Cholera in Zimbabwe
Erik Pruyt*
*Delft University of Technology, Faculty of Technology, Policy and Management
P.O. Box 5015, 2600 GA Delft, The Netherlands — E-mail: e.pruyt@tudelft.nl
July 26, 2009
Abstract
By the end of December 2008, alarming reports and articles concerning the cholera outbreak
in Zimbabwe received plenty of international media coverage. By that time nearly 30000
cases of cholera infections and 1600 cholera deaths had been reported. In the first week of
January 2009, a System Dynamics simulation model related to this cholera epidemic was
ng/teaching case. Although the model
contains some bold assumptions which require further research, the issue and dynamics are
sufficiently important and interesting to be presented here. This case is a System Dynamics
study with a special focus on exploring dynamics and uncertainties.
created which was subsequently turned into a ‘hot’ t
Keywords: Cholera, Epidemics, Zimbabwe, System Dynamics
1 Introduction
1.1 The 2008-2009 Cholera Outbreak in Zimbabwe
The deterioration of the Zimbabwean sanitary and health infra
lead to a lack of safe drinking water and health services, especially in and around the citie:
lead to a cholera outbreak in August 2008.
structures over the past years has
, which
According to the World Health Organization (2009c)|
‘Cholera is an acute enteric infection caused by the ingestion of bacterium Vibrio
aracterized in
cholerae present in faccally contaminated water or food. [... It] is
its most severe form by a sudden onset of acute watery diarrhoea that can lead to
death by severe dehydration. The extremely short incubation period two hours to
five days~ enhances the potentially explosive pattern of outbreaks, as the number of
cases can rise very quickly. About 75% of people infected with cholera do not develop
any symptoms r, the pathogens stay in their faeces for 7 to 14 days and
are shed back into the environment, possibly infecting other individuals. Cholera
is an extremely virulent disease that affects both children and adults. Unlike other
diarrhoeal diseases, it can kill healthy adults within hours. Individuals with lower
immunity, such as malnourished children or people living with HIV, are at greater risk
of death if infected by cholera.’
Howe’
Cholera may be epidemic but also endemic. Outbreaks are often associated/triggered by
si h as heavy rainfalls, floods and droughts~ which may dis.
rupt the supply of safe drinking water, aggravate hygiene conditions, and increase (per capita)
water contamination (Codeco 2001).
‘on- or climate-related factor:
The Zimbabwean Ministry of Health and Child Welfare (MoHCW) reported a total of 26497
cholera cases and 1518 cholera deaths between August 2008 and 25 December 2008
Cholera in Zimbabwe 2
Organization 2008a), a total of 79613 cases and 3731 deaths between August 2008 and 18 February
2009 (World Health Organization 2009a), a total of 91164 cases with 4037 deaths between August
2008 and 17 March 2009 (World Health Organization 2009b), and a total of 98522 cases with 4282
deaths between August 2008 and 8 June 2009. The spread on 11 Jamary 2009 is depicted in
Figure (I
(a) Cumulative CFR by district, Zimbabwe, August (b) Cumulative number of cases by district, Zim-
2008 until 11 January 2009 babwe, 18 August 2008 until 11 January 2009
Figure 1: Geographic information related to the Cholera Outbreak in Zimbabwe. Source: WHO
14/Jan/2009 — |http://gamapserver . who. int /mapLibrary/app/searchResults .aspx|
Cholera can be prevented by taking precautionary hygienic measures and/or a good sanitary
infrastructure. In case of a fast and appropriate treatment, the (weekly) Case Fatality Rate [CFR]
is usually low, below 1%. That percentage was ~and still is~ much higher in Zimbabwe: the average
weekly CFR peaked near 6% in January and stood at 2.3% in the second week of March (Wor
Health Organization 2009b), with a much higher CFR outside of cholera treatment facilities (in re-
mote areas of Zimbabwe) peaking at 62% and declining to 33% (World Health Organization 2009b).
Several international aid organisations offered to provide the necessary medical and sanitary
facilities, safe water, and programmes to train aid workers to deal with and prevent cholera.
At first, Mugabe refused international aid, but by mid December 2008, he allowed international
aid organisations to provide clean drinking water. By that time, half of the population was
undernourished ...
1.2 State of the Art of Cholera Models
Although cholera is an ‘old disease’ which is -with the exception of some underdeveloped regions~
under control, the modeling of cholera outbreaks could still be improved substantially. Possible
improvements may be the inclusion of the loss of immunity (flow from recovered to susceptible
population), of new insights related to the survival of V. cholerae in aquatic environments, of the
detailed submodels related to the indirect infection via aquatic environments (often modelled with
an abstract Ro factor), and the consideration of the long term dynamics.
Although some recently published models explicitly take the role of aquati
cholerae (Islam 1997; [Colwell and Hug 1994} |(Codeco 2001), hyper-infective vibri
servoirs of V.
in water reserves
theoretical /abstract, insufficiently focussed on the exploration of the remaining uncertainties", and
of too low a level of aggregation to inform and be helpful for policy-makers.
