diff --git a/.Rbuildignore b/.Rbuildignore
index e5e2817..d672781 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -4,4 +4,5 @@
 function_list\.ods
 popim goals and terminology\.docx
 inst/extdata/data-raw/*
+inst/extdata/hide/*
 ^\.github$
diff --git a/man/as_vacc_activities.Rd b/man/as_vacc_activities.Rd
index 2d6515e..2571ce3 100644
--- a/man/as_vacc_activities.Rd
+++ b/man/as_vacc_activities.Rd
@@ -19,7 +19,7 @@ columns and data ranges), and if so converts it to a
 \code{popim_vacc_activities} object and returns this.
 }
 \details{
-The input dataframe has to have at least teh columns \code{region},
+The input dataframe has to have at least the columns \code{region},
 \code{year}, \code{age_first}, \code{age_last}, \code{coverage}, \code{doses} and
 \code{targeting}. Any further columns are simply carried over into the
 \code{popim_vacc_activities} object.
diff --git a/vignettes/popim.Rmd b/vignettes/popim.Rmd
index 3b05a84..1e7df00 100644
--- a/vignettes/popim.Rmd
+++ b/vignettes/popim.Rmd
@@ -120,14 +120,6 @@ The mandatory columns are:
 * `targeting`: determines how doses are allocated when there is
   pre-existing immunity in the population.
 
-*to do: details of coverage/doses, include assumptions of non-waning,
-100% effectiveness, no wastage.*
-
-*to do: explain targeting.*
-
-
-
-
 | column      | type      | range             |
 |-------------|-----------|-------------------|
 | `region`    | character |                   |
@@ -138,6 +130,10 @@ The mandatory columns are:
 | `doses`     | numeric   | non-negative      |
 | `targeting` | character | `"random"`, `"correlated"`, `"targeted"` |
 
+##### Relationship between coverage, doses and target population
+
+*to do*
+
 #### Class attributes
 
 As this is a subclass of dataframe, it has the same attributes as a
@@ -153,7 +149,7 @@ modify: `complete_vacc_activities()`
 
 validate: `validate_vacc_activities()`
 
-## Primary functionality
+## Primary functionality: applying vaccination activities to a population
 
 Once objects holding data on the population and vaccination activities
 have been set up, the primary functionality provided by `popim` is to
@@ -162,13 +158,120 @@ population immunity by age over time that results from the given
 vaccination activities, which is done with the function
 `apply_vacc()`.
 
-using coverage information by preference, doses if coverage isn't available.
+### Assumptions when applying vaccination activities to the population
+
+* 100% vaccine effectiveness
+* is no wastage of doses
+* no waning immunity
+* mortality is independent of immunity status
+
+While the first two are clearly unrealistic assumptions, if there is a
+constant vaccine effectiveness (<100%), or a constant wastage factor,
+the results can easily be scaled up by these constant factors to
+obtain more realistic values for vaccine demand.
+
+For a potentially deadly disease one would expect that mortality due
+to the disease would be strongly correlated with immunity status,
+however, even the most devastating outbreaks typically only affect a
+small part of the population, and therefore all-cause mortality will
+be much less impacted by mortality due to the specific disease. This
+means that this assumption is closer to reality than it might appear
+at first.
+
+Waning immunity is a potentially important factor to consider for many
+vaccines, particularly when looking at the long term benefits of
+vaccination. However, allowing for this is currently not implemented.
+
+### Description of the algorithm
+
+The vaccination activities object has columns for `coverage`, the
+proportion ofthe target population that will be vaccinated, and
+`doses`, the number of vaccine doses to be administered in the
+activity. Given a target population size this is redundant (and
+potentially conflicting) information. The function `apply_vacc()` will
+always use `coverage` information in preference over `doses`, if this
+is non-missing. If `coverage` is missing, the target population size
+(based on the population size of the region and age groups targeted)
+will be calculated and the corresponding `coverage` calculated as
+`doses` / `target_population`.
+
+#### Vaccinating a cohort with no previous immunity
+
+When vaccination is applied to a particular birth cohort that has no
+immunity, the result is simply that the proportion of the cohort
+receiving the vaccine will be immune from the time of the vaccination
+onwards, i.e., the immunity for this cohort will be set to equal the
+coverage of the vaccination activity in question. Due to the annual
+time step, vaccination is assumed to take effect at the end of the
+year in which it is implemented, so the immunity is updated from the
+next year onwards.
+
+#### Vaccinating a cohort with previous immunity
+
+When a vaccination activity is applied to a cohort that has some
+previous immunity, we need to make some assumptions about who will be
+vaccinated in the new activity. There are 3 different options
+implemented which are governed by the parameter `targeting`, one of
+the input parameters to the function `apply_vacc()`. This parameter
+can take the values `"targeted"`, `"random"` or `"correlated"`.
+
+##### `"targeted"` targeting
+
+The most effective way to implement a new vaccination activity is to
+use `"targeted"` targeting, meaning that the vaccine is targeted at
+previously non-immunised individuals. This means that the new immunity
+of after the vaccination activity is simply the sum of the previous
+immunity and the coverage of the current vaccination activity (capped
+by 1 which indicates complete immunity):
+
+$$
+\rm{immunity}_{\rm new} =
+\min(\rm{immunity}_{\rm prev} + \rm{coverage}, 1)
+$$
+
+While this is not a realistic assumption in many settings, it can be
+useful for instance in multi-year campaigns that target the same
+region (but possibly proceed sub-region by sub-region) over several
+years. This multi-year campaign would be coded as separate vaccination
+activities for each year, using the option `targeting` = `"targeted"`.
+
+##### `"random"` targeting
+
+A reasonable first assumption might be to use `targeting` =
+`"random"`, meaning that individuals will receive vaccination
+irrespective of their previous immunity status.
+
+$$
+\rm{immunity}_{\rm new} =
+\rm{coverage} + \rm{immunity}_{\rm prev} -
+\rm{coverage}*\rm{immunity}_{\rm prev}
+$$
+
+##### `"correlated"` targeting
+
+On the opposite end of the spectrum is the most pessimistic assumption
+that might apply in situations where there is unequal access to
+vaccination: under `"correlated"` targeting, people who have
+previously been immunised get vaccinated first in the new vaccination
+activity, and those previously not immune will only receive any
+vaccine if the new coverage extends further:
+
+$$
+\rm{immunity}_{\rm new} =
+\max(\rm{immunity}_{\rm prev}, \rm{coverage})
+$$
+
+
+
+Note that the order in which vaccination activities are applied to a
+population does not matter.
+
+
+
+
+
 
-put coverage into birth cohort from year of vaccination into the
-future (no waning immunity), other assumptions: 100% effectiveness of
-the vaccine, 0 wastage.
 
-If pre-existing immunity: explain targeting.
 
 ### The inverse