polygons

Description

Calculating descriptive neighbourhood statistics based on regions (polygons) with contiguous boundaries and resulting a data frame

Usage

nbstat(
  polygon_sf, 
    ID_col, 
    link_data, 
    data_ID_col, 
    data_col, 
    func = "sum",
    row.names = NULL
  )

Arguments

polygon_sf

sf object with polygons

ID_col

Column of polygon_sf with unique ID of each polygon

link_data

data.frame to merge with

data_ID_col

Column with unique ID of each polygon in data.frame

data_col

Column with regarded numeric values in data.frame

func

Descriptive statistic (FUN) to be computed for data_col of the neighbouring regions

row.names

row.names for the sf object

Details

The function is based on spdep::poly2nb, which creates neighbours lists. The input is a sf object (spatial data frame) and the results are 1) a nb list (poly2nb result) and 2) a data.frame.

Value

list with three entries:

nbmat:

Object of class "data.frame" Dataset neighbouring regions

nbmat_data:

Object of class "data.frame" Dataset neighbouring regions and linked data

nbmat_data_aggreagte:

Object of class "data.frame" Dataset with statistic by region

Author(s)

Thomas Wieland

References

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

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. doi:10.48088/ejg.t.wie.13.4.018.033

Examples

data(RKI_Corona_counties)
# German counties (Source: Robert Koch Institute)

Corona_nbstat <- 
  nbstat (
    RKI_Corona_counties, 
    ID_col="AGS",
    link_data = RKI_Corona_counties, 
    data_ID_col = "AGS", 
    data_col = "EWZ", 
    func = "sum"
  )
Corona_nbstat$nbmat_data_aggregate
# Sum of population (EWZ) of neighbouring counties

Methods for Function `plot`

Description

Methods for function plot for different S4 classes: sbm, sbm_ci, and loggrowth.

Methods

signature(x = "sbm")

plot.sbm(x, y, ...): Plots the results of the Swash-Backwash Model. This generates two plots:

Edges over time.
Total infections per time unit.

Arguments:

x: An object of class sbm representing the results of the Swash-Backwash Model.
y: Optional argument for additional customization, such as plot style or axis labels.
...: Additional graphical parameters that can be passed to control plot appearance.

Details: This method is used to visualize the output of the Swash-Backwash Model, providing insight into the dynamics of the modeled epidemic.

signature(x = "sbm_ci")

plot.sbm_ci(x, y, ...): Plots the results of bootstrap confidence intervals for the Swash-Backwash Model. This generates a single figure with six subplots:

S_A (susceptible population),
I_A (infected population),
R_A (recovered population),
t_{FE} (final epidemic time),
t_{LE} (last epidemic time),
R_{0A} (basic reproduction number).

Arguments:

x: An object of class sbm_ci containing the bootstrap confidence intervals for the Swash-Backwash Model.
y: Optional argument for additional customization, such as plot style or axis labels.
...: Additional graphical parameters for fine-tuning the plots.

Details: This method is used to visualize the bootstrap confidence intervals for various parameters of the Swash-Backwash Model.

signature(x = "countries")

plot.sbm(x, y = NULL, col_bars = "grey", col_ci = "red"): Plots the results of the between-countries analysis via Swash-Backwash Model. This generates four plots:

Indicator for country 1
Indicator for country 2
Boxplots of the distribution of the indicator in country 1 and 2
Distribution of the difference between the indicators of country 1 and 2

Arguments:

x: An object of class countries representing the results of the Swash-Backwash Model country analysis.
y: Not relevant
col_bars: Color of bars
col_ci: Color of confidence intervals

Details: This method is used to visualize the output of the Swash-Backwash Model, providing insight into the dynamics of the modeled epidemic.

signature(x = "loggrowth")

plot.loggrowth(x, y, ...): Plots the results of the logistic growth model, including:

Observed values,
Predicted values,
First derivative (growth rate).

Arguments:

x: An object of class loggrowth containing the data for the logistic growth model.
y: Optional argument for additional customization of the plot (e.g., color, labels).
...: Additional arguments for graphical parameters.

Details: This method is useful for visualizing the observed and predicted growth patterns in an epidemic or similar phenomena modeled by logistic growth.

Author(s)

Thomas Wieland

Plots of Regional Infections Over Time

Description

Plots regional infection curves in N plots for N regions.

