Table of Contents
Stock / Flow models of blood donor restrictions: Why the vCJD problem is worse than
expected.
Tim Haslett
Department of Management
Monash University
Email: thaslett@bigpond.net.au
Abstract
This paper examines the impact of restrictions to blood donations to examine the dynamics of
the interactions between the restrictions, on one hand, and the existing donor base and the
eligible donor base, on the other. The paper suggests that when the impact of restrictions such
as those imposed for the outbreak of vCJD in the US and Australia, are modeled using
stock/flow analysis, the results suggest a much greater loss of donations than is suggested in
the literature. The paper discusses simulations of both the Australian and UK blood services
and suggests that there are similar dynamics in both systems. The required recruitment
patterns to recover from the losses were modeled and discussed.
Introduction
The Australian Red Cross Blood Service (ARCBS) is responsible for the all of the collection
and distribution of blood products in Australia and the National Health Service (NHS) has a
similar role in the UK. Both systems operate on a voluntary donation basis. This means that
the supply of blood products to the health system is very much dependent on the nature of the
relationship built up between the donors and the ARCBS and NHS. _ Recruiting and
maintaining a donor base consisting of people who regularly give the maximum of four
donations the year is therefore, a major concern for both organizations.
Restrictions to eligible donors, such as those associated with HIV, vCJD (Variant Creutzfeldt-
Jakob Disease also known as Mad Cow Disease) and Hepatitis all have an impact on the
existing donor base and, as a consequence the level of blood stocks. The outbreak of Mad
Cow disease raised the possibility of the disease being transferred through blood transfusion.
The medical aspects of the threat posed by this have been widely documented (Leikola,
(1998), Mitka (2001), Germain et al (2000), Sibbald, (1999), Hoey et al (1998), Payne, (2001)
and Jones, (2003). A number of countries imposed restrictions on blood donations imported
from European countries affected by the outbreak and on people who had traveled to those
countries.
The issue addressed in this paper
This paper examines the output of two System Dynamics models which the simulate the
donor losses as a result of the imposition of donor restrictions based on travel to areas
considered to place donors at risk of contracting vCJD. The model assumes the loss rate of
7.5% suggested by the Review of the Australian Blood Banking and Plasma Product Sector
March 2001 A report to the Commonwealth Minister for Health and Aged Care and
demonstrates that the estimated losses predicted in the Review significantly underestimate the
extent of the problem.
The issue is important for two reasons. First, introducing large step function losses into blood
systems will leave the system short of blood for lengthy periods of time because of the
boom/bust nature of donor behavior in times of shortage. Second, understanding the impact of
such decisions may lead to the examination of different policy options. In the UK, which was
worst hit by vCJD, imposing restrictions such as those imposed in the US and Australia would
have wiped out the entire donor base, as everyone would have potentially been exposed to the
disease. As a result , UK blood authorities adopted a totally different approach.
System Dynamics methodology is important in addressing this issues for two reasons. The
separation of the total donor base into stocks defined as annual donation frequency segments.
This allows the modeling of the differential impact of the any restrictions on each donation
frequency segment. While a simple distinction, the implications of this are profound. Defining
donation frequency segments demonstrates the feedback effect of deferring donors on the
recruitment of new donors. It also allows the "feed-forward" impact of the donation rates of
new donors to be simulated. The second reason is that it becomes possible to model the
feedback of policies designed to recover deferred donors. For example, it is possible to retain
a donor deferred under the vCJD restrictions, by placing them in an apheresis donation
program.
It is therefore extremely important that blood authorities develop models that increase the
accuracy of prediction of donor restrictions.
Background
The Australian and UK systems operate on a voluntary donation basis. Recruiting and
maintaining a donor base of people who regularly give the maximum of four donations the
year is therefore a major goal for both organizations. The reality falls far short of this, as the
donation rate across Australia is 1.9 donations per donor per year. However, this compares
favourably with the UK where the rate is 1.2 per year. Donation frequency varies across the
donor base. Table 1 shows the numbers in each donor segment
Donation Frequency by Donor Category
250,000
200,000 +
150,000 7~—4
Donors
100,000 7—J
50,000 7-4 im
C) 7
1 2 3 4 5
Donations per year
Table 1: Donation frequency by donor segment
Donors who give four and five times a year represent 12% of the donor base but provide 27%
of the donations. This means that any donor restrictions that affect these segments have a
disproportionately high impact on blood donations and blood stocks.
Australian Red Cross Blood Service
Across Australia, the state divisions of the ARCBS frequently find themselves in a situation
where blood supplies reach critical levels. There are a number of reasons for this including
increased demands as a result of road trauma over the Easter holiday period, lower donation
rates during winter and the "Beer Game" effect of the appeals to cover these shortages. In
general, it would be said that the balance between supply and demand is very delicate. Any
measures, which restrict the number of eligible donors, can have profound impacts on the
supply side of the ARCBS operation. The following discussion of the impact of vCJD
restrictions outlines some of the problems of predicting the impact of donor restrictions and
the need for modeling and scenario building.
Predicting the impact of restrictions on donor eligibility: vCJD.
There is currently no known screen for vCJD, a disease that is degenerative and terminal. This
poses an ethical and practical problem for Blood Agencies. Growing recognition and
discussion of the possible danger posed by blood infected by vCJD has led to wide-spread and
differing responses to the problem. One response has been restrictions in donor eligibility,
most notably on people who have traveled to, or were resident in, Europe. Another has been
the use of processing technology, namely leucodepletion, to reduce the risk.
In 1999, the US Federal Drug Administration (FDA) banned donations from people who spent
5 or more years in Europe between 1980 and1996. By June of 2001, the Red Cross, which
collects 50% of blood in the USA , had been extended this ban to include a range of people
who been in Europe. (see http://www.redcross.org/news/bm/tse/010628madcow.html)
The response to the enormity of the impact of the restrictions was an '" aggressive donor
recruitment campaign". This section of the paper looks at the hypothetical implications of this
response in Australia and in Great Britain, where the response had been to use processing
methodologies to avoid contamination through vCJD.
In Australia, where the response has been similar to that of the US.
The ARCBS has estimated that the measure is expected to result in an initial
reduction in donations of 5-10 per cent, leading to some 30,000 donors
eventually being deferred.
Review of the Australian Blood Banking and Plasma Product Sector March
2001 A report to the Commonwealth Minister for Health and Aged Care
The figure of 30,000 is actually predicated on a 7.5% loss. On these figures, and with the 1.9
annual donation rate, the expected loss would be 36,000 donations. If only donors are
considered, the answer would appear simple: recruit somewhere around 30,00 new donors.
However, the logic is wrong, it is the deferral of donors leads to the loss of donations, not the
other way around. The figure of 5-10 % is in line with overseas estimates of 7.5% loss of
donors. The problems inherent in this mental model are indicative of the problems that arise
in estimating, as distinct from modeling, the impact of these restrictions. The first step to an
accurate estimation of the problem is to separate the stocks of donors from the stocks of blood
and to understand their relationship.
Model history.
The model was developed in response to a move by the Therapeutic Goods Authority (TGA),
the Federal authority which legislates all health product standards in Australia, to lift for Hb
threshold for blood donors in Australia. Specifically, there was the need to model the impact
of two different levels of Hb which were to form the basis for new restrictions on blood
donors in Australia. These two standards were known as the Council of Europe and the UK
standard respectively. The TGA had a preference for the Council of Europe standard which
was the higher of the two. The simulation showed that the imposition of the standard did such
damage to the existing donor base, that the only way to recover would be to impose
compulsory blood donations on all adults in Australia. The simulation also demonstrated that
the imposition of the UK standard would need to be phased in over a three-year period for
there to be any chance that the donor losses could be recovered. The TGA accepted this
advice.
