?xds_setup_cohortCohort Dynamics
In some cases, it’s useful to explore the relationship between exposure and malaria epidemiology by comparing different cohorts in the same population. For this, we developed some utilities for cohort dynamics that gete set up by xds_setup_cohort(). Models returned by xds_setup_cohort() lack the MYZ and L components.
The function xds_setup_cohort() differs from other trace functions in ramp.xds in several ways. The function is defined with respect to age (\(a\)) for a cohort born on day \(\tau\), but average exposure is evaluated at time \(t=a+\tau\), so:
\[F_E(a, \tau) = E \times \omega(a) \times F_S(t=a+\tau) \times F_T(t=a+\tau)\] + \(E\) is the mean daily EIR:
\(\omega(a)\) is a function that modifies the daily EIR with respect to age;
\(F_S(t)\) is a seasonal pattern;
\(F_T(t)\) is a trend.
Since the return value is a product, the defaults return \(1.\)
If you read Trace Functions, then you already know, in principle, how to configure \(F_S\) and \(F_T\) using make_function. Configuration of \(\omega(a)\) works in the same way. Using xds_setup, these are passed from setup:
F_seasonis a function of time;season_paris a parameter list formake_functionF_trendis a function of time;trend_paris a parameter list formake_functionF_ageis a function of age;age_paris a parameter list formake_function
If season_par or trend_par or age_par is not an empty list, then the resulting functions get set up by make_function.
The function can be configured with a seasonal pattern (over time, \(t\)), an inter-annual trend (over time, \(t\)), an age weight (over age, \(a\)), and a scaling term for the mean. Since a person’s age is \(a = t-\tau,\) where \(\tau\) is the birth date,