For example: Strongly different extinction rates of toxigenic V. cholerae in aquatic environments have been
observed (Feachem, Bradley, Garelick, and Mara 1983) (Colwell and Hug 1994). It has even been shown that V.
Cholera in Zimbabwe 3
Codeco (2001)| proposes for example a formal mathematical SIR model of a hypothetical pop-
ulation of 10000 individuals with an explicit cholera reservoir —but without a return flow from
recovered individuals to susceptible individuals— in order to explore the role of the aquatic reser-
voir on the persistence of endemic cholera and to define minimum conditions for the development
of cholera.
Here, we present a model with a submodel of the V. cholerae reservoir —be it of a higher level
than the one in (Codeco_2001)— and with a return flow from the recovered population to the
susceptible population. Uncertainties will also be focussed on.
1.3. Organisation
In this paper, we present a simple System Dynamics simulation model of cholera outbreaks in
section [2|and a high-level causal loop diagram in section 3] The behaviour of the base model is
analysed in section [JI Validity, sensitivity, and uncertainties are explored in section [5] Model use
is discussed in section 6) where policy measures are tested and a teaching/testing case based on
the model is briefly presented. Further research and ding remarks are distilled in section [7]
Appendix [Al contains the ‘hot’ testing/teaching case description. And appendix |B] contains the
equations of the simulation model.
2 System Dynamics Simulation Model of Cholera Outbreaks
All explicit causal relationships of the base model are described in subsections[2.Tand 2.2] Implicit
and bold assumptions are further discussed in subsection/2.3]. The Stock-Flow Diagram of the base
model is depicted in Figure 2)
The model is in fact a SIR model extended with loss of immunity (a return flow from recov-
ered to susceptible after an average of 6 to 10 years), with different degrees of illness, mortality,
and an explicit “but boldly assumed- infection loop with a reservoir to harbor the V.cholerae.
The formulation of this ‘SIRS with infection pt simple: it contain a few
lookup/graph, max, 5 ,
The model is kept as imple. s possible: it conta sequently, many implicit assumptions
and many possibly relevant factors are omitted. For example, the model does not incorporate
births, deaths (other than cholera-caused deaths), detailed geographic/spatial information (dis-
persion, information related to aquifers and cholera reservoirs), climate/season related variables,
HIV/AIDS", etc. It contains a homogencous population (no age structure), homogenous infection
(no difference in amounts of V.cholerac and infectivity), fixed incubation and delay times, mainly
first-order delays, and several highly aggregated structures.
2.1 Susceptible, Infected, Recovered and Immune Populations
When individuals from the susceptible population become infected (cholera infections), they shift to
the recently infected population. The number of cholera infections is the product of the susceptible
population and the indirect infection rate. Those shifted to the recently infected population leave
that stock after an average incubation time of only 1 day and flow:
« as mildly infected to the mildly infected population if they show mild or moderate symptoms,
or if they are infected but do not show any symptoms at all (all asymptomatic cases);
@ as heavily infected to the heavily infected population in case of severe symptoms.
In the model, the fraction of the recently infected population getting only mildly infected depends
on the average health condition of the average Zimbabwean. The fraction used in the base model
cholerae populations may also decay into a non-culturable state and survive for more than 15 months, living in
association with aquatic organisms (Islam 1997). The mechanisms driving V. cholerae dynamics in water are still
poorly known and are therefore often omitted.
2WHO/UNAIDS estimated the 2003 Adult HIV/AIDS prevalence to range between 21.7-27.8%.
Cholera in Zimbabwe 4
cumulative
cholera laa —S2—>
Cases: infections average immunity
period
recovered to susceptible
by loss of immunity as
ay recovered
evel of connectedness [ susceptible ie edected spo mildly infected 5 — pu} temporarily
prevention aquifers | population population | say ingeced | PoPuation | recovery of | population
cholera infections silly infected
effect of preventionand =, f
sanitation on the indirect —w- indirect degree of average
degree of infection infection incubation time average duration
effect of the average health of ilaess
condition on the fraction of mildly
condition of the smoothed Racton of infected of al infected
sanity infecractore covtaminated water
| heaily
infected recovery of heavily
effect of the fraction of heavily infected i
infected on the fraction of population elected
contaminated water
effect of the average
Icholera deaths _ state of health services
fraction of infect on the fraction of
cholera deaths
a ed temporarily [cumulative]
<mildh intone | cholera
population> i URES DOD MENON: deaths average state of
health services
Figure 2: Stock-Flow Diagram of the Cholera Simulation Model
equals
statisti
5%. This number is a general estimate, not specific for Zimbabwe. It is derived from WHO
‘{a]bout 75% of people infected with cholera do not develop any symptoms
among people developing symptoms, 80% of episodes are of mild or moderate s
[Health Organization 2008b). In other words, only 5% of the recently infected population in the
base model becomes very ill after an average incubation time of 1 day. This fraction will be further
explored in section 5
All sick persons belonging to the mildly infected population shift —after an average duration of
the illness of 10 days~ as recovered from mild infection towards the recovered temporarily immune
population. The ons belonging to the heavily infected population cither die (cholera deaths)
or recover and become immune (recovered from heavy infection) after the same average duration of
. The fraction of the heavily infected population dying or recovering depends
in this model on the effect of the average state of health services on the fraction of cholera deaths,
and hence, on the average state of health services.