This model was originally developed using group modeling techniques. For the last two
years, the ARCBS has been developing a Systems Thinking and Systems Dynamics modeling
capability which meant that this model was developed with the group of experts who had
competence in causal loop diagramming and knowledge of the principles of stocks and flows.
The ARCBS also has a policy of building a dispersed Systems Thinking and Systems
Dynamics capability in all of its state branches.
The model was originally designed to be able to simulate any form of restriction on donors.
Legislated donor restrictions are an important strategic issue for blood donors services. It is
therefore important for blood services to have models to advise government on the impact the
type legislation. Restrictions related to vCJD are a current example of such legislation, or in
the case of the US, self-imposed regulation by the Red Cross Blood Service, being imposed
worldwide.
Model development methodology.
The model was derived from a series of causal loop diagrams developed with a group of
ARCBS experts. The group included specialist haematologists, medical directors, medical
scientists and logistics experts drawn from all state offices as well as from the National office.
The main-chain of the model was similar in structure to Sterman's aging chain (Sterman,
2000, p. 470). The advantages of using this structure were discussed at length with the group.
The cohorts that were used were termed "donor segments" which related to the frequency of
annual donations rather than an aging process. Sterman's transition rate was the rate at which
donors improve their donation rates. The out-flows from each of the segments were the rates
at which donors were deferred as a result of potential exposure to vCJD during travel to UK,
in this specific case, and the normal rate of deferrals associated with the medical screening
donors. The inflows to the segments were a result of the recovery of any temporarily deferred
donor.
Building the model with this structure allowed the ARCBS managers to examine a range of
strategies for dealing with the losses resulting from the vCJD restrictions. The usual method
for dealing with shortfalls in the donation levels was to recruit new donors. However, there is
a very high attrition rate in new donors, with as many as 75% not returning to give a second
donation. This attrition was worsened by the fact that a proportion of new donors were not
able to give blood as they were excluded under vCJD restrictions. It was therefore necessary
to look at alternative strategies, the use of apheresis donations, increased donation rates,
higher retention rates in new donors and the recovery of lapsed and deferred donors, all of
which could be stimulated through this model structure.
The development of a working model proved relatively easy. Accessing accurate data was
more difficult. The ARCBS is a federal system with each state keeping its own records. The
development of a general national model provides indications the impact of high-level
strategies. However, in the case of Hb restrictions, there was significant variation between the
States in the levels of Hb within the populations. This was thought to be a result of cultural
differences in dietary practices arising from the early colonization of various states. In
relation to vCJD, where the restrictions are related to travel to the UK, it is not yet fully
understood whether there is an interaction between the demographics of those travelers,
possibly in older age groups, and the frequency of donations, possibly also higher in older age
groups. The result was modeling exercise has been a significant upgrading of the database of
ARCBS.
What Stock/Flow models explain about the problem.
There are two stages to understanding why the impact of vCJD could so easily have been
underestimated. The first is in understanding the stock- flow structure shown in Figure 1. In
this basic model, deferrals of donors drives recruitment efforts, deferred donors are usually
replaced by new recruited donors. Sterman's (2000) model of product discard and replacement
purchases shows discarded adopters becoming (again) potential adopters. This is partly true of
blood donors. Those who are deferred either permanently or temporarily are seen as distinct
from potential donors and are treated differently by blood services. In the model these
deferred donors are classified according to the reason for deferral, a donor deferred because
they have a cold will be classified differently from one who tests positive to HIV. These
deferred donors are held in separate databases and specific strategies, such as iron
supplementation for iron deficient deferrals, can be used to move then back into the donor
bases much as occurs with the Sterman model. A central problem for blood service is the lack
of information about potential donors. This is becoming acute with restrictions for vCJD and
for haemoglobin levels affecting the potential donor pool (Haslett and Bird, 2002).
oH ps
i Deferral:
Recruitment ponor Base
Doantion ra’
Q LO38
Units i
Blood Stock
Figure 1: Simple Stock/Flow model of the donor system
Blood stocks are a results of the number of donors and the rate of donation. Losses through
deferrals (permanent, in the case of vCJD) are traditionally replaced by recruitment. The
problem with this model is that it simplifies the nature of the donor base. The donor base is
really a chain (termed a main chain in System Dynamics terminology), as shown in Figure 2.
DONS. #2 Donors x 2 Donors x 3 Donors x 4 Donors x 5
est 1s 5 5 om
Recruitment Conversion to Conversion to Conversion to 7 Conversion to 5
Deferrals x Deferrals x 2 Deferrals x 3 Deferrals x 4 Deferrals x
b> 8 4 & 48
Figure 2: Main chain of donor segments.
This model makes clear that losing a donor from the Donors x 5 stock means a loss of five
donations per year, every year from the time of the imposition of the restriction. Using the
Australian figures, it is possible to model the impact of a 5% and 10% donor loss from the
first year of restrictions. It also highlights an important assumption in the model: that donors
improve their donation rates over time.
The models
There were two models used in these simulations. The more complex of the two was used to
model the Australian blood service. This model was originally developed to model the impact
restrictions of new levels for Hb in donors. However, it was also designed to model of wide
range of scenarios, one of which was the restriction in relation vCJD. The model, which is a
development of the one shown in Figure 2, is shown in Figure 3.
Figure 3: ARCBS model for donor restrictions.
It consists of a main chain of donors segmented by donation frequency. In the top left-hand
comer of the diagram are a series of decision nodes representing points at which new donors
are deferred before giving blood.
The model assumes that new donors are distributed across the donors segments according to
the existing distribution of the donor base. This means that some new donors will begin
donating four times year from their recruitment. However, the vast majority of new donors do
not return to make second donation. Retention rates of new donors after their first donation
are modeled at 40%.
In the main chain, the donors segments are linked by flows. The model assumes
improvements in donation rates. These are the rates at which donors increase their annual
donation rate. These increases occur either as a natural course of events or in response to
appeals when blood stocks run low. The segment improvement rates in the Australian model
are shown in Table 2. The rate of 15% for 1 to 2 means that 15% of the 200,000 donors who
gave once a year convert to giving twice a year, and that this rate of improvement in donation
rates is maintained each year.
In the simulations, these increases in annual average donation rates meant that the annual
donation rate increased from 1.95 donations per year to 2.21 per year by the end of the
simulation period. In the UK model, a more conservative increase of 1.2 to 1.3 donations per
year was assumed. The models demonstrated high levels of sensitivity to changes in donation
rates. This is discussed in the sections on the individual models.
The out-flows from the donor segments were modeled underneath the stocks. These out-
flows model the donors are lost to the system. They may be permanently deferred, (as result
of medical condition such as a positive test to Hepatitis C.), temporarily deferred (as result of
having a cold), deferred by restrictions imposed from low Hb levels, deferred under travel
restrictions as a result of vCJD, or permanently lapsed (died, left the country). All these
deferrals, with the exception of the permanently deferred, are accumulated in stocks. This
allows the modeling of recovery strategies for these deferred groups.
There are in-flows into each donor segment. These are modeled on top of each of the
respective stocks. It is at this point that the results of the recovery strategies are flowed back
into the donor bases. The model assumes that a reactivated donor donates according to their
previous donation pattern.
The UK model, shown in Figure 4, was far a simpler model. The added complexity of the
recovery strategies in the Australian model has been left out. Most importantly, the donor
base is not modeled in donors segments. However, the UK model produced qualitatively
similar results to the more complex and sophisticated Australian. As such, this model can still
produce import insights to the dimensions of problems posed by policies relating to travel
restrictions and vCJD.
Simulation results for the ARCBS model
A single simulation was run with a loss rate from existing and new donors of 7.5% If
recruitment is was held at the rate ARCBS projected of 104,000 new donors per annum the
following shortfalls in donations occurred. This is the donation loss a result of the loss of
31,500 donors in going into 2004. . The impact of these losses is shown in Table 4.
