AgentbasedModelsinmalariaeliminationstrategydesign.pdf

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Agent-based Models in malaria elimination strategy design
J. Ferrer1*
, J. Albuquerque2
, C. Prats1
, D. López1
and J. Valls1
11
Escola Superior d'Agricultura de Barcelona, Departament de Física i Enginyeria Nuclear.
Universitat Politècnica de Catalunya. C/ Esteve Terradas, 8. E-08860 Castelldefels
(Barcelona), Spain.
1
Department de Física i Enginyeria Nuclear, Escola Superior d´Agricultura de Barcelona, Universitat Politècnica de Catalunya, Castelldefels,
Spain. jordi.ferrer-savall@upc.edu, clara.prats@upc.edu, daniel.lopez-codina@upc.edu quim.valls@upc.edu. +34.93.552.11.28.
2 Departamento de Estatística e Informática – Universidade Federal Rural de Pernambuco. Recife, PE, Brasil., joa@deinfo.ufrpe.br, ,
+55.81.3320.6491.
Abstract: The present work evaluates the methodology to plan, communicate and discuss specific interventions to tackle malaria
spreading by comparing three representative and deliberately simple epidemic models: A) an epidemic continuous model of the human
population, B) a population-based model that accounts for both hosts and vectors, and C) an Individual-based model that considers the
same scenario as in (B). The paper proposes a standard protocol and the use of open-source and user-friendly simulation environments to
communicate and discuss the models.
Keywords: Agent-based models, Malaria, Epidemiology, Computational Modeling
Acknowledgement: We thank the financial support of the Ministerio de Ciencia y Tecnología (CGL 2007-65142)

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1. BACKGROUND
1. Strategies for malaria control, elimination and eradication
Malaria is a preventable and treatable disease that kills more than one million people per
year, most of them children in the poorest countries of the equatorial and tropical biomes.
Despite the efforts carried out to fight malaria, the burden of the disease is still severe in those
regions where the disease is endemic (WHO, 2008a).
Today, malaria eradication is back on the agenda (WHO, 2008b). Global programs against
malaria tackle a complex reality and deal with socioeconomic, logistic and environmental
factors. From the scope of health care alone, the scheme to be followed must consider
medical coverage scale-up and improvement, increasing control of the disease, generalized
elimination and sustained surveillance (Molyneux et al, 2004, Greenwood, 2009). Global
strategies regard temporal scales of the order of the decades and they contemplate
unforeseen events such as the advent of new parasite resistance to drugs or the breakdown
of local health systems (WHO, 2005). Yet, global strategies finally lie on local specific
interventions, carried out by agents with a limited scope of action.
Elimination in areas of high, stable malaria transmission and with unrelenting vector
prevalence requires new tools and the combination of interventions in multiple fronts (Boni,
2008; White et al, 2009). It also requires complicity and coordination of local agents and
communities. The economic and human cost to carry out each intervention is substantial.
Therefore, strategies at a local level must be carefully planned, easily communicated and
continually evaluated (Rosensweig, 2009).

2. Epidemiology measurements and actions to tackle malaria
Planning strategies finally reposes on experience, heuristics and keen insight. However,
several tools may serve to support and guide decision making.
Impact of malaria is usually assessed through parasite prevalence (PR) and the fraction of
clinical infections (p) (Smith and Hay, 2009). Predictions on malaria spreading are usually
based on a single population-based calculated parameter: the reproduction number (R0)
(Bailey, 1982). Interventions to target malaria aim to reduce R0 through the control of the
vector population (mosquitoes), the reduction of human exposition to bites, and the treatment
of symptomatic patients. Table 1 lists the usual measurements of malaria epidemics and the
potential interventions to control the disease (White et al, 2009).