The values of the eff ‘ate of health services on the fraction of cholera deaths
and the average state of health services are guestimates (their influence will be explored in section
(5), based on the information that
of the average
e without treatment, as many as one in two people ma
« and with proper treatment, the fatality rate should stay below 1% (World Health Organiza-|
ition 2008b).
Given that —in the base model- the graph function effect of the average state of health services
on the fraction of cholera deaths only affects the heavily infected and that the fraction of heavily
infected is only 5% of all infections, the effect of the average state of health services on the fraction
of cholera deaths is assumed to be 100% in case of an average state of health services of 0%
y die (World Health Organization
Cholera in Zimbabwe 5
in case of an average state of health services of 25%, 20% in case of an average state of health
services of 50%, 5% in case of an average state of health services of 75%, and 0% in case of an
average state of health services of 100%. The average state of health services in Zimbabwe was
extremely low at the time of the outbreak until international aid agencies were allowed ace:
is expected to increase further. In the base model, the average state of health services —at le
cholera treatment~ is assumed to be 15% from day 1 till day 130 of the epidemic, and to inci
afterwards to 40% on day 183, to 70% on day 183, to 75% on day 250, and to 80% from day 300
on.
After an average immunity period of 6 years, Zimbabweans from the recovered temporarily
immune population flow back to the susceptible population.
In the base model, the number of Zimbabwean citizens belonging, at the start of the epidemic,
to the susceptible population is sct at 3000000, the recently infected population is sct at 1000,
the mildly infected population is set at 950, the heavily infected population is set at 50, and the
recovered temporarily immune population is set at 10226000 (this corresponds to the remaining
population: 13228000 - 3002000). These numbers will also be varied in section [5]
2.2 Indirect Infection
In the model, the indirect rate of infection equals the product of following three factors: the
smoothed fraction of contaminated water, the effect of prevention and sanitation on the indirect
degree of infection, and the connectedness of aquifers. The connectedness of aquifers ~a soft,
uncertain factor which is further explored in section [5}- is assumed to amount to 28% in the base
model.
The input of the effect of prevention and sanitation on the indirect degree of infection is the
maximum of two variables: the level of prevention and the state of the sanitary infrastructure.
If the maximum of these two variables is 0% then the effect on the indirect rate of infection is
assumed to amount to 100%, if it is 25% then the effect is med to amount to 90%, if it is 50%
then the effe ssumed to amount to 50%, if it is 75% then the effect is assumed to amount to
10%, and if it is 100% then the effect is assumed to amount to 0%. The level of prevention and
the state of the sanitary infrastructure lie between 0% and 100%. In Zimbabwe both are low: in
the base model, the level of prevention is initially assumed to be 10% and the state of the sanitary
infrastructure is initially assumed to be 30%. Both variables are soft and uncertain and their
influence will be explored in section [5)
The effect of the fraction of infected on the fraction of contaminated water is a graph/lookup
function: if the fraction of infected is 0% then the fraction of contaminated water is assumed to
be 0%, if it is 12.5% then the fraction of contaminated water is assumed to be 5%, if it is 25%
then the fraction of contaminated water med to be 75%, if it is 50% then the fraction of
contaminated water med to be 90%, if it is 75% then the fraction of contaminated water is
assumed to be 99%, and if it is 100% then the fraction of contaminated water is assumed to be
100%. This relationship is also a bold assumption: its influence will be explored in section 5
The smoothed fraction of contaminated water smoothes the (third order) effect of the fraction
of infected on the fraction of contaminated water with a delay of 14 days. Initially it equals 0.0004
(or 0.04%), initiating the epidemic.
And the fraction of infected equals of course the sum of the recently infected population, the
mildly infected population, and the heavily infected population, divided by the entire population.
2.3 Implicit and Bold Assumptions of the Simulation Model
As already mentioned, the model contains many explicit and implicit assumptions, some of which
correspond to boundary choi
¢ Although cholera can be transmitted through direct faecal-oral contamination and indirectly
through ingestion of contaminated water and food (World Health Organization 2008b), the
System Dynamics model only incorporates indirect transmission through contaminated wa-
ter: indirect contamination is assumed to occur much more often than direct contamination.
Cholera in Zimbabwe 6
e Although the rainy season increases the likelihood of cholera outbreaks, it has not been
included in the current model.
© The current population is focussed on, hence, population growth is not included.
¢ There are no further subdivision of subpopulations according to health, living conditions,
environmental conditions, geographic concentration, et cetera (although such subdivisions
may be introduced).
Several variables are truly uncertain or really soft. Bold assumptions have been included in
the model to incorporate them. Following assumptions included in the model are bold:
© The indirect degree of infection and its influencing factors (the connectedness of aquife
the smoothed fraction of contaminated water and the effect of the fraction of infected on the
fraction of contaminated water, and the level of prevention and the condition of the sanitary
infrastructure and their effect on the indirect degree of infection.
© The effect of the average state of health services on the fraction of cholera deaths and the
values of the average state of health services.
© The sizes of the different subpopulations, especially the sizes of the susceptible population
and the recovered temporarily immune population.
These assumptions will be explored in section 5]
3 A Causal loop diagram of the Simulation Model
ible aggregated feedback loop diagram of the simulation model is depicted in Figure|3) Both
the short term and the long term behaviour may be deduced from it.
aot —
susceptible™
Population‘ recovered temporarily
prevention and ch F immune population
sa depletion o
sanitation seers iz +
infrastructure on \ population j
the infection rate \ + seorene
recovered immune
infections loop
_ at 2 cummtative
-
indirect AD) infected population + —
+ infection loop ( ‘
fraction of infected average state of
health services
Figure 3: Aggregated causal loop diagram of the Cholera Model
The delay between the recovered temporarily immune population and the susceptible
population —represented by the dashed link in the susceptible ill recovered immune loop-
is much longer (on average 6 to 10 years) than the second longest delay (on average 14 days). It
is also much longer than the short term time horizon (see subsection 1). Hence, it does increase
the size of the susceptible population (decrease the size of the recovered temporarily immune
population) but it does not alter the short term dynamics. However, in the long run, this link
becomes extremely important and really drives the long term behaviour.
Cholera in Zimbabwe 7
If the @ indirect infection loop is strong enough, then it will lead, in the short term, to a
boom of the number of infections. However, the number of infections also drives the~depletion
of the susceptible population loop which will, in the medium term, lead to a collapse of
the susceptible population, and hence, the number of infections. In the long term, however, the
recovered temporarily immune population becomes susceptible again, through the « susceptible
ill recovered immune loop, increasing the likelihood of a new outbreak.
4 Behaviour of the Simulation Model
of the base model are discussed here.
with additional intervention pol:
The short term, medium term, and long term dynami
The short term, medium term, and long term dynamics
discussed in subsection [6.1L
ies are
4.1 Short term behaviour
The first 130, 183, or 206 days may be chosen as short term time horizon since data about the
cumulative number of cholera cases and deaths is available from mid August until 25 December
2008, until 20 February 2009, and until 14 March 2009. The period from mid August 2008 to 25
December 2008 corresponds to about 130 days, mid August 2008 to 20 February 2009 corresponds
to 183 days, and mid August 2008 to 14 March 2009 corresponds to 206 days. The three periods
are also characterised by different degrees of international medical aid, and hence the average state
of health services. The period from mid August 2008 until 14 March 2009 is depicted in the graphs
in Figure 4]
Graph for indict degree of infection Graph for recently infected population Graph for susceptible population
02 on aM
/
7 el
00s = 00 ou =
——aa ‘ a
net dpe fiction: bts Day sec te poplin sinc popei tng
(a) ind. degree of infection (ST) (b) recently infected population (ST) _ (c) susceptible population (ST)
Graph for recovered temporarily immune population Graph for cumulative cholera eases Graph for cumulative cholera deaths
uN 109.00 000
ox | ee 0.000 sao
OM ° === °
‘SOS thie eee eee ae mliire cen exes: eenng cumin ck dhs fecene ————— ponon
(d) recovered t. immune pop. (ST) —_(e) cumulative cholera cases (ST) _(f) cumulative cholera deaths (ST)
Figure 4: Short term behaviour of the Cholera Model (ST)
These graphs show that the indirect degree of infection (4a) increases exponentially, driving
the exponential increase of the recently infected population (4p), slowing ~and near the end of the
short term time horizon, stopping- the net increase of the susceptible population (42) and the net
decrease of the recovered temporarily immune population (4:1). The number of cumulative cholera
SNote that the recently infected population consists of infected individuals who will develop (mild or severe)
symptoms as well as infected individuals who will not develop any symptoms: ‘{albout 75% of people infected with
cholera do not develop any symptoms, although the pathogens stay in their faeces for 7 to 14 days and are shed
back into the environment, potentially infecting other individuals’ (World Health Organization 2008
Cholera in Zimbabwe 8
cases (4b) consequently increases exponentially, and the number of cumulative cholera deaths (48)
increases exponentially at first and converges later on —influenced by the assumed increase of the
average state of health services, brought about by the medical emergency aid of international aid
agencies.
