Time-Inhomogeneous Adult Mortality
Let us consider the case where we want to simulate a model in which
the transitions made by functions
make_transition_male_mort() and
make_transition_female_mort(), that is, the adult male and
female mosquito mortality, fire at a rate which depends on time. This
time-dependence can in general be arbitrarily complex, as long as the
rate function returns a non-negative number at any positive time \(t>0\) when it is queried. Therefore
various time-inhomogeneous effects can be taken into account in
MGDrivE2, from long-term climactic and seasonal
changes, to rapidly oscillating changes from diurnal cycles.
Sample data included in MGDrivE2
(mu_ts) provides estimated time-dependent adult mortality
rates from the Comoros Islands, between Mozambique and Madagascar. These
are hourly death rates over the course of an entire year, for Grande
Comore, Moheli, and Anjouan.
First, we load the mu_ts object, which is a matrix of
hourly death rates. Now we want to interpolate the death rates into a
function that can return a death rate at any time in the interval \(0<t<365\). We could do this with a
variety of methods, including splines and other smoothing algorithms,
but for now we will use a simple step function with steps every hour,
created with the function stepfun().
# load mortality data
data(mu_ts)
# vector of hourly timesteps
# unit is in days, so 24 steps per day, 365 days
tt_ts <- 1:nrow(mu_ts)/24
# exaggerated amplitude of Grande Comore mortality rate, for visual effect
mu_ts_par <- mu_ts[ ,1] + ( (mu_ts[ ,1] - mean(mu_ts[ ,1]) ) * 50)
# approximating step function
step_approx <- stepfun(x = tt_ts, y = c(mu_ts_par[1], mu_ts_par),
f = 0, right = FALSE)For clarity, we plot the approximating function evaluated at each hour over the year:
# long-form for ggplot2
df_ts <- data.frame("time" = tt_ts, "mu" = step_approx(v = tt_ts))
# plot
ggplot(data = df_ts) +
geom_line(aes(x = time, y = mu), alpha = 0.75, color = "dodgerblue4") +
xlab("Time (days)") +
ylab("Adult Mortality") +
theme_bw() +
ggtitle("Grande Comore: Hourly Death Rates for One Year")
We see that the data trends in a cyclic manner, consistent with proposed seasonality throughout the year. Mosquito mortality is highest in the early spring (days 50-150, approximately March to the end of May) and around the end of the year (days 325-365, the end of November through December).
