Package 'measles'

Description

Uses the epiworldR::compute_reproduction_number() function to optimize the scaling factor of the contact matrix to match a target reproduction number.

Usage

calibrate_mixing_model(
  contact_matrix,
  target_rep_number,
  infectious_period_days,
  transmission_prob,
  ...
)

Arguments

Details

In the case of the ModelMeaslesMixing(), if agents with rash are assumed to not be fully isolated, the calibration process needs to incorporate this information into the function. In practice, this means that the infectious period should include the days with rash, scaled by (1 - rash_reduction_contact_rate). For instance, if the prodromal period is 4 days, the rash period is 3 days, and the rash_reduction_contact_rate is 0.8, the effective infectious period would be 4 + 3 * (1 - 0.8) = 4.6 days.

Value

The scaling factor for the contact matrix that achieves the target reproduction number.

Examples

data(short_creek_matrix, package = "measles")

# Calibrating for a measles model with R0 of 10
# assuming agents are infectious during prodomal stage
# (isolated during rash stage)
calibrate_mixing_model(
  contact_matrix = short_creek_matrix,
  target_rep_number = 10,
  infectious_period_days = 4,
  transmission_prob = 0.2
)

# You can then use the scaling factor in a mixing
# model. Instead of using the original contact matrix,
# you would use:
#   contact_matrix * scaling_factor

Description

Create a measles post-exposure prophylaxis (PEP) intervention

Usage

InterventionMeaslesPEP(
  name,
  mmr_efficacy,
  ig_efficacy,
  ig_half_life_mean,
  ig_half_life_sd,
  mmr_willingness,
  ig_willingness,
  mmr_window,
  ig_window,
  target_states,
  states_if_pep_effective,
  states_if_pep_ineffective
)

Arguments

Details

This functions creates a global event that represents a post-exposure prophylaxis (PEP) intervention for measles. The intervention includes the administration of MMR vaccine and immunoglobulin (IG) to individuals after exposure to the virus, with the goal of reducing the probability of infection and preventing the spread of the disease.

The process involves both PEP Measles-Mumps-Rubella (MMR) vaccine and immunoglobulin (IG). The system decides which agent gets MMR or IG based on the time since exposure and the willingness to accept PEP. The flow is the following:

1. Agents in target_states are eligible for PEP if they are willing to accept it (based on pep_willingness).

2. If the agent is already infected (for example, in a latent state) for at most mmr_window days, they are offered MMR vaccine. Otherwise, they are offered IG.

3. Susceptible agents are offered the MMR vaccine, and if they accept, they are automatically moved out of the quarantine process.

4. Agents who were already infected and got either MMR or IG may move out of the quarantine process if the PEP is effective (based on mmr_efficacy or ig_efficacy). The destination state depends on whether the PEP was effective or not, and is determined by states_if_pep_effective and states_if_pep_ineffective, respectively.

Since IG winds down over time, the IG "tool" may be removed from the agent as a function of the half-life of IG (based on ig_half_life_mean and ig_half_life_sd). Particularly, after applied, the IG "tool" will have a random duration based on a normal distribution with mean ig_half_life_mean and standard deviation ig_half_life_sd. Once the duration is over, the IG "tool" is removed from the agent, and they are again eligible for PEP if they are exposed again.

Value

An object of class epiworld_globalevent representing the measles PEP intervention.

See Also

epiworldR::global-events

Description

The symmetry is achieved to ensure that n(i) * c(i, j) == n(j) * c(j, i) where n(i) is the population size of age group i and c(i, j) is the contact rate from age group i to age group j.

Usage

make_cmat_symmetric(cmat, pop)

Arguments

Details

This function was adapted from that described in socialmixr::symmetrise() to work with a simple matrix and population vector. The process is implemented as described in the original function, replacing the ij-th entries with (c_ij * N_i + c_ji * N_j) / 2 and divided by the population size of the respective age group to ensure that the resulting matrix is symmetric with respect to the population sizes.

The resulting matrix will satisfy the condition that n(i) * c(i, j) == n(j) * c(j, i) for all age groups i and j, ensuring that the total number of contacts from age group i to age group j is equal to the total number of contacts from age group j to age group i.

The operation will change the row and column sums of the contact matrix.

Examples

cmat <- c(4, 2, 1, 3, 5, 6, 4, 5, 2) |>
  matrix(nrow = 3, byrow = TRUE)
pop <- c(100, 200, 300)

cmat_symm <- make_cmat_symmetric(cmat, pop)

# Checking symmetry
cmat_symm * pop == t(cmat_symm * pop)

Description

ModelMeaslesMixing creates a measles epidemiological model with mixing between different population groups. The model includes vaccination, quarantine, isolation, and contact tracing mechanisms.