Annual Shortfalls 2003 - 2010
190000
80000
60000 +
49000 +
Shortfall
20000
Cy)
Shortfall by Year
Table 2: Donation shortfall with the loss of 7.5% of donors.
These figures look disproportionately high given the donor losses. This is because, as the
main chain in Figure 2 showed, one lost donor does not equal one lost donation. It is clear that
not analyzing the systems using the Stock/flow structure greatly underestimates the impact of
the restrictions.
Whereas non-Stock/Flow thinking suggests a worst case scenario with a loss of 36,000
donations at 7.5% donor losses, Stock/Flow thinking suggests a worst case scenario of 91,000
lost donations by 2004. This suggests that the magnitude of the difference is significant for
planning purposes. It is also clear that the simulation model produces markedly different
outcomes from those suggested in the Review of the Australian Blood Banking and Plasma
Product Sector.
There is a second reason why the simulation figures are much higher. While deferrals have a
"once-only" impact on the existing donor base, they have on ongoing impact on the
recruitment of new donors. This means that new donor recruitment rates will be down by the
deferral percentage for the foreseeable future as the inflow to the donor base is restricted as
shown in Figure 4.
Losses to rechyitme
Donors x
@ O28
Recruitment Conversion to 2
Deferrals
Figure 4: Model with ongoing new donor losses included.
Deferrals are traditionally replaced by recruitment. ARCBS figures show that loss rates of
first time donors vary between 40 - 70% in Australia. This means that a large number of
people who become donors only ever give blood once. The correct mental model for this
Losses to recrditm i,
Losses to donor base
LO
Recruitment Conversion to 2
Deferrals
Figure 5: Losses of "once only" donors from donor base.
process is shown in Figure 5.
aus
Recovery by increased recruitment of new donors.
Traditionally the method for the meeting of shortfalls has been to recruit new donors. Figure 5
shows the required recruitment pattern and Table 4 shows the numbers of donors needed to
meet a 7.5% donor loss from vCJD.
Donors Required Annually
250,000
200,000
150,000
& 100,000
50,000
0
Table 3: New donors required with 7.5% donor loss from vCJD.
e
Recruited donors 2
1: 309000
i ashe VAN
",
1 1
1 oF
2003.00, 2008.75 2008.50 2008.25 2010.00
NIG EFA 2 crap ts ps (untitled) Years 8:12 AM Tue, 1 Apr 2003
Figure 6: Recovery by recruitment (7.5% loss)
The model suggests that an increase from the projected figure of 104,000 to 134,00 in 2003
would be needed to begin to redress the problem. This figure jumps to 207,600 in the next
year when the full impact is felt. This spike, in the first two years, means that the
accumulation in the stock of retained donors allows the ARCBS to recruit at a slightly lower
level than the projected 104,000 and still meet a 3% growth target.
This strong recovery rate is greatly helped by the improved annual donations rates. These
improvements mean that more people give more frequently. If this does not occur the model
predicts that the need to recruit will be 50 - 60% higher each year.
Modeling the UK situation.
A simulation of the impact of a hypothetical set of restriction was run on the UK figures as a
comparison with the Australian figures. The UK has adopted a different approach, through the
use of leucodepletion, to the vCJD problem, so this discussion is hypothetical. This simulation
was used to show that problems arising from vCJD restriction are systemic to blood services
rather than specific to individual countries.
The findings from the model of the Australian figures were further emphasized by an
examination of the UK figures. The National Health Service takes 2.4m donations from 1.9m
people at a rate of 1.2 donations per year, less than in Australia. Table 4 shows the
fundamental dynamics of the UK system. New donors enrolled are those recruited, however a
smaller number (designated by the conversion rate)"attend", and give blood. Enrolling
442,550 donors leads to a 3.7% increase in the donor base of 1.9m. Significant numbers of
donors lapse and these numbers are made up from the new donors.
1998 - 99 1999 - 2000
New donors enrolled 408,043 442,550
New donors attending 279,409 268,739
Conversion rate 68% 60%
Lapsed donors 218,116 196,863
Net gain 61293 71876
(attending - lapsed)
% gain to donor base 3.2% 3.7%
(1.9m donors)
Table 4: New donors, conversions and gains (UK).
It is clear from this table that, as in Australia, large enrolment numbers only convert to
relatively small increases in the donor base as a result of low conversion rates from enrolled to
attending and the added impact of lapsed donors.
The following simulations show what the impact of travel based restrictions, such as those
imposed in Australia and US, would be in the UK. The model is simplified to a single stock of
donors, which does not take into account increased impact of the loss of high frequency
donors. The model therefore tends to underestimate the impact of the restrictions. This
discussion is based on a hypothetical imposition of the percentages estimated in the US and
Australia. Had the UK decided to impose US and Australian level restrictions on donors as a
result of vCJD, it would have wiped out the entire donor base.
The model in Figure 6 was used to simulate the potential impact of a 7.5% deferral as a result
of vCJD on the UK National Blood Service.
vCJD Switch
vCJD loss rate
@ Demand
vCJD losge:
i)
Increase jin
ND enrolle
‘oss\from vCJD
Donor base
Annual Increase in Demand
he,
ND attendir Lapsed donors
ND Loss from vCJD @
Conversiy
fonation Shortfal
Donation Rate Improvement Improvement switct
Figure 6: Model of UK donor system
Table 4 shows donor base would decline by 142,000, with a one-off hit in the first year and
there is a growing deficit over the next four years as a result of new donor losses
Year Donor base Losses ND enrolled ND attending ND vCJD losses Donations
1 1,900,000 142,500 442,600 245,643 33,195 2,280,000
2 1,913,155 442,600 245,643 33,195 2,295,786
3 1,961,935 442,600 245,643 33,195 2,354,322
4 2,010,715 442,600 245,643 33,195 2,412,858
Table 5: Hypothetical donor losses in the UK at 7.5%.
Annual UK Shortfalls
160,000
140,000
120,000
190,000
80,000
60,000
40,000
20,000
1 2 3 4 5 6 7 8
Donations
Table 6: UK shortfall figures with the introduction of vCJD restrictions.
To maintain the existing donor base requires an additional 1.8m donors in the first two years
of the hypothetical introduction of vCJD, however, as Figure 7 and Table 6 below show, this
does not need to be maintained. This scenario constitutes a 39.5 % increase in new donors
enrolled over the first two years. The actual increase in new donor enrolled from 1999 - 2000
was 9.2% and this increase is not factored into the figures. This scenario assumes that all
donor losses occur and are replaced in the first two years after the imposition of the
restrictions. If this is possible, there would be not ongoing need to recruit new donors each
year, and still meet growth targets of 3% which currently covers increased demand.
9: wo enrotted
1: 790000
1
1 1s 1s
1: 350000
1: ot
2003.00 2008.75 2008.50 2008.25 2010.08
NIG EF Graph 2: p2 (Untitled) Months 11:45 AM Wed, 26 Mar 2003
Figure 7: Recovery by recruitment (UK)
New Donors Required
800000
700000
600000
“
'e 500000
&
@ 400000
300000
=
200000
100000
)
Table 7: Figures for Recovery by recruitment (UK)
The implications of recovery through recruitment.
Figures that are generated by models indicate that the numbers required by recruiting new
donors are extremely high in both the UK and Australian. Using Australian figures has an
illustration, it is necessary to recruit just under 1 million new donors in an eight year period.
Australia has a population of 18 million, of whom roughly 50% are of eligible donation age,
with 50% of the age eligible population actually able to give blood. This provides an eligible
donor pool of roughly 4.5m. This means recruiting approximately 25% of the eligible donor
population. Given that the current participation rate is around 10% of the eligible population,
this will be a significant task.
