Age-structured model inputs for human and pig demographics

In the age-structured model, human and pig compartments are stratified into age groups. For pigs, there are 150 age groups (one month per group) in the default model, which can be viewed (and modified) through the following input number_age_classes_pig = 150 for the number of pig age classes, and pig_age_class_width = 1 for the width (in months) of these age groups.

For humans in the default model, there are 7 age groups, representing 0 - 4.99, 5 - 9.99, 10 - 14.99, 15 - 29.99, 30 - 49.99, 50 - 69.99 and 70 - 89.99 years. These age groups are structured to include school-age children (5 - 9.99 & 10 - 14.99 yrs). While there is an input to change these number_age_classes_human = 7, currently EPICYST is not configured to enable differing numbers of human age classes (future developments will address this).

Figure 1 below provides a representation of the age-structure in the model, including demographic and transmission parameters.

Other key input parameters in the age-structured pig model

Input parameters into set_up() specify additional age-specific features in the pig age-structured model. Firstly, the slaughter_age_min = 6 input specifies the minimum age (in months) in which pigs are slaughtered, which is set to 6 months in the default model. Secondly, the slgEP = 1 specifies the number of years pigs are expected live, on average, after reaching slaughter age (a default for the average natural life expectancy for pigs is also specified by LEP = 10).

Figure 2 below highlights how pig demographics have been incorporated into the age-structured EPICYST, which simulates pigs before the minimum slaughter age experiencing a constant natural mortality rate (dP; the reciprocal of the natural life expectancy parameter, LEP), and pigs after reaching the minimum slaughter age experiencing an additional mortality rate associated with reduced survival due to slaughter (dPslg; the reciprocal of the average life expectancy after reaching slaughter age, slgEP). Equally, humans are only exposed to infected pork from slaughter age animals.

Other modifiable parameter inputs, impacting baseline demographic parameters in set_up(), human population size HPS, pig population size PPS, human life expectancy (in years) LEH, and the rate of pork meal procurement in humans chi.

EPICYST can also be parameterised for specific epidemiological conditions by specifying epidemiological parameters in set_up(), including Egg to pig transmission coefficient tau_input, Egg to pig transmission coefficient theta_input, Pig to human transmission coefficient beta_input, and the proportion of pigs with low-cyst burden phi.

Diagnostic adjustment to adjust true modelled prevalence to observed modelled prevalence

The user can also specify diagnostic parameters in set_up() to adjust modelled prevalence to observed/apparent prevalence by providing the sensitivity and specificity characteristics of a particular diagnostic test. This will allow the user to plot both the true modelled prevalence, and adjusted observed/apparent prevalence, as described in Figure 3 below

To run this in the model, this can be specified as (e.g. with a hypothetical 90% sensitivity and 80% specificity of a porcine cysticercosis diagnostic test) :

# Set up the model, specifying diagnostic parameters for pig cysticerosis prevalence adjustment
 s1 <- set_up(PC_sens=0.9, PC_spec=0.8)
# Run the model, with new input parameters and initial conditions
 m4 <- run_model(time = 50, burn_in = 100, params = s1[[1]], initial_states = s1[[2]])

Specifying the non age-structured model

The age-structured model can be configured to remove age-structuring, and therefore provide the original model presented in Winskill et al. 2017. To specify the non age-structured model, the following parameter inputs need to be included in set_up(). :

# Set up the model, specifying the non age-structured model
 s1 <- set_up( number_age_classes_human = 1, number_age_classes_pig = 1, slaughter_age_min = 0)
# Run the model, with new input parameters and initial conditions
 m5 <- run_model(time = 50, burn_in = 100, params = s1[[1]], initial_states = s1[[2]])

This will collapse age groups so that only one age group is modelled for human and pig state variables:

If the user wishes to specify the complete original model presented in Winskill et al. 2017 with no age-structuring, and no pre-patent compartment in pigs (Pp compartments in Figure 1), then the user can set the rate at which pigs progress from the pre-patent compartment to a very high value (by setting the average duration pig remain in the pre-patent compartment parameter psi to a very small value i.e. 1 / 0.0000001) to effectively negate the use of this compartment as follows:

# Set up the model, specifying the non age-structured model
 s1 <- set_up( number_age_classes_human = 1, number_age_classes_pig = 1, slaughter_age_min = 0,
               psi = 1/ 0.0000001)
# Run the model, with new input parameters and initial conditions
 m6 <- run_model(time = 50, burn_in = 100, params = s1[[1]], initial_states = s1[[2]])

# Plot the output in base R
plot(m6$Pig_Cysticercosis_prev*100 ~ m6$t, type="l", col="darkmagenta", ylim=c(0,30), ylab = 'prevalence (%)', xlab = 'time (months)')
lines(m6$Human_Cysticercosis_prev*100 ~ m6$t, type="l", col="deeppink")
lines(m6$Human_Taeniasis_prev*100 ~ m6$t, type="l", col="dodgerblue")
legend('topright', c('porcine cysticercosis', 'human cysticercosis', 'human taeniasis'), lty = c(1, 1, 1),
       col=c('darkmagenta', 'deeppink', 'dodgerblue'))

The user should note that the model has been updated to include a pre-patent period in pigs given that pigs are generally slaughtered within 6-36 months of age, and the pre-patent period (time from oncosphere/egg exposure to developing a mature larval-stage infection) is 2-3 months, so this is a non-negligible time period compared to the life-expectancy of the pig. Therefore, the pre-patent period should be included in the model.

Guidance for modelling interventions in age-structured EPICYST can be found in the next vignette: