Package 'mitey' reference manual

Title:	Serial Interval and Case Reproduction Number Estimation
Description:	Provides methods to estimate serial intervals and time-varying case reproduction numbers from infectious disease outbreak data. Serial intervals measure the time between symptom onset in linked transmission pairs, while case reproduction numbers quantify how many secondary cases each infected individual generates over time. These parameters are essential for understanding transmission dynamics, evaluating control measures, and informing public health responses. The package implements the maximum likelihood framework from Vink et al. (2014) <doi:10.1093/aje/kwu209> for serial interval estimation and the retrospective method from Wallinga & Lipsitch (2007) <doi:10.1098/rspb.2006.3754> for reproduction number estimation. Originally developed for scabies transmission analysis but applicable to other infectious diseases including influenza, COVID-19, and emerging pathogens. Designed for epidemiologists, public health researchers, and infectious disease modelers working with outbreak surveillance data.
Authors:	Kylie Ainslie [aut, cre, cph]
Maintainer:	Kylie Ainslie <[email protected]>
License:	EUPL-1.2
Version:	0.4.0
Built:	2026-06-04 23:14:14 UTC
Source:	https://github.com/kylieainslie/mitey

Compare Serial Interval Models Across Different Numbers of Transmission Routes

Description

Fits the serial interval mixture model for each number of transmission routes from 2 up to n_routes_max, computes model selection criteria (AIC and BIC) for each fit, and prints a summary table to help identify the optimal number of routes.

Usage

compare_n_routes(dat, n_routes_max = 8L, dist = "normal", n = 50, ...)
compare_n_routes(dat, n_routes_max = 8L, dist = "normal", n = 50, ...)

Arguments

dat

numeric vector; index case-to-case (ICC) intervals in days.

n_routes_max

integer; maximum number of transmission routes to evaluate. Models are fitted for n_routes from 2 to n_routes_max. Defaults to 8L.

dist

character; assumed parametric family for the serial interval distribution. Must be either "normal" (default) or "gamma".

n

integer; number of EM algorithm iterations passed to si_estim. Defaults to 50.

...

additional arguments passed to si_estim.

Details

For each value of n_routes in 2:n_routes_max, the function:

Calls si_estim to fit the mixture model and retrieve the log-likelihood and estimated weights.
Counts the number of free parameters $p$ :
- Normal distribution: $p = 2 + (2 \times n\_routes - 2)$
- Gamma distribution: $p = 2 + (n\_routes - 1)$
Computes AIC and BIC:

$AIC = -2 \ell + 2p$

$BIC = -2 \ell + p \log(n)$
Prints the fitted mixture plot via plot_si_fit_result.

The model with the lowest BIC (or AIC) is reported as the best-fitting number of routes.

Value

A data frame (returned invisibly) with one row per value of n_routes and the following columns:

n_routes: Number of transmission routes fitted.
mu: Estimated mean of the serial interval (days).
sigma: Estimated standard deviation of the serial interval (days).
loglik: Log-likelihood of the fitted model.
aic: Akaike Information Criterion.
bic: Bayesian Information Criterion.
n_params: Number of free parameters in the model.
converged: Logical; whether the EM algorithm converged.
iterations: Number of EM iterations performed.

A summary table and the best n_routes according to BIC and AIC are printed as side effects.

Examples


set.seed(42)
icc_data <- c(
  abs(rnorm(30, mean = 0,  sd = 2)),
  rnorm(80, mean = 12, sd = 3),
  rnorm(30, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))

# Compare 2 to 6 routes with normal distribution
results <- compare_n_routes(icc_data, n_routes_max = 6, dist = "normal", n = 50)

# Compare using gamma distribution
results_gam <- compare_n_routes(icc_data, n_routes_max = 5, dist = "gamma", n = 50)

set.seed(42)
icc_data <- c(
  abs(rnorm(30, mean = 0,  sd = 2)),
  rnorm(80, mean = 12, sd = 3),
  rnorm(30, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))

# Compare 2 to 6 routes with normal distribution
results <- compare_n_routes(icc_data, n_routes_max = 6, dist = "normal", n = 50)

# Compare using gamma distribution
results_gam <- compare_n_routes(icc_data, n_routes_max = 5, dist = "gamma", n = 50)

Generate Synthetic Epidemic Data Using the Renewal Equation

Description

Simulates epidemic incidence data with known reproduction numbers using the renewal equation framework. This function is useful for testing and validating reproduction number estimation methods, as it generates synthetic outbreaks with ground truth R values that can be compared against estimated values.