The are two points to be made in relation to this discussion. The first point is that, unless the
impact of such restrictions are modeled with appropriate stock/flows structures, it is highly
likely that targets of recruitment that are may ultimately be unachievable, will be seen as a
solution to the problem.
The second point is that it is necessary to model the resource implications of any recovery
strategies. If it is possible to recruit large numbers of new donors, the next important question
is whether the system has the capacity to process this number of new donors. The feed-
forward and feed-back implications of this, are best understood through model building
Sensitivity of models to improvements in donation rates
Both models show that a spike in recruitment can overcome the loss from vCJD and allow
recruitment at lower than projected levels. This is because both models include a continuous
improvement in donation rates. The improvement in annual donation rates in the Australian
model is from 1.95 to 2.21. International comparisons suggest that this will be extremely
difficult to do. The model is very sensitive to these improvements. If the assumption that these
rates can be maintained is not correct, the need for new donors increases. It is worth noting
that the projected recruitment rate was 104,000 pa. The figures in Table 7 indicate that
recruitment would need to double in 2003 and increase by a factor of 2.7 in 2004.
Comparison: With and without
improvements
300000
250000
200000
j 150000
© 100000
50000
)
Table 8: Sensitivity of new donors required to improvements in donation rates (Australia).
Without improved donation rates on left, with improved donation rates on right
The same was observed in the UK model, where a large increase in donors is needed to meet
the initial impact of vCJD. This allows lower levels of recruiting in future years (412,000 v
projected 442,000) because of the improvement in donation rates from 1.2 to 1.3 donations a
year over 8 years. Table 8 shows the annual improvement rate, the cumulate improvement is
10% over eight years, marginally over 1% per year but the impact on shortfalls and the
recruitment required is disproportionate high. The annual donation rate changes from 1.2 to
1.3 over eight years. The cumulative effect of this is very strong. Table 9 compares the
differences in donations, with and without the donation improvement rate.
Comparison With and Without
Improvements
800,000
700,000
600,000
500,000
i 400,000
& 300,000
200,000
100,000
OC)
Table 9: Sensitivity of new donors required to improvements in donation rates (UK).
Without improved donation rates on left, with improved donation rates on right
Discussion of model outcomes.
The models showed the numbers of new recruits that would be needed to meet losses from the
vCJD restrictions. The models illustrate the enormity of the task of using recruitment as a
means for overcoming this problem. It is important that targets of 39% increases in new
donors in two years in the case of the UK should be modeled against the systems capacity to
handle that number.
In addition to the logistics of such a rapid ramp-up of donor supply, there are a number of
other complicating factors. The UK figures suggest a 60% conversion of enrolled to new
donors. In a study of 14-month study period, 1,000 first-time donors Royse (1999) found that
this sample of donors gave an average of 1.89 donations in their lifetime, compared with 1.2
donations annually from continuing donors. This suggests that the on-going commitment of
this group may not be high. The importance of ongoing commitment is emphasized by
Ferguson and Bibby (2002) who reported a study of 630 donors that past behavior was
predictive for regular donors (5 or more previous blood donations), indicating the need to
establish patterns of behaviour in the donor base. This problem is compounded by the problem
represented by donation frequency profile, which is the number of times a donor gives blood
each year.
Restrictions, such as those imposed in response to vCJD, impact across the complete range of
the donation frequency profile. The recruitment of new donors may not necessarily replace the
losses across the profile. It may well be that new donor recruitment programs may replace
losses with lower frequency donors, thus creating an additional problem of lowered overall
donation rates. This highlights the importance of establishing high frequency donation
patterns with new donors. Evidence of the importance of establishing donation patterns is
provided by Koesterich (1983) who reported on the American Red Cross "Donor 17" program
which was designed to establish the habit of donating blood regularly in high school age
youth. She observed that Donor 17 participants donated significantly more blood and also
donated during more years than nonparticipating peers.
The point of this discussion is that unless the assumptions underlying the mental models of
decision-makers are surfaced and modeled, recovery strategies may be suggested and
implemented, that are unsustainable in the long run.
Directions for future research
As noted earlier in the paper, the ARCBS exercise identified areas where there was
incomplete or no data. Much of the research will need to be in developing data bases to
support the models. The lack of information linking travel patterns to donation frequency has
been noted. The relationship between frequency of blood donation and Hb levels needs to be
understood. It is suspected that the attrition for the Hb restrictions will have a disproportionate
affect on higher frequency donors. There is little useful information on the causal factors
relating to donation frequency, with some suggestion that the patterns are best established
when the donor is (a) young and (b) a new donor. Given that the ideal donor makes a long-
term commitment of frequent donation understanding this dynamic is critical.
In terms of model development within Australia, the ARCBS is currently developing state-
based models of all aspects of blood collection. In Australia, blood collections are
geographically dispersed across a country roughly the size of the US but with 10% of the
population. Collection is logistically complicated and expensive and there is increasing
scrutiny by the Federal government, which funds the ARCBS, of the costs of blood collection.
Further work is needed developing models that simulate the complex social, logistic and
economic factors in blood collection.
Conclusion.
The aim of this paper was to demonstrate that the application of System Dynamics modeling
to the problems of international blood services provides insights that are not currently
available to senior decision-makers. The ARCBS is currently using this technology to model
the impact of Hb restrictions and gaining new insights into the dynamics of this process
(Haslett and Bird, 2002).
This paper has demonstrated the insights that can be generated from the use of modeling and
also the sensitivity of the blood donation systems to variations in certain assumptions, in this
case, improvements in donation rate. It is highly likely that similar sensitivity in
demonstrated in relation to other variables in the model, for example, the retention rates of
new donors. The use of System Dynamics modeling not only allows the decision-makers to
test the sensitivity of the these assumptions, but also to create scenarios that model one or a
combination of recovery strategies.
References
Ferguson, E. & Bibby, P. (2002) Predicting future blood donor returns: Past behavior,
intentions, and observer effects. Health Psychology. Vol 21(5) pp 513-518.
Germain M. Decary F. Chiavetta J. Goldman M. (2000) Variant Creutzfeldt-Jakob disease
and the Quebec blood supply. Canadian Medical Association Journal. 163(4) pp 412-3.
Haslett, T. & Bird, P. (2002). Modeling donor restrictions in the Australian Red Cross Blood
Service. Published in the Proceedings of the 8" ANZSYS Conference. Mooloolaba, Dec, 2002
(eds) Ledington, J & Ledington, P. University of the Sunshine Coast.
Hoey J. Giulivi A. Todkill AM. (1998) New variant Creutzfeldt-Jakob disease and the blood
supply: is it time to face the music? Canadian Medical Association Journal. 159(6) pp 669-
70.
Jones RL. (2003) The blood supply chain, from donor to patient: a call for greater
understanding leading to more effective strategies for managing the blood supply.
Transfusion. 43(2):pp132-4.
Koesterich (1983) Motivation and Retention of Participants of the Red Cross Donor 17 Blood
Drive Program. New York State Sociological Association, 1983
Leikola J.(1998). Achieving self sufficiency in blood across Europe. British Medical Journal.
316(7130), pp489-90,
Milling P. and Zahn E (eds) Computer based management of complex systems. Springer
Verlager,
Mitka M. (2001). FDA wants more restrictions on donated blood. Journal of the American
Medical Association. 286(4). pp408.
Payne D. (2001). Ireland fears blood shortage with new ban on donors. British Medical
Journal 323(7311) pp 469.
The National Blood Service: Report by the Comptroller and Auditor General. The
Comptroller and Auditor General, HC 6 Session 2000-2001: 20 December 2000
Report of the Working Group on Overall Blood Supply Strategy with regard to vCJD,
National Advisory Committee "Blood" of the German Federal Ministry of Health, August
2001
Review of the Australian Blood Banking and Plasma Product Sector March 2001. A report to
the Commonwealth Minister for Health and Aged Care, Commonwealth Government,
Australia.