4.2 Medium term behaviour
A Medium Term (MT) time horizon of 1 year is opted for. The behaviour of the model in the
short and medium term is displayed in Figure{5)
Graph for indirect degre of incton Graph for recently infected population Graph for susceptible population
oa 00% a
7 ~~ =
niet ep fice bene ey nied pope tease sce popn hse
(a) ind. degree of infection (MT) —(b) recently infected pop. (MT) —_(c) susceptible population (MT)
Graph for recovered temporarily immune population Graph for cumulative cholera cases Graph for cumulative cholera deaths
20M iM 20,000
|
— =e
ey ei pee tatane “ps cme ce exes ease cotati ce dnb fates pron
(a) recovered t. immune pop. (MT) (e) cumulative cholera cases (MT) _ (f) cumulative cholera deaths (MT)
Figure 5: Medium term behaviour of key variables of the Cholera Model (MT)
Looking only at these graphs, one may be tempted to conclude that the indirect degree of
infection (5a) and recently infected population (5b) have peaked and are on their way down,
that the susceptible population (5t) is reduced to less then half its initial value, that the recovered
temporarily immune population (5H) has been lifted to a higher level, that the number of cumulative
cholera cases (5b) enters the last phase of an S-shaped growth, and that the number of cumulative
cholera deaths (5f) seems to be leveling off! Towards the very end of the medium term time
eem to improve. One may even be tempted to conclude that the medical
horizon, all variable
short term intervention —the international medical intervention leading to an improvement of the
— may solve the problem in the long term...
average state of health servic
4.3 Long term behaviour
However, simulating the model over the long term -say 10 years~ may lead to very different
conclusions. The long term behaviour of the simulation model is displayed in Figure |6)
Note that these simulation results only correspond to the real-world epidemic if the model is a
good representation of the real-world problem — in other words, if the ensemble of (bold) assump-
tions holds. It should also be kept in mind that (rainy) seasons, social-geographic conditions, et
cetera, are not taken into account here.
The graphs of the long term simulations show that -even with the international medical
intervention— the indirect degree of infection (6h), the recently infected population (6b), the sus
ceptible population (6) and the recovered temporarily immune population (6H) oscillate, be it in
“The leveling off is clear if a lightly larger time horizon is used.
Cholera in Zimbabwe
Graph for indirect degree of infection
Graph for recently infected population
Graph for susceptible population
“lA
090
aes
se Dna
niet tne isin tema Dy
(a) ind. degree of infection (LT)
Graph for recovered temporarily immune population
scented poplatoncbaeese
(b) recently infected pop. (LT)
Graph for cumulative cholera eases
sat pp tne
(c) susceptible population (LT)
Graph for cumulative cholera deaths
2M on = 0000
uae a eat 0000 aa
————— Feet
(a) recovered t. immune pop. (LT) (e) cumulative cholera cases (LT) _(f) cumulative cholera deaths (LT)
Figure 6: Long term behaviour of the Cholera Model (LT)
a damped way, and that the cumulative cholera cases (62) and cumulative cholera deaths (6?)
keep on rising... These cyclic epidemic periods becoming endemic after a while- are of course
extremely undesirable.
First it is tested in section [5] whether this problematic behaviour is caused by some bold
assumptions or whether it s es within the problem itself. Then additionally needed
policies -to solve the cholera problem in Zimbabwe- are tested in subsection 6.1]
5 Exploration of Validity, Sensitivity, and Uncertainty
The model has not been validated by Cholera experts yet. Currently it contains some bold
assumptions: Cholera experts may be able to refine/improve some parts of the model and/or fill
in certain (data) gaps.
However, there will always be deep uncertainties that cannot be reduced by further research
or more expertise. Some of these uncertainties may be dealt with by means of exploration as
suggested by Lempert, Popper, and Bankes (2003)| and [Pruyt (2007)| (see subsection ??).
ing the real-world behaviour is not aimed
s and cholera deaths with the cholera cases
Although it should be clear that perfectly mimi
at, a (rough) comparison of the reported cholera cas
and cholera deaths generated with the simulation model (sce Figures{dp and {Zf) may provide some
confidence: After about 206 days, 4037 cumulative cholera deaths and 91164 cumulative cholera
sases were reported by the MoHCW (World Health Organization 2009b), compared to about 4540
simulated cholera deaths and 85000 simulated cholera cases (with mild and severe symptoms ~ the
total number of infected —including all those infected without any symptoms~ amounts to almost
303000).
Performing traditional sensitivity analyses, it can be concluded that the model is:
« numerically sensitive to changes of the value of the connectedness of the aquife
in the effect of the fraction infected on the fraction contam-
ensitive if the lookup function is shifted downward.
numerically sensitive to chang
inated water and behaviourally
Cholera in Zimbabwe 10
e strongly (numerically and behaviourally) sensitive to changes in the level of prevention and
the condition of the sanitary infrastructure.
e strongly (numerically and behaviourally) sensitive to changes in the average state of the
health services, although only in terms of the (cumulative) number of cholera deaths.
The main (poli
model are that:
) conclusions following from these sensitivity anal;
performed on the base
« Drastic and sustained improvements of the level of prevention and/or the condition of the
sanitary infrastructure are absolutely required to prevent cholera epidemics from reoccurring
in Zimbabwe (see subsection [6-1).
« A drastic and sustained improvement of the average state of health servic
reduce the number of cholera deaths in the current (and future) epidemic.
is necessary to
Since these improvements are feasible (but require political will, investments, and time), cholera
outbreaks in Zimbabwe ought to belong to the past.