Usage

ModelMeaslesMixing(
  n,
  prevalence,
  contact_matrix,
  vax_reduction_recovery_rate = 0.5,
  transmission_rate = 0.9,
  prop_vaccinated,
  vax_efficacy = 0.97,
  quarantine_period = 21,
  quarantine_willingness = 1,
  isolation_willingness = 1,
  isolation_period = 4,
  incubation_period = 12,
  prodromal_period = 4,
  rash_period = 3,
  hospitalization_rate = 0.2,
  hospitalization_period = 7,
  days_undetected = 2,
  contact_tracing_success_rate = 1,
  contact_tracing_days_window = 4,
  rash_reduction_contact_rate = 1
)

Arguments

Details

The contact_matrix is a square matrix of contact rates between entities. Entry ⁠[i, j]⁠ gives the expected number of contacts that an agent in entity i has with agents in entity j during a time step. The matrix should have one row and one column per entity in the model.

The model includes three distinct phases of measles infection: incubation, prodromal, and rash periods. Vaccination provides protection against infection and may reduce recovery time.

The epiworldR::initial_states function allows the user to set the initial state of the model. In particular, the user can specify how many of the non-infected agents have been removed at the beginning of the simulation.

Value

• The ModelMeaslesMixing function returns a model of classes epiworldR::epiworld_model and epiworld_measlesmixing.

Contact Rate Reduction During Rash Period

The default behavior of the model is that agents in the rash period are self-isolated. Nonetheless, since version 0.3.2-0, the user can set the rash_reduction_contact_rate parameter to a value between 0 and 1 to allow agents with Rash to still contact other agents, albeit at a reduced rate. For example, if the user sets rash_reduction_contact_rate to 0.8, agents in the rash period will have 20% of the contact rates specified in the contact_matrix instead of 0%.

The basic reproduction number (R0) of the model can be computed as

$\mathcal{R}_0 = p_t c (D_p + (1-r_r) D_r)$

Where $p_t$ is the transmission_rate, $c$ is the average number of contacts per time step (given by the contact_matrix), $D_p$ is the duration of the prodromal period, $D_r$ is the duration of the rash period, and $r_r$ is the rash_reduction_contact_rate. Therefore, when calibrating the model, the effective infectious period should be considered as the sum of the prodromal period and the rash period scaled by (1 - rash_reduction_contact_rate).

Hospitalization Probability

Instead of hospitalization probability, the model uses hospitalization rate. The following equation describes the hospitalization probability as a function of the hospitalization rate and recovery rate (from rash):

$P(\text{hospitalization}) = \frac{ \text{hospitalization}_\text{rate}}{ \text{hospitalization}_\text{rate} + \text{recovery}_\text{rate} }$

Where the $\text{recovery}_\text{rate}$ is given by the rash period (1/duration of it). In other words, to match a desired hospitalization probability, the user needs to use the following:

h_rate <- p_hosp * (1/rash_days) / (1 - p_hosp)

Model diagram

See Also

epiworld-methods

Other Models: ModelMeaslesMixingRiskQuarantine(), ModelMeaslesSchool()

Other measles models: ModelMeaslesMixingRiskQuarantine(), ModelMeaslesSchool()

Examples

# Start off creating three entities.
# Individuals will be distributed randomly between the three.
e1 <- entity("Population 1", 3e3, as_proportion = FALSE)
e2 <- entity("Population 2", 3e3, as_proportion = FALSE)
e3 <- entity("Population 3", 3e3, as_proportion = FALSE)

# Contact matrix including within- and between-group contact rates
cmatrix <- (c(
  c(0.9, 0.05, 0.05),
  c(0.1, 0.8, 0.1),
  c(0.1, 0.2, 0.7)
) * 15) |> matrix(byrow = TRUE, nrow = 3)

N <- 9e3

measles_model <- ModelMeaslesMixing(
  n                        = N,
  prevalence               = 1 / N,
  transmission_rate        = 0.9,
  vax_efficacy             = 0.97,
  vax_reduction_recovery_rate = 0.8,
  incubation_period        = 10,
  prodromal_period         = 3,
  rash_period              = 7,
  contact_matrix           = cmatrix,
  hospitalization_rate     = 0.1,
  hospitalization_period   = 10,
  days_undetected          = 2,
  quarantine_period        = 14,
  quarantine_willingness   = 0.9,
  isolation_willingness    = 0.8,
  isolation_period         = 10,
  prop_vaccinated          = 0.95,
  contact_tracing_success_rate = 0.8,
  contact_tracing_days_window = 4
)

# Adding the entities to the model
measles_model |>
  add_entity(e1) |>
  add_entity(e2) |>
  add_entity(e3)

set.seed(331)
run(measles_model, ndays = 100)
summary(measles_model)

Description

ModelMeaslesMixingRiskQuarantine creates a measles epidemiological model with mixing between different population groups and risk-based quarantine strategies. The model includes vaccination, quarantine with three risk levels (high, medium, low), isolation, and contact tracing mechanisms.