Royse (1999) Exploring Ways to Retain First-Time Volunteer Blood Donors. Research on
Social Work Practice, Vol 9, 1, pp 76-85
Sibbald B. (1999) Blood-donor ban for UK visitors stems from Krever report. Canadian
Medical Association Journal. 161(7) pp790.
Sterman, J. (2000). Business Dynamics. Irwin McGraw Hill, Boston.
Appendix 1 Equations for UK model
Demand(t) = Demand(t - dt) + (Increase_in_Demand) * dt
INIT Demand = 2280000
INFLOWS:
Increase_in_Demand = Demand*Annual_Increase_in_Demand
Donor_base(t) = Donor_base(t - dt) + (ND_attending - Lapsed_donors) * dt
INIT Donor_base = 1900000
INFLOWS:
ND_attending = New_donors_after_vCJD*(Conversion)
OUTFLOWS:
Lapsed_donors = 196863 + Donor_Loss_from_vCJD
Annual_Increase_in_Demand = .03
Conversion = .6
Donations = (if Improvement_switch=1 then Improvement else Donation_Rate)*Donor_base
Donor_Loss_from_vCJD =
( if time =2004 then Donor_base*vCJD_losses else 0)
Improvement_switch = 0
ND_Loss_from_vCJD = ND_enrolled-New_donors_after_vCJD
New_donors_after_vCJD = ND_enrolled*(1-vCJD_losses)
Shortfall = Demand-Donations
vCJD_losses = if vVCJD_Switch = 1 then vCJD_loss_rate else 0
vCJD_loss_rate = .075
vCJD_Switch = 0
Donation_Rate = GRAPH(TIME)
(2003, 1.20), (2004, 1.20), (2005, 1.20), (2006, 1.20), (2007, 1.20), (2008, 1.20), (2009, 1.20), (2010,
1.20)
Improvement = GRAPH(TIME)
(2003, 1.20), (2004, 1.22), (2005, 1.23), (2006, 1.25), (2007, 1.26), (2008, 1.27), (2009, 1.29), (2010,
1.30)
ND_enrolled = GRAPH(TIME)
(1.00, 442550), (2.00, 442550), (3.00, 442550), (4.00, 442550), (5.00, 442550), (6.00, 442550), (7.00,
442550), (8.00, 442550)
New_donors_No_IDR = GRAPH(TIME)
(2003, 458000), (2004, 724000), (2005, 464000), (2006, 467000), (2008, 470000), (2009, 473000),
(2010, 479000), (2011, 481000), (2012, 484000)
New_donor_IDR = GRAPH(TIME)
(2003, 411000), (2004, 671000), (2005, 414000), (2006, 427000), (2008, 432000), (2009, 419000),
(2010, 427000), (2011, 471000), (2012, 474000)
Appendix 2 Equations for Australian model
Cumulative New_WB_Recruit_Hb_loss(t) = Cumulative _New_WB_Recruit_Hb_loss(t - dt) +
(Recruit_Hb_loss_rate - Conversion_of_new_WB__to_Apheresis) * dt
INIT Cumulative _New_WB_Recruit_Hb_loss = 0
INFLOWS:
Recruit_Hb_loss_rate = Recruited_donors*uk_haemoglobin_loss_A
OUTFLOWS:
Conversion_of_new_WB_ to_Apheresis
Cumulative New_WB_Recruit_Hb_loss*Rate_of_conversion_to_Apheresis_Donors
Total_Lapsed__donors_x4(t) = Total_Lapsed__donors_x4(t - dt) + (Lapsed_donor_x_1__4 -
Recovery_of Lapsed__Donors_x4) * dt
INIT Total_Lapsed__donors_x4 = 3000
INFLOWS:
Lapsed_donor_x_1__4 = WB_Donor_Base_x_4*Lapsed_Donor_Rate
OUTFLOWS:
Recovery_of_ Lapsed__Donors_x4 = Total_Lapsed__donors_x4*Recovery_rate_of__Lapsed_Donors
Total_Lapsed__donors_x5(t) = Total_Lapsed__donors_x5(t - dt) + (Lapsed_donor_x5 -
Recovery_of_Lapsed__Donors_x_5) * dt
INIT Total_Lapsed__donors_x5 = 1000
INFLOWS:
Lapsed_donor_x5 = (WB_Donor_Base_x_5*Lapsed_Donor_Rate)
OUTFLOWS:
Recovery_of Lapsed__Donors_x_5 = Total_Lapsed__donors_x5*Recovery_rate_of _Lapsed_Donors
Total_Lapsed__donors_x_1(t) = Total_Lapsed__donors_x_1(t - dt) + (Lapsed_donor_x_l_ -
Recovery_of_Lapsed__Donors_x1) * dt
INIT Total_Lapsed__donors_x_1 = 20000
INFLOWS:
Lapsed_donor_x_1_ = WB_Donor_Base_x_1*Lapsed_Donor_Rate
OUTFLOWS:
Recovery_of Lapsed__Donors_x1 = Total_Lapsed__donors_x_1*Recovery_rate_of _Lapsed_Donors
Total_Lapsed__donors_x_2(t) = Total_Lapsed__donors_x_2(t - dt) + (Lapsed_donor_x_1__ 2 -
Recovery_of Lapsed__Donors_x_2) * dt
INIT Total_Lapsed__donors_x_2 = 12000
INFLOWS:
Lapsed_donor_x_1__2 = WB_Donor_Base_x_2*Lapsed_Donor_Rate
OUTFLOWS:
Recovery_of Lapsed__Donors_x_2 =
Total_Lapsed__donors_x_2*Recovery_rate_of__Lapsed_Donors
Total_Lapsed__donors_x_3(t) = Total_Lapsed__donors_x_3(t - dt) + (Lapsed_donor_x_1__ 3 -
Recovery_of_Lapsed__Donors_x_3) * dt
INIT Total_Lapsed__donors_x_3 = 5000
INFLOWS:
Lapsed_donor_x_1__3 = WB_Donor_Base_x_3*Lapsed_Donor_Rate
OUTFLOWS:
Recovery_of Lapsed__Donors_x_3 =
Total_Lapsed__donors_x_3*Recovery_rate_of__Lapsed_Donors
Total_Once__only_losses(t) = Total_Once__only_losses(t - dt) + (Once_only_loss -
Once_only_recoveries) * dt
INIT Total_Once__only_losses = 150000
INFLOWS:
Once_only_loss = Once_only__to_1*Cv_to_Base
OUTFLOWS:
Once_only_recoveries = Total_Once__only_losses*Once_only_recovery_rate
Total_x1_Donors_UK__Hb_Loss(t) = Total_x1_Donors_UK__Hb_Loss(t - dt) +
(UK_Haemoglobin__Loss_x_1 - Reentry_from_X1__UK_Hb_Loss -
Conversion_of_x1_to_New_Apheresis_Donor - Venous_Hb_x1) * dt
INIT Total_x1_Donors_UK__Hb_Loss = 0
INFLOWS:
UK_Haemoglobin__Loss_x_1 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_1*Hb_implementation___%_rate_2) ELSE 0
OUTFLOWS:
Reentry_from_X1__ UK_Hb_Loss = Total_x1_Donors_UK__Hb_Loss*Reentry_Rate_of__Hb_Loss
Conversion_of_x1_to_New_Apheresis_Donor =
Total_x1_Donors_UK__Hb_Loss*Rate_of_conversion_to_Apheresis_Donors
Venous_Hb_x1 = Total_x1_Donors_UK__Hb_Loss*Venous_Hb_Recovery_rate