Usage

generate_synthetic_epidemic(
  true_r,
  si_mean,
  si_sd,
  si_dist = "gamma",
  initial_cases = 10
)
generate_synthetic_epidemic(
  true_r,
  si_mean,
  si_sd,
  si_dist = "gamma",
  initial_cases = 10
)

Arguments

true_r

numeric vector; the true time-varying reproduction numbers. The length of this vector determines the number of days in the simulated epidemic

si_mean

numeric; the mean of the serial interval distribution in days

si_sd

numeric; the standard deviation of the serial interval distribution in days

si_dist

character; the distribution family for the serial interval. Must be either "gamma" (default) or "normal". Gamma is recommended as it naturally restricts to positive values

initial_cases

integer; the number of cases on the first day of the epidemic. Defaults to 10

Details

The function implements the discrete renewal equation:

$\lambda_t = \sum_{s=1}^{t-1} I_s \cdot R_s \cdot w(t-s)$

where $\lambda_t$ is the expected number of new infections at time $t$ , $I_s$ is the incidence at time $s$ , $R_s$ is the reproduction number at time $s$ , and $w(t-s)$ is the probability mass function of the serial interval distribution for interval $t-s$ .

New cases at each time point are drawn from a Poisson distribution with mean $\lambda_t$ , introducing realistic stochastic variation while maintaining the specified reproduction number trajectory.

The serial interval distribution is truncated at the 99th percentile to avoid computationally expensive calculations for very long tails. For the normal distribution, the probability mass function is normalized to ensure proper probability weights.

This function is particularly useful for:

Validating reproduction number estimation methods
Testing the performance of epidemiological models
Generating realistic epidemic scenarios for research
Creating training data for machine learning approaches

Value

A data frame with three columns:

date: Date sequence starting from "2023-01-01"
true_r: The input reproduction number values
incidence: Simulated daily case counts

References

Fraser C (2007). Estimating individual and household reproduction numbers in an emerging epidemic. PLoS One, 2(8), e758.

Cori A, Ferguson NM, Fraser C, Cauchemez S (2013). A new framework and software to estimate time-varying reproduction numbers during epidemics. American Journal of Epidemiology, 178(9), 1505-1512.

Examples

# Simple epidemic with constant R = 1.5
constant_r <- rep(1.5, 30)
epidemic1 <- generate_synthetic_epidemic(
  true_r = constant_r,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma"
)
head(epidemic1)

# Epidemic with declining R (e.g., intervention effect)
declining_r <- seq(2.0, 0.5, length.out = 50)
epidemic2 <- generate_synthetic_epidemic(
  true_r = declining_r,
  si_mean = 5,
  si_sd = 2,
  si_dist = "gamma",
  initial_cases = 5
)

# Epidemic with seasonal pattern
days <- 100
seasonal_r <- 1.2 + 0.5 * sin(2 * pi * (1:days) / 365 * 7) # Weekly seasonality
epidemic3 <- generate_synthetic_epidemic(
  true_r = seasonal_r,
  si_mean = 6,
  si_sd = 2.5,
  si_dist = "normal"
)

# Plot the results
if (require(ggplot2)) {
  library(ggplot2)
  ggplot(epidemic1, aes(x = date)) +
    geom_col(aes(y = incidence), alpha = 0.7) +
    geom_line(aes(y = true_r * 10), color = "red") +
    labs(title = "Synthetic Epidemic",
         y = "Daily Incidence",
         subtitle = "Red line: True R × 10")
}
# Simple epidemic with constant R = 1.5
constant_r <- rep(1.5, 30)
epidemic1 <- generate_synthetic_epidemic(
  true_r = constant_r,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma"
)
head(epidemic1)

# Epidemic with declining R (e.g., intervention effect)
declining_r <- seq(2.0, 0.5, length.out = 50)
epidemic2 <- generate_synthetic_epidemic(
  true_r = declining_r,
  si_mean = 5,
  si_sd = 2,
  si_dist = "gamma",
  initial_cases = 5
)

# Epidemic with seasonal pattern
days <- 100
seasonal_r <- 1.2 + 0.5 * sin(2 * pi * (1:days) / 365 * 7) # Weekly seasonality
epidemic3 <- generate_synthetic_epidemic(
  true_r = seasonal_r,
  si_mean = 6,
  si_sd = 2.5,
  si_dist = "normal"
)