Following uncertain variables/functions may have to be explored, both univariate and multi-
variate, too: the function of the indirect degree of infection, effect of the fraction of infected on
the fraction of contaminated water and the delay of smoothed fraction of contaminated water®),
the effect of prevention and sanitation on the indirect degree of infection, the level of prevention
and the condition of the sanitary infrastructure, the effect of the average state of health services
on the fraction of cholera deaths and the average state of health services, the connectedness of
aquifers, the effect of the average health condition on the fraction of mildly infected of all infected,
the average immunity period, the initial sizes of the subpopulations, and the influence of seasonality.
6 Model Use
The System Dynamics model could be used for several purposes. It may be used to increase the
anding of the link between structure and dynamics of cholera epidemics. It may be used
ing policies (see subsection 61). It may also be used as a ‘hot’ testing/teaching case (see
subsection (6.2).
6.1 Testing Policies
Four policies are simulated by means of the System Dynamics model and their corresponding long
term simulation results are compared:
1. The first intervention policy [ASHSonly]
there the average state of health services increases from a disastrous 15% from day 1 till day
130, to 40% on day 183, 70% on day 183, 75% on day 250, and 80% from day 300 on.
is a gradual medical intervention of the base case:
2. The second intervention policy [PrevInfraOnly] is a policy focussed on gradually improving
the level of prevention and the condition of the sanitary infrastructure without the gradual
medical intervention as in the base case. The level of prevention is assumed to increase from
10% from day 1 till day 130, to 30% on day 183, to 50% on day 206, to 80% from day 365
onl The condition of the sanitary infrastructure is assumed to improve more slowly, from
50% on day 1, to 55% on day 183,to 60% on day 365, to 85% on day 1825, and to 90% on
day 3650. These improvements may be too optimistic given the current political situation.
>The importance of the role of aquatic reservoirs of V. cholerae and their interaction with other factors for
driving cholera epidemic is largely unknown (Codeco 2001): the uncertainties are explored here, instead of omitted.
It is assumed that the level of prevention will never be water tight.
Cholera in Zimbabwe ll
. The third intervention policy [ASHSandPrevInfre
combines a medium term improvement
of the average state of health services as in the base case, with gradual improvements of the
level of prevention and the condition of the sanitary infrastructure as in the second policy
[PrevInfraOnly].
. The fourth intervention policy [NoIntery] consists of ‘no intervention at all’ (corresponding
to Mugabe’s initial line of policy).
ie cap gst sap pak scarermacaus
(a) ind. degree of infection (LT) (b) recently infected population (c) susceptible population (LT)
(LT)
Graph for recovered temporarily immmune population Graph for cunulative cholera cases Graph for cumulative cholera deaths
2M om 0,000
° S55 ° o
‘Tine (Dav) on Time Des) ~ “Tae Da) “eS
(4)
Figure 7: Policies:
recovered t. immune pop. (LT) (e) cumulative cholera cases (UT) (f) cumulative cholera deaths (LT)
ASHSonly (blue), PrevInfraOnly (red), ASHSandPrevInfra (green), NoInter-
vention (grey)
The graphs of the long term consequences of the different polici
The policies dis
or less to WHO po!
see Figure[7) show that:
A sufficient level of prevention and a decent sanitary infrastructure are neces
the indirect degree of infection, recently infected population and the
in the short and medium term, and to prevent future cholera outbre
(see Figures 7a, [7b, and |78).
The susceptible population will consequently increase and the recovered temporarily immune
population will decrease (see Figures [7p and {7il).
sary to decrease
mulative cholera cases
s in the longer term
The number of cumulative cholera deaths cannot be controlled with medical interventions
alone.
Prevention and infrastructure are beneficial in the longer term in terms of the cumulative
number of cholera deaths.
Medical intervention+prevention+infrastructure is an even better option in the short and
long term in terms of cholera deaths.
Lack of intervention has disastrous consequences in terms of cholera deaths (see Figure [7?)
and future cholera outbreaks.
ed above are not abrupt, nor are they innovative. They correspond more
and take difficulties of field interventions in third world countries into
account:
Cholera in Zimbabwe 12
¢ ‘Once an outbreak is detected, the usual intervention strategy aims to reduce mortality —
ideally below 1%~ by ensuring access to treatment and controlling the spread of disease’
(World Health Organization 2009¢).
for the prevention of cholera mostly consist of providing clean water and proper
anitation [ ...,] health education and good food hygiene’ (World Health Organization]
(2009e).
e ‘Given the outbreak’s dynamic, in the context of a dilapidated water and sanitation infras-
tructure and a weak health system, the practical implementation of control measures remains
a challenge’ (World Health Organization 2009a).
6.2 ‘Hot’ Teaching/Testing Case
This model was developed in the first week of January, was converted into a ‘Hot’ System Dynamics
Testing/Teaching Case (see (Pruyt 2009b) and (Pruyt, Slinger, van Daalen, Thissen, and Yucell
(2009), and was used a on 14 January 2009 (SEPAM BSc exam at the Faculty of
Technology, Policy and Management of Delft University of Technology). Other recent examples
of ‘Hot Testing/Teaching Cases’ developed and used at Delft University of Technology include
and (Pruyt 2009a).