WB_Donor_Base_x_1(t) = WB_Donor_Base_x_1(t - dt) + (flow_to_x1 + Returns_to_x! -
Lapsed_donor_x_1_ - flow_to_x_2 - vCJD_Deferral__V2_x_1 - UK_Haemoglobin_Loss_x_1 -
X1_T_D - Once_only_loss - x1_PD) * dt
INIT WB_Donor_Base_x_1 = 207605
INFLOWS:
flow_to_xl =Once_only__to_1
Returns_to_x! =
Recovery_from_X1_vCJD__V2_Loss+Recovery_of_Lapsed__Donors_x1+Reentry_from_X1__UK_
Hb_Loss+Venous_Hb_x1+x1_TD_recoveries+x1_TD_recoveries+Once_only_recoveries
OUTFLOWS:
Lapsed_donor_x_1_ = WB_Donor_Base_x_1*Lapsed_Donor_Rate
flow_to_x_2 =(WB_Donor_Base_x_1*Cv_x1)
vCJD_Deferral__V2_x_1 = vCJD_from_x1*WB_Donor_Base_x_1
UK_Haemoglobin__Loss_x_1 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_1*Hb_implementation___%_rate_2) ELSE 0
X1_T_D= WB_Donor_Base_x_1*Temp_Deferral_Rate
Once_only_loss = Once_only__to_1*Cv_to_Base
x1_PD = WB_Donor_Base_x_1*Perm_Deferral_Rate
WB_Donor_Base_x_2(t)= WB_Donor_Base_x_2(t - dt) + (flow_to_x_2 + Returns_to_x2 -
flow_to_x3 - UK_Haemoglobin__Loss_x_2 - vCJD_Deferral__V2_x_2 - Lapsed_donor_x_1__2-
x 2 P D-X2 tT _D)*dt
INIT WB_Donor_Base_x_2 = 107100
INFLOWS:
flow_to_x_2 =(WB_Donor_Base_x_1*Cv_x1)
Returns_to_x2=
Recovery_from_X2_vCJD__V2_Loss+Recovery_of_Lapsed__Donors_x_2+Reentry_from_X2__UK_
Hb_Loss+Venous_Hb_x2+x2_TD_recoveries+Once_only__to_2
OUTFLOWS:
flow_to_x3 = WB_Donor_Base_x_2*Cv_x_2
UK_Haemoglobin__Loss_x_2 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_2*Hb_implementation___%_rate_2 ) ELSE 0
vCJD_Deferral__V2_x_2 = vCJD_from_x2*WB_Donor_Base_x_2
Lapsed_donor_x_1__2 = WB_Donor_Base_x_2*Lapsed_Donor_Rate
) tT] _ - Base_x_2*Temp_Deferral_Rate
WB_Donor_Base_x_3(t)= WB_Donor_Base_x_3(t - dt) + (flow_to_x3 + Returns_to_x3 - flow_to_x4
- UK_Haemoglobin__Loss_x_3 - vCJD_Deferral__V2_x_3 - Lapsed_donor_x_1__ 3 - x3_P_D-
x3_T_D) *dt
INIT WB_Donor_Base_x_3 = 67700
INFLOWS:
flow_to_x3 = WB_Donor_Base_x_2*Cv_x_2
Returns_to_x3 =
Recovery_from_x3_vCJD__V2_Loss+Recovery_of_Lapsed__Donors_x_3+Reentry_from_x3__UK_
Hb_Loss+Venous_Hb_x3+x3_T_D_recoveries+Once_only__to_3
OUTFLOWS:
flow_to_x4=(WB_Donor_Base_x_3 * Cv_x_3)
UK_Haemoglobin__Loss_x_3 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_3*Hb_implementation___%_rate_2 ) ELSE 0
vCJD_Deferral__V2_x_3 = vCJD_from_x3*WB_Donor_Base_x_3
Lapsed_donor_x_1__3 = WB_Donor_Base_x_3*Lapsed_Donor_Rate
x3_P_D=WB Donor Base_x_3*Perm_Deferral_Rate
x3_T_D=WB_Donor_Base_x_3*Temp_Deferral_Rate
WB_Donor_Base_x_4(t) = WB_Donor_Base_x_4(t - dt) + (flow_to_x4 + Returns_to_x4 - flow_to_x5
- UK_Haemoglobin__Loss_x_4 - Lapsed_donor_x_1__4- vCJD_Deferral__V2_x_4-x4_T_D-
x4 P_D)*dt
INIT WB_Donor_Base_x_4 = 43700
INFLOWS:
flow_to_x4=(WB_Donor_Base_x_3 * Cv_x_3)
Returns_to_x4=
Recovery_from_X1_vCJD__V2_Loss_4+Recovery_of_Lapsed__Donors_x4+Reentry_from_x4__UK
_Hb_Loss+Venous_Hb_x4+x4_TD_recoveries+Once_only__to_4
OUTFLOWS:
flow_to_x5 =(WB_Donor_Base_x_4 *Cv_x_4)
UK_Haemoglobin__Loss_x_4 = IF uk_haemoglobin =| THEN
(WB_Donor_Base_x_4*Hb_implementation___%_rate_2 ) ELSE 0
Lapsed_donor_x_1__4= WB_Donor_Base_x_4*Lapsed_Donor_Rate
vCJD_Deferral__V2_x_4 = vCJD_from_x_4*WB_Donor_Base_x_4
x4_T_D=WB_Donor_Base_x_4*Temp_Deferral_Rate
x4_P_D=WB Donor _Base_x_4*Perm_Deferral_Rate
WB_Donor_Base_x_5(t) = WB_Donor_Base_x_S(t - dt) + (flow_to_x5 + Returns_to_x5 -
vCJD_Deferral__V2_x_5 - UK_Haemoglobin__Loss_x_5 - Lapsed_donor_x5 - x5_P_D-x5_T_D)*
dt
INIT WB_Donor_Base_x_5 = 10900
INFLOWS:
flow_to_x5 =(WB_Donor_Base_x_4 *Cv_x_4)
Returns_to_x5=
Recovery_from_x5_vCJD__V2_Loss+Recovery_of_Lapsed__Donors_x_5+Reentry_from_x5__UK_
Hb_Loss+Venous_Hb_x5+x5_TD_recoveries+Once_only__to_5
OUTFLOWS:
vCJD_Deferral__V2_x_5 = vCJD_from_x5*WB_Donor_Base_x_5
UK_Haemoglobin__Loss_x_5 = IF uk_haemoglobin =1 THEN (Hb_implementation___%_rate_2 *
WB_Donor_Base_x_5) ELSE 0
Lapsed_donor_x5 = (WB_Donor_Base_x_5*Lapsed_Donor_Rate)
x5_P_D=WB_Donor_Base_x_5*Perm_Deferral_Rate
x5_T_D=WB_Donor_Base_x_5*Temp_Deferral_Rate
X1_Donors_VCJD_V2_Loss(t) = X1_Donors_VCJD_V2_Loss(t - dt) + (vCJD_Deferral__V2_x_1 -
Recovery_from_X1_vCJD__V2_Loss) * dt
INIT X1_Donors_VCJD_V2_Loss =0
INFLOWS:
vCJD_Deferral__V2_x_1 = vCJD_from_x1*WB_Donor_Base_x_1
OUTFLOWS:
Recovery_from_X1_vCJD__V2_Loss=0
x1_T_Deferred(t) = x1_T_Deferred(t - dt) + (X1_T_D - x1_TD_recoveries) * dt
INIT x1_T_Deferred = 20000
INFLOWS:
X1_T_D=WB_Donor_Base_x_1*Temp_Deferral_Rate
OUTFLOWS:
x1_TD_recoveries = x1_T_Deferred*T_D_Recovery_rate
x2_Donors_UK__Hb_Loss(t) = x2_Donors_UK__Hb_Loss(t - dt) + (UK_Haemoglobin__Loss_x_2 -
Reentry_from_X2__ UK_Hb_Loss - Conversion_of_x2_donors_to_Apheresis - Venous_Hb_x2) * dt
INIT x2_Donors_UK__Hb_Loss =0
INFLOWS:
UK_Haemoglobin__Loss_x_2 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_2*Hb_implementation___%_rate_2 ) ELSE 0
OUTFLOWS:
Reentry_from_X2__UK_Hb_Loss = x2_Donors_UK__Hb_Loss*Reentry_Rate_of__Hb_Loss
Conversion_of_x2_donors_to_Apheresis =
x2_Donors_UK__Hb_Loss*Rate_of_conversion_to_Apheresis_Donors
Venous_Hb_x2 = x2_Donors_UK__Hb_Loss*Venous_Hb_Recovery_rate