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Basic measurements in malaria epidemiology
(i) Parasite prevalence (PR), (v) Number and location of sick people
(ii) Fraction of clinical infections (p) (vi) Location and density of vector populations
(iii) Fraction of infected mosquito vectors (vii) Entomological Inoculation Rate (EIR)
(iv) Average duration of host immunity while not
exposed to the parasite
(viii) Infective persistence of the parasite in blood
(ix) Average parasite load in blood
Interventions for malaria control and elimination
(1) RTS: vaccination or profilaxis. Induced reduction of the susceptibility to infection of hosts.
(2) MAST: mass-screen and treatment of host population. Reduction of the infected population that shows clinical symptoms
or detectable parasite load.
(3) TBDH: transmission-blocking drug mass treatment. Target: hepatocytes, to prevent vector > human transmission
(4) TBDG: transmission-blocking drug mass treatment. Target: gametocytes, to prevent human > vector transmission
(5) ITN: insecticide-treated bed nets. Reduction of host-vector transmissions.
(6) IVM: integrated vector management. Control and elimination of mosquito population.
Table 1: Current measurements of malaria impact and field actions against the spreading of the infection.
It must be pointed out that the coverage, continuity and monitoring of the interventions is
determinant to the effectiveness of any attempt to control and eliminate malaria.
3. Models: an indispensable tool to design and evaluate strategies
Models are abstract constructions by which we represent reality. Mathematical modeling
and computer simulations are indispensable tools in science. They allow the quantitative
analysis of problems to perform testable predictions with a defined degree of confidence.
They are also communication tools that provide a common scaffold to understand reality,
interpret observations and design strategies (Knols, 2010).
Population-based Models (PbMs) are top-down approaches that describe the dynamics of
populations as a whole, usually by means of differential equations. They are well established
in malaria fight (Bailey, 1982; Koella, 1991) and they are used to plan and evaluate global
long-term strategies for malaria control (Maude et al, 2009). They may include age structure
(Aguas et al, 2007) and heterogeneity (Lloyd, 2007) of the population, as well as stochasticity
in the modeled rules. This has the cost of increasing the model complexity and making it less
clear than an equivalent simpler model (White et al, 2009).
Individual-based Models (IbMs) (a.k.a. Agent-based Models, in social sciences) are
bottom-up approaches to complex systems, complementary to PbMs, that describe the
behavior of individual entities and which compute the evolution of the population from the
individual interactions with each other and with their local environment. (Grimm et al, 2005).

The main role of IbM in malaria is to provide a better understanding of the host-vector system
(Mckenzie et al, 1998; Keeling and Grenfell, 2000; Gu et al, 2003).
IbMs are mechanistically rich: they offer an explicit connection between the parameters and
structure of the model and the mechanisms operating in reality (Ferrer et al, 2008). In
consequence, they are a clear and intuitive representation of the reality, as it is experienced
by the local agents (i.e. policy managers, health care workers and affected communities).
The purpose of this paper is to illustrate the suitability of the IbM approach as a prediction
and communication tool in the design implementation and evaluation of field interventions at a
local and short-range scales, complementary to the established PbM approach. It also
proposes the use of standard forms to communicate and analize models.
2. METHODS
We present three deliberately simple epidemiological models of stable falciparum malaria in
endemic region, we briefly review their structure and compare them one with each other and
with experimental data. These models are too naive to capture important features of the
disease, such as seasonality, multiplicity and coexistence of Plasmodium species and strains
or age structure in the host population, yet, they can provide deeper insight regarding
methodological issues. For this reason, their calibration is qualitative, and their comparison to
reality is approximate.
Two of the models are PbMs (Models A and B), and the third one is an IbM with the same
scheme as model B (Model C). Extended descriptions of each model and simulator are
presented in the Appendix (see Additional file). The three models have been implemented
and solved in the simulator platform NetLogo 4.1 (Wilensky, 1999).
2.1 Presentation of the models
Model A - SI1RI2: PbM that represents a constant (with no birth/death rates) host population
divided into four segments corresponding to four infection states: naïve susceptible (S),
infected showing clinical symptoms (I1), infected and asymptomatic (I2), and recovered and
partially immunized but susceptible (R). The fraction of population in each state varies
according to a set of transition rates defined in order to best fit the experimental
measurements, as shown in Figure 1. This model is inspired on two recognized PbMs (Aguas
et al, 2008; White et al, 2009).