Usage

plot_regions(
  object, 
  col = "red", 
  scale = FALSE, 
  normalize_by_col = NULL, 
  normalize_factor = 1
  )

Arguments

object

object of class sbm

col

Color of line plot

scale

Set y axis of the plots uniformly based on the maximum value across all regions? (boolean, default: FALSE)

normalize_by_col

Normalize infection numbers by stating a column in the input data frame (e.g., regional population)

normalize_factor

Multiply density/incidence with a factor (say, 100,000 inhabitants)

Details

Plots regional infection curves in N plots for N regions, with the number of columns equals 4 and the number of rows is calculated based the size of N.

Value

Plot, only no returned value

Author(s)

Thomas Wieland

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)

plot_regions(CH_covidwave1)
# Plot of regional infections

Methods for Function `plot_regions`

Description

Methods for function plot_regions

Methods

signature(object = "sbm", col = "red", scale = FALSE, normalize_by_col = NULL, normalize_factor = 1): Plots regional infection curves in N plots for N regions, with the number of columns equals 4 and the number of rows is calculated based the size of N. Set the color by the argument col. If scale is TRUE, the y axis of the plots is set uniformly based on the maximum value across all regions. If the input data contains a column to normalize the infection numbers (such as regional population), the user may use this data to normalize the infection numbers by setting normalize_by_col. If this density value should be multiplied by a factor (e.g. regional infections per 100,000 inhabitants), this can be set with the argument normalize_by_col (default: 1).

Author(s)

Thomas Wieland

Methods for Function `print`

Description

Methods for function print

Methods

signature(x = "sbm"): Prints an sbm object; use summary(sbm) for results
signature(x = "sbm_ci"): Prints an sbm_ci object; use summary(sbm_ci) for results

Computing Quantiles for a given Numeric Vector

Description

Computes quantiles for a given vector x and the related confidence intervals (lower, upper).

Usage

quantile_ci(
  x, 
  alpha = 0.05
  )

Arguments

x

A numeric vector

alpha

Significance level \alpha for 1-\alpha*100 confidence intervals

Details

Helper function for plot(sbm_ci), but may be used separately.

Value

A numeric vector with lower and upper quantile

Author(s)

Thomas Wieland

Examples

numeric_vector <- c(1,9,5,6,3,10,20,6,9,14,3,5,8,6,11)
# any numeric vector

quantile_ci(numeric_vector)

Class `"sbm"`

Description

The class "sbm" contains the results of the Swash-Backwash Model and the related input data as well as additional information. Use summary(sbm) and plot(sbm) for results summary and plotting, respectively.

Objects from the Class

Objects can be created by the function swash.

Slots

R_0A:: Object of class "numeric" Model result: spatial reproduction number R_{0A}
integrals:: Object of class "numeric" Model result: integrals S_A, I_A, and R_A
velocity:: Object of class "numeric" Model result: velocity measures t_{FE} and t_{LE}
occ_regions:: Object of class "data.frame" Model result: Occurence at regional level
SIR_regions:: Object of class "data.frame" Model result: Susceptible, infected and recovered regions over time
cases_by_date:: Object of class "data.frame" Total cases by date
cases_by_region:: Object of class "data.frame" Cumulative cases by region
input_data:: Object of class "data.frame" Input data
data_statistics:: Object of class "numeric" Diagnostics of input data
col_names:: Object of class "character" Original column names in input data

Methods

confint: signature(object = "sbm"): Creates bootstrap confidence intervals for sbm objects.
plot: signature(x = "sbm"): Plots the results of the Swash-Backwash Model; two plots: edges over time, total infections per time unit
print: signature(x = "sbm"): Prints an sbm object; use summary(sbm) for results
show: signature(object = "sbm"): Prints an sbm object; use summary(sbm) for results
summary: signature(object = "sbm"): Prints a summary of sbm objects (results of the Swash-Backwash Model)
growth: signature(object = "sbm"): Estimates logistic growth models from sbm objects
growth_initial: signature(object = "sbm"): Estimates exponential growth models from sbm objects for a given time period

Author(s)

Thomas Wieland

References

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

Wieland T (2020) Flatten the Curve! Modeling SARS-CoV-2/COVID-19 Growth in Germany at the County Level. REGION 7(2), 43–83. doi:10.18335/region.v7i2.324

Examples

showClass("sbm")

Class `"sbm_ci"`

Description

The class "sbm_ci" contains the results of the Swash-Backwash Model, confidence intervals for the model estimates, and the related input data as well as additional information. Use summary(sbm_ci) and plot(sbm_ci) for results summary and plotting, respectively.