The case description of the ‘Cholera in Zimbabwe’ case is included in the appendix [Al This
a classic System Dynamics case in the sense that students are asked to make a System
Dynamics simulation model corresponding to the case description (sce Figure 2), to make an ag-
gregated feedback loop diagram of the simulation model (sce Figure|3), to simulate the short term
behaviour (first 150 days) and make specific graphs (sce Figure|4), to validate the model briefly7!to
simulate the long term behaviour (10 years) and make graphs (see Figure|6), to perform sensitiv-
ity/uncertainty analyses, to propose and test policies, and to formulate a policy recommendation.
an exam case
7 Conclusions and Further Research
7.1 Conclusions
Although further research and validation is required to reduce/explore uncertain relationships
and gain more confidence in the System Dynamics model of the cholera epidemic in Zimbabwe, it
promises to be useful. Using the model, it c
¢ Drastic and sustained improvements of the level of prevention and/or the condition of the
sanitary infrastructure are absolutely necessary to prevent the current Zimbabwean cholera
epidemic from recurring and becoming endemic.
e A drastic and sustained improvement of the average state of health servi
reduce the number of cholera deaths in the current ~and future~ epidemi
e A short term medical emergency response should go hand in hand with long term educational
action related to cholera prevention and improvement of the sanitary infrastructure.
e Since these improvements are feasible, Zimbabwean cholera outbreaks ought to belong to
the past soon.
e Further research may be focussed on the bold assumptions, as well as on the inclusion
of the impact of rainy season, the poss
environmental details.
bility of direct contamination, social, geographic,
THere students are among other things required to apply several validation tests and to (roughly) compare the
reported cholera cases and cholera deaths with the model outputs. In order to to this, students need to add the
cumulative cholera cases stock variable.
Cholera in Zimbabwe 13
Hence, future cholera outbreaks can and ought to be prevented in Zimbabwe. Drastic and sus-
tained improvements of the level of prevention and/or the condition of the sanitary infrastructure
are needed to prevent the 2008-2009 cholera epidemic from recurring and becoming endemic.
Concerning the hot teaching/testing case, it can be concluded that the
simple, but good, hot teaching & testing cas
is a relatively
¢ for introductory System Dynamics
sours
References
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Cholera in Zimbabwe 4
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{http: //www.who.int/cholera/technical/prevention/control/en/index.html] [1| 12)
Appendices
A Open System Dynamics Modelling Question: The Cholera
Epidemic in Zimbabwe ( /25)
A.1 Introduction (background information)
‘The deterioration of the Zimbabwean sanitary and health infrastructures over the past years has lead to a lack of
safe drinking water and health services, especially in and around the cities, which lead to a cholera outbreak in
August 2008.
Cholera is an infectious disease caused by the ingestion of bacterium Vibrio cholerae present in faccally contam-
inated water. Symptoms are severe diarrhoea and dehydration. The extremely short incubation period is about 1
day.
‘The Zimbabwean Ministry of Health and Child Welfare (MoHCW) and the WHO reported a total of almost
30000 cholera cases and almost 1600 cholera deaths between August 2008 and January 2009
However, cholera can be prevented (rather easily) by taking the necessary precautionary hygienic measures
and/or a good sanitary infrastructure. In case of a fast and appropriate treatment, the mortality is low, about 1%.
‘That percentage was much higher in Zimbabwe.
Several international aid organisations offered to provide the necessary medical and sanitary facilities, safe water,
and programmes to train aid workers to deal with and prevent cholera. At first, Mugabe refused international aid,
but by mid December 2008, he allowed international aid organisations to provide clean drinking water. By that
time, half of the population was undernourished
A.2 Susceptible, Infected, Recovered and Immune Populations
When individuals from the susceptible population become infected (cholera infections), they shift to the recently
infected population. The number of cholera infections is the product of the susceptible population and the indirect
infection rate. Those shifted to the recently infected population leave that stock after an average incubation time
of only 1 day and flov
@ as mildly infected to the mildly infected population if they show mild or moderate symptoms, or if they are
infected but do not show any symptoms at all (all asymptomatic cases);
@ as heavily infected to the heavily infected population in case of severe symptoms.
The fraction of the recently infected population getting only mildly infected depends on the average health condition
of the average Zimbabwean. The fraction used in the base model equals 95%. In other words, only 5% of the recently
infected population in the base model becomes very ill after an average incubation time of 1 day.
All sick persons belonging to the mildly infected population shift —after an average duration of the illness of
10 days— as recovered from mild infection towards the recovered temporarily immune population. The sick persons
belonging to the heavily infected population either die (cholera deaths) or recover and become immune (recovered
from heavy infection) after the same average duration of the illness of 10 days. The fraction of the heavily infected
population dying or recovering depends on the effect of the average state of health services on the fraction of cholera
deaths, and hence, on the average state of health services.