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Model B - H(SI1RI2)-M(SI): PbM with the same structure as Model A for the host population
(S, I1, I2 and R) but which also considers a mosquito population divided into two segments:
susceptible (MS) and infectious (MI) vectors (Figure 1). It uses the same set of transition rates
as Model A but includes two new parameters for transitions between vector subpopulations.
Model C: Spatially explicit IbM operating with the scheme of Model B applied to each
individual (Figure 1). Its parameters are defined at an individual level and can be related to
field measurements.
A B
+
S I1
I2
R
MS
MI
1
1
τ

 
pM
rM
C
2
1
τ
A B
+
S I1
I2
R
MS
MI
1
1
τ

 
pM
rM
C
2
1
τ
Figure 1: Schemes of the three models. Model A: PbM SI1RI1, Model B: PbM H(SI1RI2)-M(SI). Model C: IbM H(SI1RI2)-M(SI). Human
figures represent subpopulations in A,B and individuals in C, in the infection states: susceptible -green, S-, clinically infected -red, I1--
asymptomatic infected -orange, I2- and recovered -grey, R-. Mosquitoes represent infectious and susceptible vector populations in Models A,
B and individuals in Model C. Black –healthy mosquito MS -, and white – infected carrier MI- . force of infection, irecovery time of
infection stage i, rate of loss of acquired immunity, pM: probability of infection of vector, rM: renewal rate of vector.
The direct outputs of the models are parasite prevalence (PR) and fraction of clinical
infections (p). They are obtained at each time step (t) with:
(t)
I
+
(t)
I
+
R(t)
+
S(t)
(t)
I
+
(t)
I
=
(t)
PR
2
1
2
1
[1]
(t)
I
(t)
I
=
(t)
p
2
1
. [2]
Model C has two additional output variables, the force of infection, , and the Entomological
Inoculation Rate, (EIR, Kelly-Hope and McKenzie, 2009) which can be compared with field
measurements and with the input parameters of the PbMs.
ness
contagious
of
duration
x
hosts
e
susceptibl
of
Number
contagions
host
of
Number
=
λ(t) [3]
hosts
of
Number
contagions
host
of
Number
=
EIR(t) . [4]

2.2 Relation between the parameters of the models and the real measurements
Parameter and biological meaning Models
Real-world
observation
* Real-world action
*
force of infection A (i)-(viii) (1)-(6)
irecovery rate of Ii A,B,C (viii) (2)
relative infectivity of 1 to 2 A,B,C (viii) (1)
loss of immunity A,B,C (iv) -
pH: infection probability of host B,C (vii) (1,3,5)
pM: infection probability of vector B,C (vi) ( 4, 5)
rM: death rate of vectors B,C (iii) (6)
Table 2: Parameters of equivalent PbM and IbM models and their relation with the real-world measurements and field interventions (* see
Table 1).
Table 2 presents the model parameters and relates them with real interventions and
measurements. Their values are inferred from data in the literature, taken from average
measurements or adjusted in such a way that model outcomes best fit the field observations
(Aguas et al, 2008). Table 2 shows that Model A is highly aggregated (Ferrer et al, 2009): it
incorporates a lot of the measurable information into a single parameter, the force of infection
( ). This makes it quite obscure, as alone mainly drives the evolution of the infection.
Moreover, this parameter is defined rather circularly:
 
2
1
2
0
I
+
R
+
I
+
S
α
I
+
I
R
=
λ 1
, [5]
where







 
2
1
0
1
τ
p
+
τ
p
β·
=
R , [6]
and
2
φI
+
I
λ
=
β
1
. [7]
Actually, this poses no problem from the practical point of view, as its value is set to best fit
the field data. Nevertheless, it makes  a blind hodgepodge parameter, barely usable for the
design of particular strategies.
Model B replaces the parameter  by the infection probability of hosts (pH), and adds two
parameters for the vector population: infection probability of (pM) and renewal rate (rM).
Shifting from Model B to Model A only requires calculating as:

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M
M
H
r
·p
p
=
λ [8]
Model C uses the same infection scheme as Model B but its parameters are individually
defined. For instance, pH stands for the probability of a host being infected when coming upon
a carrier vector, rather than the rate of vectors infecting hosts. Thus, they are more easily
linked one-to-one with real-world phenomena, which may be independently modified by
different field interventions.
3 RESULTS AND DISCUSSION
3.1 Comparison of the outcome of the three models
Models A, B and C have been compared one to each other and to experimental data
available in the literature (Aguas et al, 2008; White et al, 2009). As a result of this
comparison, it is found that:
1. the three models show similar temporal evolutions for compatible sets of parameters
(Figure 2),
C
B
A C
B
A
Figure 2: Temporal evolutions of the three models after a one-time intervention that reduced parasite prevalence. Each line shows the
percentage of the segments of host population through time.
2. the outcome (long-term parasite prevalence, PR, and reproduction number, R0) of all
three models can be fitted to different sets of regional experimental data (Figure 3).