Objects from the Class

Objects can be created by the function confint(sbm).

Slots

R_0A:: Object of class "numeric" Model result: spatial reproduction number R_{0A}
integrals:: Object of class "numeric" Model result: integrals S_A, I_A, and R_A
velocity:: Object of class "numeric" Model result: velocity measures t_{FE} and t_{LE}
occ_regions:: Object of class "data.frame" Model result: Occurence at regional level
cases_by_date:: Object of class "data.frame" Total cases by date
cases_by_region:: Object of class "data.frame" Cumulative cases by region
input_data:: Object of class "data.frame" Input data
data_statistics:: Object of class "numeric" Diagnostics of input data
col_names:: Object of class "character" Column names in input data
integrals_ci:: Object of class "list" Confidence intervals for integrals S_A, I_A, and R_A
velocity_ci:: Object of class "list" Confidence intervals for velocity measures t_{FE} and t_{LE}
R_0A_ci:: Object of class "numeric" Confidence intervals for spatial reproduction number R_{0A}
iterations:: Object of class "data.frame" Results of bootstrap sampling iterations
ci:: Object of class "numeric" Lower and upper confidence intervals based on user input
config:: Object of class "list" Configuration details for bootstrap sampling

Methods

plot: signature(x = "sbm_ci"): Plots the results of bootstrap confidence intervals for the Swash-Backwash Model; one figure with six plots: S_A, I_A, R_A, t_{FE}, t_{LE}, and R_{0A}
print: signature(x = "sbm_ci"): Prints an sbm_ci object; use summary(sbm_ci) for results
show: signature(object = "sbm_ci"): Prints an sbm_ci object; use summary(sbm_ci) for results
summary: signature(object = "sbm_ci"): Prints a summary of sbm_ci objects (bootstrap confidence intervals for Swash-Backwash Model estimates)

Author(s)

Thomas Wieland

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. doi:10.1007/s10109-006-0027-8

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). doi:10.1016/B978-0-12-817815-7.00013-0

Examples

showClass("sbm_ci")

Methods for Function `show`

Description

Methods for function show

Methods

signature(object = "sbm"): Prints an sbm object; use summary(sbm) for results
signature(object = "sbm_ci"): Prints an sbm_ci object; use summary(sbm_ci) for results

Methods for Function `summary`

Description

Methods for function summary

Methods

signature(object = "sbm"): Prints a summary of sbm objects (results of the Swash-Backwash Model)
signature(object = "sbm_ci"): Prints a summary of sbm_ci objects (bootstrap confidence intervals for Swash-Backwash Model estimates)
signature(object = "countries"): Prints a summary of a countries object built with the function compare_countries

Swash-Backwash Model for the Single Epidemic Wave

Description

Analysis of regional infection/surveillance data using the Swash-Backwash Model for the single epidemic wave by Cliff and Haggett (2006)

Usage

swash(
  data, 
  col_cases, 
  col_date, 
  col_region
  )

Arguments

data

data.frame with regional infection data

col_cases

Column containing the cases (numeric)

col_date

Column containing the time points (e.g., days)

col_region

Column containing the unique identifier of the regions (e.g., name, NUTS 3 code)

Details

The function performs the analysis of the input panel data using the Swash-Backwash Model. The output is an object of class "sbm". The results can be viewed using summary(sbm). The user must state panel data with daily infections.

Value

object of class sbm-class

Author(s)

Thomas Wieland

References

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

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

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

Description

Details

Author(s)

References

Examples

Switzerland Daily COVID-19 cases by region

Description

Usage

Format

Details

Source

Examples

Austria Daily COVID-19 cases by region 2020-02-26 to 2020-05-31

Description

Usage

Format

Details

Source

Examples

German Counties with COVID-19 Cases

Description

Usage

Format

Details

Source

Examples

Effective Reproduction Number for Epidemic Data

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Correction of Non-balanced Panel Dataset with Regional Infection Data

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Two-country Comparison of Swash-Backwash Model Parameters

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Methods for Function confint

Description

Methods

Author(s)

References

See Also

Class "countries"

Description

Objects from the Class

Slots

Methods

Author(s)

Examples

Exponential Growth Model for Epidemic Data

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Methods for Function `confint`

Class `"countries"`

Methods for Function `growth`

Methods for Function `growth_initial`

Class `"loggrowth"`