SEIR4AgeClasses {EpiDynamics}

SEIR model with 4 age classes and yearly aging (P 3.4).

Description

Solves a SEIR model with four different age-groups and yearly "movements" between the groups mimicking the school year

Usage

SEIR4AgeClasses(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with: a matrix with the transmission rates, the rate at which individuals move from the exposed to the infectious classes, the recovery rate, a vector with death rates in each age group, and a vector with birth rates into the childhood class. The names of these elements must be "beta", "sigma", "gamma", "mu", and "nu", respectively, see example.

init

vector with 16 values: initial proportions of the population that are susceptible, exposed, infectious and recovered in a particular age group. The vector must be named, see example. Requirements: S + E + I <= n for each age group and all values must be positive.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.4 from page 87 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All rates are specified in days. Moreover, a vector n with the proportion of each age group. All parameters must be positive.

Value

list of class SolveSIR4ACYA. The first element, *$model, is the model function. The second, third and fourth elements are vectors (*$pars, *$init, *$time, respectively) containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, exposed, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

See Also

ode.

Examples

# Parameters and initial conditions.
parameters <- list(beta = matrix(c(2.089, 2.089, 2.086, 2.037,
                                   2.089, 9.336, 2.086, 2.037,
                                   2.086, 2.086, 2.086, 2.037,
                                   2.037, 2.037, 2.037, 2.037),
                                 nrow = 4, ncol = 4),
                    sigma = 0.125, gamma = 0.2,
                    mu = c(0, 0, 0, 1) / (55 * 365),
                    nu = c(1 / (55 * 365), 0, 0, 0),
                    n = c(6, 4, 10, 55) / 75)
                          
initials <- c(S = c(0.05, 0.01, 0.01, 0.008), 
              E = c(0.0001, 0.0001, 0.0001, 0.0001),
              I = c(0.0001, 0.0001, 0.0001, 0.0001),
              R = c(0.0298, 0.04313333, 0.12313333, 0.72513333))

# Solve and plot.
# Uncomment the following lines (running it takes more than a few seconds):
# seir4.age.classes <- SEIR4AgeClasses(pars = parameters, 
#                                      init = initials,
#                                      time = 0:36500)
# PlotMods(seir4.age.classes,
#          variables = c('I1', 'I2', 'I3', 'I4'), grid = F)