# Plot the results
if (require(ggplot2)) {
  library(ggplot2)
  ggplot(epidemic1, aes(x = date)) +
    geom_col(aes(y = incidence), alpha = 0.7) +
    geom_line(aes(y = true_r * 10), color = "red") +
    labs(title = "Synthetic Epidemic",
         y = "Daily Incidence",
         subtitle = "Red line: True R × 10")
}

Visualize Serial Interval Distribution Fit to Outbreak Data

Description

Creates a diagnostic plot showing the fitted serial interval mixture distribution overlaid on a histogram of observed index case-to-case (ICC) intervals from outbreak data.

Usage

plot_si_fit(
  dat,
  mean,
  sd,
  weights,
  dist = "normal",
  scaling_factor = 1,
  n_routes = 4L
)
plot_si_fit(
  dat,
  mean,
  sd,
  weights,
  dist = "normal",
  scaling_factor = 1,
  n_routes = 4L
)

Arguments

dat

numeric vector; the index case-to-case (ICC) intervals in days.

mean

numeric; the estimated mean of the serial interval distribution in days.

sd

numeric; the estimated standard deviation of the serial interval distribution in days.

weights

numeric vector of length n_routes - 1; the estimated weights for each transmission route component, starting from Co-primary. The last route weight is derived internally as 1 - sum(weights).

dist

character; the distribution family. Must be either "normal" (default) or "gamma".

scaling_factor

numeric; multiplicative factor to adjust the height of the fitted density curve. Defaults to 1.

n_routes

integer; number of transmission routes modelled. Must be >= 2. Defaults to 4. Must match the value used in si_estim().

Value

A ggplot2 object.

References

Vink MA, Bootsma MCJ, Wallinga J (2014). Serial intervals of respiratory infectious diseases: A systematic review and analysis. American Journal of Epidemiology, 180(9), 865-875.

Examples

# Example 1: 4 routes, normal distribution
set.seed(123)
icc_data <- c(
  rnorm(20, mean = 0, sd = 2),
  rnorm(50, mean = 12, sd = 3),
  rnorm(20, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))

plot_si_fit(
  dat = icc_data,
  mean = 12.5,
  sd = 3.2,
  weights = c(0.2, 0.6, 0.15, 0.05),
  dist = "normal",
  n_routes = 4
)

# Example 2: 5 routes, gamma distribution
plot_si_fit(
  dat = icc_data,
  mean = 12.0,
  sd = 3.5,
  weights = c(0.25, 0.65, 0.05, 0.03, 0.02),
  dist = "gamma",
  n_routes = 5,
  scaling_factor = 0.8
)

# Example 1: 4 routes, normal distribution
set.seed(123)
icc_data <- c(
  rnorm(20, mean = 0, sd = 2),
  rnorm(50, mean = 12, sd = 3),
  rnorm(20, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))

plot_si_fit(
  dat = icc_data,
  mean = 12.5,
  sd = 3.2,
  weights = c(0.2, 0.6, 0.15, 0.05),
  dist = "normal",
  n_routes = 4
)

# Example 2: 5 routes, gamma distribution
plot_si_fit(
  dat = icc_data,
  mean = 12.0,
  sd = 3.5,
  weights = c(0.25, 0.65, 0.05, 0.03, 0.02),
  dist = "gamma",
  n_routes = 5,
  scaling_factor = 0.8
)

Plot Serial Interval Fit from si_estim Result

Description

A convenience wrapper for plot_si_fit that accepts the output from si_estim directly, automatically handling the weight aggregation for different distribution types and number of routes.

Usage

plot_si_fit_result(
  si_result,
  dat,
  dist = c("normal", "gamma"),
  scaling_factor = 1
)
plot_si_fit_result(
  si_result,
  dat,
  dist = c("normal", "gamma"),
  scaling_factor = 1
)

Arguments

si_result

list; the output from si_estim containing mean, sd, wts, and n_routes components.

dat

numeric vector; the index case-to-case (ICC) intervals in days.

dist

character; the distribution family. Must be either "normal" (default) or "gamma". Should match the distribution used in si_estim().

scaling_factor

numeric; multiplicative factor to adjust the height of the fitted density curve. Defaults to 1.