Usage

ModelMeaslesMixingRiskQuarantine(
  n,
  prevalence,
  contact_matrix,
  transmission_rate = 0.9,
  prop_vaccinated,
  vax_efficacy = 0.97,
  quarantine_period_high = 21,
  quarantine_period_medium = 14,
  quarantine_period_low = 7,
  quarantine_willingness = 1,
  isolation_willingness = 1,
  isolation_period = 4,
  incubation_period = 12,
  prodromal_period = 4,
  rash_period = 3,
  hospitalization_rate = 0.2,
  hospitalization_period = 7,
  days_undetected = 2,
  detection_rate_quarantine = 0.5,
  contact_tracing_success_rate = 1,
  contact_tracing_days_window = 4
)

Arguments

Details

The contact_matrix is a square matrix of contact rates between entities. Entry ⁠[i, j]⁠ gives the expected number of contacts that an agent in entity i has with agents in entity j during a time step. The matrix should have one row and one column per entity in the model.

The model includes three distinct phases of measles infection: latent (incubation), prodromal, and rash periods. Vaccination provides protection against transmission.

Risk-based quarantine strategies assign different quarantine durations based on exposure risk:

• High Risk: Unvaccinated agents who share entity membership with the case

• Medium Risk: Unvaccinated agents who contacted an infected individual but don't share entity membership

• Low Risk: Other unvaccinated agents

The epiworldR::initial_states function allows the user to set the initial state of the model. In particular, the user can specify how many of the non-infected agents have been removed at the beginning of the simulation.

The model uses hospitalization rates instead of probabilities. To learn more about this, see the documentation in ModelMeaslesMixing().

Value

• The ModelMeaslesMixingRiskQuarantine function returns a model of classes epiworldR::epiworld_model and epiworld_measlesmixingriskquarantine.

Model diagram

See Also

epiworld-methods

Other Models: ModelMeaslesMixing(), ModelMeaslesSchool()

Other measles models: ModelMeaslesMixing(), ModelMeaslesSchool()

Examples

# Start off creating three entities.
# Individuals will be distributed randomly between the three.
e1 <- entity("Population 1", 3e3, as_proportion = FALSE)
e2 <- entity("Population 2", 3e3, as_proportion = FALSE)
e3 <- entity("Population 3", 3e3, as_proportion = FALSE)

# Contact matrix including within- and between-group contact rates
cmatrix <- c(
  c(0.9, 0.05, 0.05),
  c(0.1, 0.8, 0.1),
  c(0.1, 0.2, 0.7)
) |> matrix(byrow = TRUE, nrow = 3) * 15

N <- 9e3

measles_model <- ModelMeaslesMixingRiskQuarantine(
  n                        = N,
  prevalence               = 1 / N,
  transmission_rate        = 0.9,
  vax_efficacy             = 0.97,
  incubation_period        = 10,
  prodromal_period         = 3,
  rash_period              = 7,
  contact_matrix           = cmatrix,
  hospitalization_rate     = 0.1,
  hospitalization_period   = 10,
  days_undetected          = 2,
  quarantine_period_high   = 21,
  quarantine_period_medium = 14,
  quarantine_period_low    = 7,
  quarantine_willingness   = 0.9,
  isolation_willingness    = 0.8,
  isolation_period         = 10,
  prop_vaccinated          = 0.95,
  detection_rate_quarantine = 0.5,
  contact_tracing_success_rate = 0.8,
  contact_tracing_days_window = 4
)

# Adding the entities to the model
measles_model |>
  add_entity(e1) |>
  add_entity(e2) |>
  add_entity(e3)

set.seed(331)
run(measles_model, ndays = 100)
summary(measles_model)

Description

Implements a Susceptible-Latent-Infectious-Hospitalized-Recovered (SLIHR) model for Measles within a school. The model includes isolation of detected cases and optional quarantine of unvaccinated individuals.

Usage

ModelMeaslesSchool(
  n,
  prevalence = 1,
  contact_rate = 15/transmission_rate/prodromal_period,
  transmission_rate = 0.9,
  vax_efficacy = 0.97,
  incubation_period = 12,
  prodromal_period = 4,
  rash_period = 3,
  days_undetected = 2,
  hospitalization_rate = 0.2,
  hospitalization_period = 7,
  prop_vaccinated = 1 - 1/15,
  quarantine_period = 21,
  quarantine_willingness = 1,
  isolation_period = 4,
  ...
)

ModelMeaslesQuarantine(...)