The values of the effect of the average state of health services on the fraction of cholera deaths and the average
state of health services can be estimated based on WHO information: suppose that the effect of the average state
of health services on the fraction of cholera deaths is 100% in case of an average state of health services of 0%, 50%
in case of an average state of health services of 25%, 20% in case of an average state of health servi of 50%, 5%
in case of an average state of health services of 75%, and 0% in case of an average state of health services of 100%.
The average state of health services in Zimbabwe was extremely low at the time of the outbreak (until international
aid agencies were allowed access): assume that the average state of health services amounts to 15%.
‘After a first-order average immunity period of 6 years, Zimbabweans from the recovered temporarily immune
population flow back to the susceptible population.
‘The number of Zimbabwean citizens belonging, at the start of the epidemic, to the susceptible population can be
assumed to amount to 3000000, the recently infected population to 1000, the mildly infected population to 950, the
heavily infected population to 50, and the recovered temporarily immune population to 10226000 (this corresponds
to the remaining population: 13228000 - 3002000).
Cholera in Zimbabwe 15
A.3 Indirect Infection
The indirect rate of infection equals the product of following three factors: the smoothed fraction of contaminated
water, the effect of prevention and sanitation on the indirect degree of infection, and the connectedness of aquifers.
The connectedness of aquifers is assumed to amount to 28% in the base model.
The input of the effect of prevention and sanitation on the indirect degree of infection is the maximum of
two variables: the level of prevention and the state of the sanitary infrastructure. If the maximum of these two
variable: 0% then the effect on the indirect rate of infection is assumed to amount to 100%, if it is 25% then
the effect is assumed to amount to 90%, if it is 50% then the effect is assumed to amount to 50%, if it is 75% then
the effect is assumed to amount to 10%, and if it is 100% then the effect is assumed to amount to 0%. The level of
prevention and the state of the sanitary infrastructure lie between 0% and 100%. In Zimbabwe both are low: in
the base model, the level of prevention is initially assumed to be 10% and the state of the sanitary infrastructure
is initially assumed to be 30%.
The effect of the fraction of infected on the fraction of contaminated water is a graph/lookup function: if the
fraction of infected is 0% then the fraction of contaminated water is assumed to be 0%, if it is 12.5% then the
fraction of contaminated water is assumed to be 5%, if it is 25% then the fraction of contaminated water is assumed
to be 75%, if it is 50% then the fraction of contaminated water is assumed to be 90%, if it is 75% then the fraction
of contaminated water is assumed to be 99%, and if it is 100% then the fraction of contaminated water is assumed
to be 100%.
‘The smoothed fraction of contaminated water smoothes the (third order) effect of the fraction of infected on
the fraction of contaminated water with a delay of 14 days. Initially it equals 0.0004 (or 0.04%), initiating the
epidemic
‘And the fraction of infected equals of course the sum of the recently infected population, the mildly infected
population, and the heavily infected population, divided by the entire population.
A.4 Questions:
1. (_/7.5) Make a System Dynamics simulation model of the Zimbabwean cholera epidemic as described above
in subsections{A,2)en[A.3) Save the model on the exam drive. Verify your model.
2. ( /4) Make an (extremely) aggregated/simplified ‘causal loop diagram’ of this model.
3. ( /3) Simulate the model over the first 150 days of the cholera epidemic. Make graphs of the evolution
of the heavily infected population, the number of cumulative cholera deaths and the smoothed fraction of
contaminated water.
4. (_ /3) Validate the model. Propose 3 appropriate validation tests (except traditional sensitivity analysis),
apply these validation tests and describe your results/conclusions. Use for example the WHO information
that about 30000 cholera infections and about 1600 cholera deaths were reported after about 100 days. [Hint:
Create a new structure to keep track of the number of cholera infections since the outbreak of the epidemic.]
5. (_/2) It should be clear that this cholera epidemic will carry on unless drastic action is taken. The risk that
drastic action is not taken is real as long as Mugabe is in power. Simulate the model over a period of 10
years. Make graphs of the evolution of all subpopulations and the cumulative cholera infections and cholera
deaths (on the computer and your paper copy). What could be concluded from this long-term simulation?
6. (_/2.5) Investigate (not too detailed!) the sensitivity of the model given small changes of following variables:
the connectedness of the aquifers, the effect of the fraction of infected on the fraction of contaminated water,
the level of prevention, and the average state of health services. Describe your conclusions as concisely as
possible.
7. (_/3) Suppose that following measures are implemented abruptly 150 days after the outbreak of the cholera
epidemic:
© The level of prevention is changed abruptly from 10% to 70% (by means of water filters, decontami-
nation pills,...).
© The average state of health services is increased suddenly from 35% to 70% (by means of field /emergency
hospitals and the arrival of international aid organisations and large numbers of qualified medical per-
sonnel)
What are the consequences in terms of the number of cumulative cholera deaths and the cholera infections?
Draw the graphs on your exam copy. Are these measures sufficient?
B_ Equations of the System Dynamics Model
The model/equations can be derived from the case description. It will be provided upon request.