Details

This function reads n_routes directly from the si_result object and aggregates component weights automatically:

For normal distribution: the Co-primary weight is taken directly, and weights for routes 2 to n_routes are aggregated by summing the two symmetric components (positive and negative).
For gamma distribution: weights are taken directly as the first n_routes - 1 values from si_result$wts.

Value

A ggplot2 object.

Examples

set.seed(123)
icc_data <- c(
  abs(rnorm(15, mean = 0, sd = 2)),
  rnorm(40, mean = 12, sd = 3),
  rnorm(15, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))


# 4 routes (default)
result <- si_estim(icc_data, n = 50)
plot_si_fit_result(result, icc_data, dist = "normal")

# 5 routes
result5 <- si_estim(icc_data, n = 50, n_routes = 5)
plot_si_fit_result(result5, icc_data, dist = "normal")


set.seed(123)
icc_data <- c(
  abs(rnorm(15, mean = 0, sd = 2)),
  rnorm(40, mean = 12, sd = 3),
  rnorm(15, mean = 24, sd = 4)
)
icc_data <- round(pmax(icc_data, 0))


# 4 routes (default)
result <- si_estim(icc_data, n = 50)
plot_si_fit_result(result, icc_data, dist = "normal")

# 5 routes
result5 <- si_estim(icc_data, n = 50, n_routes = 5)
plot_si_fit_result(result5, icc_data, dist = "normal")

Estimate Serial Interval Distribution Using the Vink Method

Description

Estimates the mean and standard deviation of the serial interval distribution from outbreak data using the Expectation-Maximization (EM) algorithm developed by Vink et al. (2014). The serial interval is defined as the time between symptom onset in a primary case and symptom onset in a secondary case infected by that primary case.

Usage

si_estim(
  dat,
  n = 50,
  dist = "normal",
  init = NULL,
  tol = 1e-06,
  n_starts = 1,
  n_routes = 4L,
  wind = 1
)
si_estim(
  dat,
  n = 50,
  dist = "normal",
  init = NULL,
  tol = 1e-06,
  n_starts = 1,
  n_routes = 4L,
  wind = 1
)

Arguments

dat

numeric vector; index case-to-case (ICC) intervals in days.

n

integer; number of EM algorithm iterations to perform. Defaults to 50.

dist

character; the assumed parametric family for the serial interval distribution. Must be either "normal" (default) or "gamma".

init

numeric vector of length 2; initial values for the mean and standard deviation. If NULL (default), uses the sample mean and sample standard deviation.

tol

numeric; convergence tolerance for the EM algorithm. Defaults to 1e-6.

n_starts

integer; number of random restarts for the EM algorithm. Defaults to 1.

n_routes

integer; number of transmission routes to model. Must be >= 2. Defaults to 4 (Co-Primary, Primary-Secondary, Primary-Tertiary, Primary-Quaternary). Increasing this allows modelling longer transmission chains.

wind

The window censure interval

Value

A named list containing:

mean: Estimated mean of the serial interval distribution (days)
sd: Estimated standard deviation of the serial interval distribution (days)
wts: Numeric vector of estimated component weights. Length is 2*n_routes - 1 for normal distribution, n_routes for gamma distribution.
converged: Logical indicating whether the algorithm converged.
iterations: Integer indicating the number of iterations performed.
loglik: Log-likelihood of the fitted model.
n_restarts: Number of restarts performed.
n_routes: Number of transmission routes used.

References

Vink MA, Bootsma MCJ, Wallinga J (2014). Serial intervals of respiratory infectious diseases: A systematic review and analysis. American Journal of Epidemiology, 180(9), 865-875. doi:10.1093/aje/kwu209

Examples

# Example 1: Basic usage with simulated data, default 4 routes
set.seed(123)
simulated_icc <- c(
  rep(1, 20), rep(2, 25), rep(3, 15), rep(4, 8)
)
result <- si_estim(simulated_icc)


# Example 2: Using 5 routes
result_5routes <- si_estim(simulated_icc, n_routes = 5)

# Example 3: Using gamma distribution with 3 routes
result_gamma <- si_estim(simulated_icc, dist = "gamma", n_routes = 3)


# Example 1: Basic usage with simulated data, default 4 routes
set.seed(123)
simulated_icc <- c(
  rep(1, 20), rep(2, 25), rep(3, 15), rep(4, 8)
)
result <- si_estim(simulated_icc)


# Example 2: Using 5 routes
result_5routes <- si_estim(simulated_icc, n_routes = 5)

# Example 3: Using gamma distribution with 3 routes
result_gamma <- si_estim(simulated_icc, dist = "gamma", n_routes = 3)

Apply Moving Average Smoothing to R Estimates

Description

Applies temporal smoothing to reproduction number estimates using a centered moving average window. Handles missing and infinite values appropriately.

