Parameters and literature references

This vignette documents the parameters of the measles models in this package: their default values, where those values come from, and how far each has been verified. The same information is available as a data frame through measles_parameters(), which reads the file inst/extdata/measles_parameters.csv. That file is the canonical parameter table for our measles projects; projects that use different values should list them next to the package defaults and explain why.

library(measles)

Loading required package: epiworldR

Thank you for using epiworldR! Please consider citing it in your work.
You can find the citation information by running
  citation("epiworldR")

Using measles in your research? Please cite it: citation("measles")

params <- measles_parameters()

The parameter table

Each row of the table is a parameter, with its default value, units, and source. The current edition of the Utah DHHS Measles Disease Plan cited here was last updated on March 26, 2026 (footer dated February 2026) (Utah Department of Health and Human Services 2026).

The models column lists the functions that take each argument. For instance, the parameters of ModelMeaslesSchool() are:

measles_parameters("ModelMeaslesSchool")[, c("r_argument", "default", "units")]

               r_argument
1                       n
2              prevalence
3         prop_vaccinated
4       transmission_rate
5            contact_rate
6       incubation_period
7        prodromal_period
8             rash_period
9            vax_efficacy
10   hospitalization_rate
11 hospitalization_period
12        days_undetected
13       isolation_period
14      quarantine_period
15 quarantine_willingness
                                                Default (units)
1                                                              
2                                      1 (agents or proportion)
3                                         1 - 1/15 (proportion)
4                                             0.9 (per contact)
5  15 / transmission_rate / prodromal_period (contacts per day)
6                                                     12 (days)
7                                                      4 (days)
8                                                      3 (days)
9                                   0.97 (per vaccinated agent)
10                                                0.2 (per day)
11                                                     7 (days)
12                                                     2 (days)
13                                                     4 (days)
14                                                    21 (days)
15                                                1 (per agent)

InterventionMeaslesPEP() has no default values; the table lists the values used in vignette("school").

Calibrating to R0

Measles is highly transmissible, with a basic reproduction number (R0) usually reported between 12 and 18 (Guerra et al. 2017). Our models target R0 = 15, the midpoint of that range, which implies a herd-immunity threshold of 1 − 1/R₀ ≈ 93%.

Instead of estimating both the transmission probability and the contact rate, we fix the transmission probability at a high value (0.9, consistent with the Utah DHHS plan statement that 90% of susceptible contacts develop disease) and calibrate the number of contacts to match the target R0.

In ModelMeaslesSchool(), agents are infectious during the prodromal period only (detected cases with rash are isolated), so

R₀ = p_t × c × D_p,

where p_t is transmission_rate, c is contact_rate, and D_p is prodromal_period. The default contact rate solves this equation for R0 = 15:

15 / 0.9 / 4

[1] 4.166667

In the mixing models, the contact matrix holds the expected number of contacts between groups. The next-generation-matrix method (Diekmann et al. 2010) gives R0 as the spectral radius of the matrix of expected secondary infections. calibrate_mixing_model() finds the factor that scales the contact matrix so it matches the target R0. When agents with rash are not fully isolated (rash_reduction_contact_rate < 1 in ModelMeaslesMixing()), the infectious period used for calibration is D_p + (1 − r_r)D_r, where D_r is the rash period and r_r is the reduction in contacts during rash.

Hospitalization: rate vs probability

The models take a daily hospitalization rate, not a probability. During the rash period, an agent competes between hospitalization (rate h) and recovery (rate 1/D_r), so the probability of being hospitalized is

$$ P(\text{hospitalization}) = \frac{h}{h + 1/D_r}. $$

With the defaults, h = 0.2 and D_r = 3 days, this probability is:

h <- 0.2
rash_period <- 3
h / (h + 1 / rash_period)

[1] 0.375

To match a target probability p, invert the formula, h = p × (1/D_r)/(1 − p). For example, recent analyses use p = 0.1, which is consistent with the 8% overall (9% among the unvaccinated) reported in Utah (Jones et al. 2026):

p_hosp <- 0.1
p_hosp * (1 / rash_period) / (1 - p_hosp)

[1] 0.03703704

The default of 0.2 is an assumption, chosen as a conservative value. For comparison, 18.5% of patients were hospitalized during the 2025 outbreak in West Texas (Wang et al. 2026).

Inactive parameters

The argument vax_reduction_recovery_rate of ModelMeaslesMixing() is not active. The C++ model registers it as “(IGNORED) Vax improved recovery”, and it has no effect on the simulations. ModelMeaslesSchool() no longer takes it.

References