Arguments

Details

This model can be described as a SLIHR model with isolation and quarantine. The infectious state is divided into prodromal and rash phases. Furthermore, the quarantine state includes latent, susceptible, prodromal, and recovered states.

The model is a perfect mixing model, meaning that all agents are in contact with each other. The model is designed to simulate the spread of Measles within a school setting, where the population is assumed to be homogeneous.

The quarantine process is triggered any time that an agent with rash is detected. The agent is then isolated and all agents who are unvaccinated are quarantined (if willing). Isolated agents then may be moved out of the isolation in isolation_period days. The quarantine willingness parameter sets the probability of accepting quarantine. If a quarantined agent develops rash, they are moved to isolation, which triggers a new quarantine process.

The basic reproductive number in Measles is estimated to be about 15. By default, the contact rate of the model is set so that the R0 matches 15.

When quarantine_period is set to -1, the model assumes there is no quarantine process. The same happens with isolation_period. Since the quarantine process is triggered by an isolation, then isolation_period = -1 automatically sets quarantine_period = -1.

The model uses hospitalization rates instead of probabilities. To learn more about this, see the documentation in ModelMeaslesMixing().

Value

• The ModelMeaslesSchool function returns a model of classes epiworldR::epiworld_model and epiworld_measlesschool.

Model diagram

Note

As of version 0.10.0, the parameter vax_improved_recovery has been removed and is no longer used (it never had a side effect). Future versions may not accept it.

Author(s)

This model was built as a response to the US Measles outbreak in 2025. This is a collaboration between the University of Utah (ForeSITE center grant) and the Utah Department of Health and Human Services.

References

Jones, Trahern W, and Katherine Baranowski. 2019. "Measles and Mumps: Old Diseases, New Outbreaks."

Liu, Fengchen, Wayne T A Enanoria, Jennifer Zipprich, Seth Blumberg, Kathleen Harriman, Sarah F Ackley, William D Wheaton, Justine L Allpress, and Travis C Porco. 2015. "The Role of Vaccination Coverage, Individual Behaviors, and the Public Health Response in the Control of Measles Epidemics: An Agent-Based Simulation for California." BMC Public Health 15 (1): 447. doi:10.1186/s12889-015-1766-6.

"Measles Disease Plan." 2019. Utah Department of Health and Human Services. https://epi.utah.gov/wp-content/uploads/Measles-disease-plan.pdf.

See Also

epiworld-methods

Other Models: ModelMeaslesMixing(), ModelMeaslesMixingRiskQuarantine()

Other measles models: ModelMeaslesMixing(), ModelMeaslesMixingRiskQuarantine()

Examples

# An in a school with low vaccination
model_measles <- ModelMeaslesSchool(
  n = 500,
  prevalence = 1,
  prop_vaccinated = 0.70
)

# Running and printing
run(model_measles, ndays = 100, seed = 1912)
model_measles

plot(model_measles)

Description

A dataset containing population information for the Short Creek area (Hildale city, Utah, Colorado City town, Arizona, and Centennial Park, Arizona) organized by age groups.

Usage

short_creek

Format

A data frame with 15 rows and 4 columns:

age_labels

character. Labels describing the age groups.

agepops

numeric. Population counts for each age group.

agelims

numeric. Age limit boundaries for each group.

vacc_rate

numeric. Vaccination rate for each age group.

Details

This dataset provides demographic information for the Short Creek area (Hildale city, Utah, Colorado City town, Arizona, and Centenial Park, Arizona), with population data disaggregated by 15 age categories. This dataset matches the short_creek_matrix matrix.

This data uses real vaccination rates from publicly available school records, and population age structure and composition from the latest US census. Vaccination rates for the non-school-aged population were imputed based on assumptions and do not reflect the actual vaccination information for those age groups.

Source

The data was generated using the multigroup.vaccine R package: Toth D (2025). multigroup.vaccine: Multigroup Vaccine Model. R package version 0.1.0, commit 3047ebf568c9b2028336dc14af587a282de9e225, https://github.com/EpiForeSITE/multigroup-vaccine. The source code is available at https://github.com/UofUEpiBio/measles

Examples

data(short_creek)
head(short_creek)

Description

A matrix containing spatial data for the Short Creek area (Hildale city, Utah, Colorado City town, Arizona, and Centenial Park, Arizona). The matrix provides an estimate of the mixing rates between schools and the rest of the population in the area.

Usage

short_creek_matrix

Format

A row-stochastic matrix (rows add up to one) with 15 rows and 15 columns with the

Source

The data was generated using the multigroup.vaccine R package: Toth D (2025). multigroup.vaccine: Multigroup Vaccine Model. R package version 0.1.0, commit 3047ebf568c9b2028336dc14af587a282de9e225, https://github.com/EpiForeSITE/multigroup-vaccine. The source code is available at https://github.com/UofUEpiBio/measles