X2_Donors_VCJD_V2_Loss(t) = X2_Donors_VCJD_V2_Loss(t - dt) + (vCJD_Deferral__V2_x_2 -
Recovery_from_X2_vCJD__V2_Loss) * dt
INIT X2_Donors_VCJD_V2_Loss = 0
INFLOWS:
vCJD_Deferral__V2_x_2 = vCJD_from_x2*WB_Donor_Base_x_2
OUTFLOWS:
Recovery_from_X2_vCJD__V2_Loss=0
x2_T_deferred(t) = x2_T_deferred(t - dt) + (X2_tT_D - x2_TD_recoveries) * dt
INIT x2_T_deferred = 12000
INFLOWS:
X2_tT_D=WB_Donor_Base_x_2*Temp_Deferral_Rate
OUTFLOWS:
x2_TD_recoveries = x2_T_deferred*T_D_Recovery_rate
x3_Donors_UK__Hb_Loss(t) = x3_Donors_UK__Hb_Loss(t - dt) + (UK_Haemoglobin__Loss_x_3 -
Reentry_from_x3__ UK_Hb_Loss - Conversion_of_x3_donors__to_Apheresis - Venous_Hb_x3) * dt
INIT x3_Donors_UK__Hb_Loss =0
INFLOWS:
UK_Haemoglobin__Loss_x_3 = IF uk_haemoglobin =1 THEN
(WB_Donor_Base_x_3*Hb_implementation___%_rate_2 ) ELSE 0
OUTFLOWS:
Reentry_from_x3__ UK_Hb_Loss = x3_Donors_UK__Hb_Loss*Reentry_Rate_of__Hb_Loss
Conversion_of_x3_donors__to_Apheresis =
x3_Donors_UK__Hb_Loss*Rate_of_conversion_to_Apheresis_Donors
Venous_Hb_x3 = x3_Donors_UK__Hb_Loss*Venous_Hb_Recovery_rate
x3_Donors_VCJD_V2_Loss(t) = x3_Donors_VCJD_V2_Loss(t - dt) + (vCJD_Deferral__V2_x_3 -
Recovery_from_x3_vCJD__V2_Loss) * dt
INIT x3_Donors_VCJD_V2_Loss = 0
INFLOWS:
vCJD_Deferral__V2_x_3 = vCJD_from_x3*WB_Donor_Base_x_3
OUTFLOWS:
Recovery_from_x3_vCJD__V2_Loss =0
x3_T_Deferred(t) = x3_T_Deferred(t - dt) + (x3_T_D - x3_T_D_recoveries) * dt
INIT x3_T_Deferred = 5000
INFLOWS:
x3_T_D=WB_Donor_Base_x_3*Temp_Deferral_Rate
OUTFLOWS:
x3_T_D_recoveries = x3_T_Deferred*T_D_Recovery_rate
x4_Donors_UK__Hb_Loss(t) = x4_Donors_UK__Hb_Loss(t - dt) + (UK_Haemoglobin__Loss_x_4 -
Reentry_from_x4__ UK_Hb_Loss - Conversion_of_x4_donors_to_Apheresis - Venous_Hb_x4) * dt
INIT x4_Donors_UK__Hb_Loss =0
INFLOWS:
UK_Haemoglobin__Loss_x_4 = IF uk_haemoglobin =| THEN
(WB_Donor_Base_x_4*Hb_implementation___%_rate_2 ) ELSE 0
OUTFLOWS:
Reentry_from_x4__ UK_Hb_Loss = x4_Donors_UK__Hb_Loss*Reentry_Rate_of__Hb_Loss
Conversion_of_x4_donors_to_Apheresi
x4_Donors_UK__Hb_Loss*Rate_of_conversion_to_Apheresis_Donors
Venous_Hb_x4 = x4 _Donors_UK__Hb_Loss*Venous_Hb_Recovery_rate
x4_Donors_VCJD_V2_Loss(t) = x4_Donors_VCJD_V2_Loss(t - dt) + (vCJD_Deferral__V2_x_4 -
Recovery_from_X1_vCJD__V2_Loss_4) * dt
INIT x4_Donors_VCJD_V2_Loss = 0
INFLOWS:
vCJD_Deferral__V2_x_4 = vCJD_from_x_4*WB_Donor_Base_x_4
OUTFLOWS:
Recovery_from_X1_vCJD__V2_Loss_4=0
x4_TDeferred(t) = x4_TDeferred(t - dt) + (x4_T_D - x4_TD_recoveries) * dt
INIT x4_TDeferred = 2000
INFLOWS:
x4_T_D=WB_Donor_Base_x_4*Temp_Deferral_Rate
OUTFLOWS:
x4_TD_recoveries = x4_TDeferred*T_D_Recovery_rate
x5_Donors_UK__Hb_Loss(t) = x5_Donors_UK__Hb_Loss(t - dt) + (UK_Haemoglobin__Loss_x_5 -
Reentry_from_x5__ UK_Hb_Loss - Conversion_of_x5_donors_to_Apheresis - Venous_Hb_x5) * dt
INIT x5_Donors_UK__Hb_Loss =0
INFLOWS:
UK_Haemoglobin_Loss_x_5 = IF uk_haemoglobin =] THEN (Hb_implementation___%_rate_2 *
WB_Donor_Base_x_5) ELSE 0
OUTFLOWS:
Reentry_from_x5__ UK_Hb_Loss = x5_Donors_UK__Hb_Loss*Reentry_Rate_of__Hb_Loss
Conversion_of_x5_donors_to_Apheresis =
x5_Donors_UK__Hb_Loss*Rate_of_conversion_to_Apheresis_Donors
Venous_Hb_x5 = x5_Donors_UK__Hb_Loss*Venous_Hb_Recovery_rate
X5_Donors_VCJD_V2_Loss(t) = X5_Donors_VCJD_V2_Loss(t - dt) + (vCJD_Deferral__V2_x_5 -
Recovery_from_x5_vCJD__V2_Loss) * dt
INIT X5_Donors_VCJD_V2_Loss = 0
INFLOWS:
vCJD_Deferral__V2_x_5 = vCJD_from_x5*WB_Donor_Base_x_5
OUTFLOWS:
Recovery_from_x5_vCJD__V2_Loss=0
x5_T_Deferred(t) = x5_T_Deferred(t - dt) + (x5_T_D - x5_TD_recoveries) * dt
INIT x5_T_Deferred = 1000
INFLOWS:
x5_T_D = WB_Donor_Base_x_5*Temp_Deferral_Rate
OUTFLOWS:
x5_TD_recoveries = x5_T_Deferred*T_D_Recovery_rate
Conversion = Once_only_donors*First_tme_retention
Cv_of_once_only = | - First_tme_retention
Cv_to_Base = 1-First_tme_retention
Cv_x1 = (if Segment_conversion=1 then .15 else 0) * Segment_Conversion_Rate_Improvement
Cv_x_2 = (if Segment_conversion=1 then .12 else 0) * Segment_Conversion_Rate_Improvement
Cv_x_3 = (if Segment_conversion=1 then .06 else 0) * Segment_Conversion_Rate_Improvement
Cv_x_4= (if Segment_conversion=1 then .035 else 0) * Segment_Conversion_Rate_Improvement
Lapsed_Donor_Rate = 0
ND_vCJD_losses = Recruited_donors-Once_only_donors
Noname_29 = flow_to_x_2+Once_only_loss+X1_T_D+Lapsed_donor_x_1_
Once_only_donors = (Recruited_donors - (Recruited_donors*vCJD_New_Donors))
Once_only_recovery_rate = 0
Once_only__to_1 = Cv_of_once_only*Once_only_donors
Once_only__to_2 = .246*Conversion
Once_only__to_3 =.155*Conversion
Once_only__to_ 4 *Conversion
Once_only__to_5 = .025*Conversion
Perm_Deferral_Rate = 0
Rate_of_conversion_to_Apheresis_Donors = 0
RDI=1
Recovery_rate_of__Lapsed_Donors = 0
Recruited_donors = if RD_1 = 1 then Recruited_donors_1 else Recruited_donors_2
Segment_conversion = 0
Segment_Conversion_Rate_Improvement = 1
uk_haemoglobin = 1
uk_haemoglobin_loss_A = IF uk_haemoglobin =1 THEN Hb_implementation___%_rate ELSE 0