a) b)
Bakau
Foni Kansala
Kilifi
a) b)
Bakau
Foni Kansala
Kilifi
Figure 3: Parasite prevalence as a function of the force of infection . a) Experimental and simulated data, reprinted from Aguas et al,
2008, PlosOne 3 (3) e17676, showing parasite prevalence for different regions characterized by different forces of infection. b) Simulation
outcomes obtained with models A, B and C.
These results show that the three models are alike, in accordance with what previous
results indicated (White et al, 2009). Nevertheless, they have some intrinsic differences,
which are outlined below.
First, PbMs and IbMs cope with different sets of field measurements and perform optimally
at different levels of description. While IbMs can include detail for specific measurements and
interventions, PbMs are better to deal with average magnitudes that do not account for such
particularities. In particular, results obtained from an IbM may be used to define the input
parameters of a PbM.
Second, PbMs are easily handled with mathematical analysis. Their interpretation is
straightforward and only requires mathematical skills, while IbMs require the use of computers
and performing a statistical number of simulations to obtain significant outcomes. Recent
efforts have been addressed to build a standard formalism for analyzing and communicating
IbMs (Grimm et al, 2006; Grimm et al, 2010).
Third, PbMs use real numbers instead of the whole numbers used by IbMs. This allows
dealing with great populations, but presents problems for smaller ones due to the original
discrete essence of humans and mosquitoes. For instance, below the threshold of disease
elimination (R0 <1), PbMs asymptotically tend towards the disease elimination (PR→0) but,
unlike IbMs, never reach it. This is usually solved by considering that the disease has been
eliminated when PR reaches a prefixed negligible value, but poses a problem when dealing
with small populations or segments of the population (e.g. when a single carrier can import
the infection into a naive population).

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Finally, simple PbMs are often deterministic but IbMs usually consider stochasticity. Thus, a
PbM always gives the same outcome for a fixed set of parameters. An indirect consequence
of this is that qualitative changes in the outcome of a PbM may occur in very sharp
transitions. For instance, in the threshold R0 ≈ 1, if the model concludes that a certain
intervention must be maintained for a span teff in order to lead to elimination, it is actually
stating that any intervention lasting t = teff -is ineffective, while it works well as soon as t =
teff + , even for minute values of  (Aguas et al, 2008). Such non-realistic behavior of
deterministic PbMs arises from the fact that continuous variables may present mathematical
singularities near some particular values. A similar phenomenon occurs due to the chaotic
behavior of the deterministic equations for certain sets of parameters. In this case, the
outcome is highly sensitive to initial conditions, rendering long-term prediction impossible. In
contrast, the dynamics of IbMs usually evolve towards fixed or limited attractors, this meaning
that their predictions are circumscribed around an average outcome, and show a definite
variance.
3.2 Results obtained with the IbM
Over 10,000 simulations have been carried out to scan the parameter space of Model C in a
closed system, in the short and middle-term (each run representing 1 year). Some general
results are listed below.
 Stochastic variability of the model outcome is PR < 5 % after modifying only the
random seed.
 Modifications on the density of host and/or vector populations strongly influence the
simulator outcome.
 Several modeled actions may lead to local disease elimination:
 Reducing the transmission rates pH and pM. These represent RTS and TBDH, and
TBDG strategies, respectively, in the real world. In order to reduce pM, it is important
to block the transmission from both the clinically infected and asymptomatic hosts.
 Permanently reducing the population density of vectors, so that the host-vector
encounter is less probable. This represents IVM interventions.
 The number of infective encounters is also reduced with ITN, which can be
represented in the model by the joint reduction of pM and pH.
 Reducing the population of infected hosts, either through one-time interventions
that directly affect the percentage of I1 and I2 segments, or by reducing the duration
of contagiousness, 1 and 2, permanently or during lasting interventions.
Elimination strategies usually entail tackling both people with clinical malaria and
with an asymptomatic infection (Figure 4a). These modifications represent MAST
interventions in the real systems.