Usage

smooth_estimates(r_estimate, window)
smooth_estimates(r_estimate, window)

Arguments

r_estimate

numeric vector; reproduction number estimates to smooth. Can contain NA or infinite values

window

integer; size of the smoothing window in time units. Window is centered around each point

Value

numeric vector; smoothed reproduction number estimates of the same length as input. Returns NA for points with insufficient valid neighboring values

Estimate Time-Varying Case Reproduction Number Using Wallinga-Lipsitch Method

Description

Estimates the time-varying case reproduction number (R_c) from daily incidence data using the method developed by Wallinga and Lipsitch (2007). The case reproduction number represents the average number of secondary infections generated by cases with symptom onset at time t, making it useful for retrospective outbreak analysis.

Usage

wallinga_lipsitch(
  incidence,
  dates,
  si_mean,
  si_sd,
  si_dist = "gamma",
  smoothing = 0,
  bootstrap = FALSE,
  n_bootstrap = 1000,
  conf_level = 0.95,
  shift = FALSE
)
wallinga_lipsitch(
  incidence,
  dates,
  si_mean,
  si_sd,
  si_dist = "gamma",
  smoothing = 0,
  bootstrap = FALSE,
  n_bootstrap = 1000,
  conf_level = 0.95,
  shift = FALSE
)

Arguments

incidence

numeric vector; daily case counts. Must be non-negative integers or counts. Length must match dates

dates

vector; dates corresponding to each incidence count. Must be the same length as incidence. Can be Date objects or anything coercible to dates

si_mean

numeric; mean of the serial interval distribution in days. Must be positive. Typically estimated from contact tracing data or literature

si_sd

numeric; standard deviation of the serial interval distribution in days. Must be positive

si_dist

character; distribution family for the serial interval. Options:

"gamma" (default): Recommended for most applications as it naturally restricts to positive values
"normal": Allows negative serial intervals, useful when co-primary infections are suspected

smoothing

integer; window size for temporal smoothing of R estimates. Use 0 for no smoothing (default), or positive integers for moving average smoothing over the specified number of days

bootstrap

logical; whether to calculate bootstrap confidence intervals. Defaults to FALSE. Setting to TRUE increases computation time but provides uncertainty quantification

n_bootstrap

integer; number of bootstrap samples when bootstrap = TRUE. More samples provide more stable intervals but increase computation time. Defaults to 1000

conf_level

numeric; confidence level for bootstrap intervals, between 0 and 1. Defaults to 0.95 (95% confidence intervals)

shift

logical; whether to shift R estimates forward by one mean serial interval. When TRUE, adds a shifted_date column for comparison with instantaneous reproduction number estimates. Defaults to FALSE

Details

The method calculates the relative likelihood that each earlier case infected each later case based on their time differences and the serial interval distribution, then aggregates these likelihoods to estimate reproduction numbers. The approach makes minimal assumptions beyond specifying the serial interval distribution.

Key features:

Pairwise likelihood approach: Considers all epidemiologically plausible transmission pairs (earlier to later cases)
Right-truncation correction: Adjusts for unobserved future cases (see calculate_truncation_correction)
Bootstrap confidence intervals: Quantifies estimation uncertainty
Temporal shifting: Optional alignment with instantaneous R estimates
Flexible smoothing: User-controlled temporal smoothing of estimates

The Wallinga-Lipsitch method estimates the case reproduction number by:

Computing transmission likelihoods from each earlier case to each later case based on the serial interval distribution
Normalizing these likelihoods so they sum to 1 for each potential infectee
Aggregating normalized likelihoods to estimate expected secondary cases per primary case
Applying corrections for right-truncation bias

Right-truncation correction accounts for secondary cases that may occur after the observation period ends (see calculate_truncation_correction). This correction is particularly important for recent cases in the time series.

Bootstrap confidence intervals are calculated by resampling individual cases with replacement, providing non-parametric uncertainty estimates that account for both Poisson sampling variation and method uncertainty.