vCJD_deferral_rate = .031
vCJD_from_x1 = if vCJD_switch = | then (if time = 2004 then vCJD_deferral_rate else 0) else 0
vCJD_from_x2 = if vCJD_switch = | then (if time = 2004 then vCJD_deferral_rate else 0) else 0
vCJD_from_x3 vCJD_switch = | then (if time = 2004 then vCJD_deferral_rate else 0) else 0
vCJD_from_x5 = if vCJD_switch = | then (if time = 2004 then vCJD_deferral_rate else 0) else 0
vCJD_from_x_4 = if vCJD_switch = | then (if time = 2004 then vCJD_deferral_rate else 0) else 0
vCJD_New_Donors = if vCJD_switch = 1 then vCJD_deferral_rate else 0
vCJD_switch = 0
Venous_Hb_Recovery_rate = 0
First_tme_retention = GRAPH(TIME)
(2003, 0.39), (2004, 0.39), (2005, 0.39), (2006, 0.39), (2007, 0.39), (2008, 0.39), (2009, 0.39), (2010,
0.39), (2011, 0.39), (2012, 0.39), (2013, 0.39)
Hb_implementation___%_rate = GRAPH(TIME)
(2003, 0.00), (2004, 0.046), (2005, 0.035), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2008, 0.00),
(2009, 0.00), (2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_implementation___%_rate_2 = GRAPH(TIME)
(2003, 0.00), (2004, 0.046), (2005, 0.035), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2008, 0.00),
(2009, 0.00), (2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_X1_ Females = GRAPH(TIME)
(2003, 0.00), (2004, 0.301), (2005, 0.229), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_X1_Females_2 =GRAPH(TIME)
(2003, 0.00), (2004, 0.323), (2005, 0.246), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_X1_Females_3 =GRAPH(TIME)
(2003, 0.00), (2004, 0.329), (2005, 0.251), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_X1_Females_4 =GRAPH(TIME)
(2003, 0.00), (2004, 0.368), (2005, 0.281), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_x1_ Males = GRAPH(TIME)
(2003, 0.00), (2004, 0.125), (2005, 0.095), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_x1_Males 2 =GRAPH(TIME)
(2003, 0.00), (2004, 0.176), (2005, 0.133), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_x1_ Males 3 = GRAPH(TIME)
(2003, 0.00), (2004, 0.215), (2005, 0.161), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00),
(2010, 0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Hb_x1_ Males 4 =GRAPH(TIME)
(2003, 0.00), (2004, 0.34), (2005, 0.26), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00), (2010,
0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Recruited_donors_1 = GRAPH(TIME)
(2003, 108000), (2004, 108000), (2005, 108000), (2006, 108000), (2007, 108000), (2009, 108000),
(2010, 108000), (2011, 108000), (2012, 108000), (2013, 108000)
Recruited_donors_2 = GRAPH(TIME)
(2003, 0.00), (2004, 0.00), (2005, 0.00), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00), (2010,
0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Reentry_Rate_of _Hb_Loss = GRAPH(TIME)
(2003, 0.00), (2004, 0.00), (2005, 0.00), (2006, 0.00), (2007, 0.00), (2008, 0.00), (2009, 0.00), (2010,
0.00), (2011, 0.00), (2012, 0.00), (2013, 0.00)
Stored_values = GRAPH(TIME)
(2003, 130000), (2004, 175000), (2005, 108000), (2006, 101000), (2007, 99000), (2008, 97000),
(2009, 98000), (2010, 98000), (2011, 98000), (2012, 98000), (2013, 98000)
Temp_Deferral_Rate = GRAPH(TIME)
(2003, 0.09), (2004, 0.09), (2005, 0.09), (2006, 0.09), (2007, 0.09), (2008, 0.09), (2009, 0.09), (2010,
0.09), (2011, 0.09), (2012, 0.09), (2013, 0.09)
T_D_Recovery_rate = GRAPH(TIME)
(2003, 0.25), (2004, 0.25), (2005, 0.25), (2006, 0.25), (2007, 0.25), (2008, 0.25), (2009, 0.25), (2010,
0.25), (2011, 0.25), (2012, 0.25), (2013, 0.25)
Calculations
Demand(t) = Demand(t - dt) + (Increase_in_Demand) * dt
INIT Demand = 854000
INFLOWS:
Increase_in_Demand = Demand*Demand_%_
Total_New_Donors(t) = Total_New_Donors(t - dt) + (Increase_to_Total_Donors) * dt
INIT Total_New_Donors = 0
INFLOWS:
Increase_to_Total_Donors = Recruited_donors
Total_Recruited_Donors(t) = Total_Recruited_Donors(t - dt) + (Increase_in_Total_Recruited_donors)
* dt
INIT Total_Recruited_Donors = 0
INFLOWS:
Increase_in_Total_Recruited_donors = Recruited_donors
Annual_Hb_loss =
UK_Haemoglobin__Loss_x_1+UK_Haemoglobin__Loss_x_2+UK_Haemoglobin__Loss_x_3+UK_H
aemoglobin__Loss_x_4+UK_Haemoglobin__Loss_x_5
Donation_rate = Total WB__Donations/Total_Donor_Base
Donor_losses_vCJD =
vCJD_Deferral__V2_x_1+vCJD_Deferral__V2_x_2+vCJD_Deferral__V2_x_3+vCJD_Deferral__V2
_x_4+vCJD_Deferral__V2_x_5
Rate_of RBC_per_WB = 0.85
RBC_production = Rate_of_ RBC_per_WB*Total_WB_ Donations
Shortfall = Demand-Total_WB__ Donations
Total_Donor_Base =
WB_Donor_Base_x_1+WB_Donor_Base_x_2+WB_Donor_Base_x_3+WB_Donor_Base_x_4+WB_
Donor_Base_x_5
Total_WB__ Donations =
(WB_Donor_Base_x_1*1)+(WB_Donor_Base_x_2*2)+(WB_Donor_Base_x_3*3)+(WB_Donor_Bas
e_x_4*4)+(WB_Donor_Base_x_5*5)+Venous_Hb_x1+(Venous_Hb_x2*2)+(Venous_Hb_x3*3)+(Ve
nous_Hb_x4*4)+(Venous_Hb_x5*5)
Demand_%_=GRAPH(TIME)
(2003, 0.03), (2004, 0.03), (2005, 0.03), (2006, 0.03), (2007, 0.03), (2008, 0.03), (2009, 0.03), (2010,
0.03), (2011, 0.03), (2012, 0.03), (2013, 0.03)