Control IVM 50% ITN 50%
PR = 37%
 = 0.51
EIR = 0.023
PR = 21.4%
 = 0.23
EIR = 0.007
PR = 8.7%
 = 0.11
EIR = 0.003
Model
output:
Model Scenario
Host
population
b)
Prevalence
1 (days)
2
(days)
_1
100
1000
100
10
a)
Control IVM 50% ITN 50%
PR = 37%
 = 0.51
EIR = 0.023
PR = 21.4%
 = 0.23
EIR = 0.007
PR = 8.7%
 = 0.11
EIR = 0.003
Model
output:
Model Scenario
Host
population
b)
Prevalence
1 (days)
2
(days)
_1
100
1000
100
10
a)
Figure 4: Simulation results of Model C. a) Response of the IbM to variation of the duration of clinical infection (1) and asymptomatic
infection (2). The model shows that elimination can be achieved by reducing 1 and 2. b) Comparison between the effect of reducing vector
density (IVM) and mosquito bites (ITN) by 50% on a given scenario. PR: parasite prevalence, l: force of infection and EIR: Entomological
Inoculation Rate.
This naive IbM allows comparing two different interventions on the same scenario, which
may be useful to evaluate cost efficiency of alternative options. For instance, comparing
MAST addressed either to asymptomatic or to clinically infected people (Figure 4a), or
comparing a reduction of 50% vector population with IVM against protecting half of the people
with ITN (Figure 4b).
4. CONCLUSIONS AND FURTHER WORK
Models are an essential tool to help decision making and to evaluate specific strategies.
Simple mathematical models based on a population approach are a good tool to deal with the
long-term (i.e. covering several years or even decades) evolution of the disease at a regional
scale but find some limitations to capture features of smaller communities and shorter time
scales.
IbMs are not necessarily more complicated than population models based on continuous
equations. Their parameters have a more direct connection with field measurements and/or
specific actions and campaigns. This also entails that they are quite data-hungry, this makes
them less appropriate to study systems where the specific measurements are hardly
obtained.
IbMs are versatile. They can include heterogeneity among the population (e.g. in their
access and response to treatments), and can easily incorporate external fluxes (e.g. imported

ISSN 1726-670X
malaria), discrete interventions and unexpected events (e.g. abrupt cessation of interventions)
with slight modification of the model structure. For this reason, they represent a good tool for
the planning and evaluation of realistic field strategies in short temporal scales.
NetLogo and other user-friendly IbM modeling environments are appropriate frameworks to
use IbMs as communication tools, to represent and discuss local strategies against malaria
with decisive agents (MOSIMBIO, 2010). They are adequate for non-modelers and policy
makers because they present very simple interfaces that allow an easy manipulation of the
real-world schemes.
The models presented here are deliberately simple in nature. They are put forward to
illustrate essential differences in the methodological approaches to model malaria epidemics,
rather than to present realistic results on specific systems. Nevertheless, even such simple
models provide important insight. The most remarkable result in this sense is that
asymptomatic infected people represent a permanent pool of the parasite that must be
tackled to achieve elimination.
Perspectives for the current model include its application to the analysis of past and future
strategies for controlled real-world communities, for instance, IBMs can include Geographic
Information Systems (GIS) in spatially explicit frameworks and they can account for
particularities of specific scenarios (Perez and Dragicevic, 2009). The IbM is currently in the
process of being adapted to allow for the description of the epidemiology in the national park
of Jaú, Brasil. This requires an increase of complexity of the model to incorporate
geoepidemiological constraints of the rainforest biomes, ecological landscapes of multiple
parasite and strains, and specific traits of P. vivax. Nevertheless, these improvements do not
affect the scaffolding of the model and can be easily integrated in the IbM structure.
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AUTHOR INFORMATION AND CONTRIBUTIONS
DL and JV are senior researchers in IbM of complex systems in the context of theoretical ecology and applied microbiology. JF and CP are
two postdocs from the same group, MOSIMBIO. JA is a Professor at the Department of Statistics and Informatics of the Federal Rural
University of Pernambuco, Brazil, where he coordinates the Research Group for Computational Modeling..
JF designed the models and carried out the simulations. CP and DL proposed the virtual experiments and criteria to compare the models
with each other and with the experimental results. CP and JV assisted in the calibration, analysis of sensitivity and optimization of the
simulator. JF and JA shaped the discourse of the manuscript

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