Value

A data frame with the following columns:

date: Original input dates
incidence: Original input case counts
R: Estimated case reproduction number
R_corrected: Case reproduction number with right-truncation correction
R_lower, R_upper: Bootstrap confidence intervals for R (if bootstrap = TRUE)
R_corrected_lower, R_corrected_upper: Bootstrap confidence intervals for R_corrected (if bootstrap = TRUE)
shifted_date: Dates shifted forward by mean serial interval (if shift = TRUE)

Note

The case reproduction number differs from the instantaneous reproduction number in timing: R_c reflects the reproductive potential of cases by their symptom onset date, while instantaneous R reflects transmission potential at the time of infection. Use shift = TRUE for comparisons with instantaneous R estimates.

References

Wallinga J, Lipsitch M (2007). How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences, 274(1609), 599-604. doi:10.1098/rspb.2006.3754

Examples

# Example 1: Basic usage with synthetic data
set.seed(123)
dates <- seq(as.Date("2023-01-01"), by = "day", length.out = 30)
incidence <- c(1, 2, 4, 7, 12, 15, 18, 20, 22, 19,
               16, 14, 11, 9, 7, 5, 4, 3, 2, 1,
               rep(0, 10))

# Estimate reproduction number
result <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma"
)

# View results
head(result)

# Example 2: With bootstrap confidence intervals
result_ci <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma",
  bootstrap = TRUE,
  n_bootstrap = 500  # Reduced for faster example
)

# Plot results with confidence intervals
if (require(ggplot2)) {
  library(ggplot2)
  ggplot(result_ci, aes(x = date)) +
    geom_ribbon(aes(ymin = R_corrected_lower, ymax = R_corrected_upper),
                alpha = 0.3, fill = "blue") +
    geom_line(aes(y = R_corrected), color = "blue", size = 1) +
    geom_hline(yintercept = 1, linetype = "dashed", color = "red") +
    labs(x = "Date", y = "Reproduction Number",
         title = "Time-varying Reproduction Number") +
    theme_minimal()
}

# Example 3: With smoothing and shifting
result_smooth <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma",
  smoothing = 7,  # 7-day smoothing window
  shift = TRUE    # Shift for comparison with instantaneous R
)

# Example 4: Using normal distribution for serial interval
result_normal <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 6,
  si_sd = 2,
  si_dist = "normal",
  smoothing = 5
)

# Example 1: Basic usage with synthetic data
set.seed(123)
dates <- seq(as.Date("2023-01-01"), by = "day", length.out = 30)
incidence <- c(1, 2, 4, 7, 12, 15, 18, 20, 22, 19,
               16, 14, 11, 9, 7, 5, 4, 3, 2, 1,
               rep(0, 10))

# Estimate reproduction number
result <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma"
)

# View results
head(result)

# Example 2: With bootstrap confidence intervals
result_ci <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma",
  bootstrap = TRUE,
  n_bootstrap = 500  # Reduced for faster example
)

# Plot results with confidence intervals
if (require(ggplot2)) {
  library(ggplot2)
  ggplot(result_ci, aes(x = date)) +
    geom_ribbon(aes(ymin = R_corrected_lower, ymax = R_corrected_upper),
                alpha = 0.3, fill = "blue") +
    geom_line(aes(y = R_corrected), color = "blue", size = 1) +
    geom_hline(yintercept = 1, linetype = "dashed", color = "red") +
    labs(x = "Date", y = "Reproduction Number",
         title = "Time-varying Reproduction Number") +
    theme_minimal()
}

# Example 3: With smoothing and shifting
result_smooth <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 7,
  si_sd = 3,
  si_dist = "gamma",
  smoothing = 7,  # 7-day smoothing window
  shift = TRUE    # Shift for comparison with instantaneous R
)

# Example 4: Using normal distribution for serial interval
result_normal <- wallinga_lipsitch(
  incidence = incidence,
  dates = dates,
  si_mean = 6,
  si_sd = 2,
  si_dist = "normal",
  smoothing = 5
)

Package 'mitey'

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Compare Serial Interval Models Across Different Numbers of Transmission Routes

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Generate Synthetic Epidemic Data Using the Renewal Equation

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Visualize Serial Interval Distribution Fit to Outbreak Data

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Plot Serial Interval Fit from si_estim Result

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Estimate Serial Interval Distribution Using the Vink Method

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Apply Moving Average Smoothing to R Estimates

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Estimate Time-Varying Case Reproduction Number Using Wallinga-Lipsitch Method

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