A Multiagent-based Simulation of the Infection of the Macrophage by

Trypanosoma Cruzi in the Acute Phase of Chagas’ Disease: Inﬂuence of

the Initial Inoculum and Protozoan Escape Factor

Willian Cordeiro Farago

, Alcione de Paiva Oliveira

, Rodrigo Siqueira-Batista

Andr´eia Patr´ıcia Gomes

, Juliana Lopes Rangel Fietto

, F´abio Ribeiro Cerqueira

and Luiz Alberto Santana

Departamento de Inform´atica, Universidade Federal de Vic¸osa, 36570-900, Vic¸osa, Brazil

Departamento de Medicina e Enfermagem, Universidade Federal de Vic¸osa, 36570-900, Vic¸osa, Brazil

Departamento de Bioqu´ımica e Biologia Molecular, Universidade Federal de Vic¸osa, 36570-900, Vic¸osa, Brazil

Keywords:

Multiagent System, Immune System Simulation, Chagas’ Disease.

Abstract:

Chagas’ disease presents a wide distribution in Latin America. Some epidemiological studies show that there

are a prevalence of 16 to 18 million people affected by the disease and at least 100 million people at risk of be-

ing infected on these areas. Recently, due to the globalization, the disease, which was previously endemic only

in countries of Central America and South America, is now presenting cases in other regions such as North

America and Europe. Trypanosoma cruzi, the etiological agent, has the ability to promote changes in the tis-

sues of the vertebrate host with signiﬁcant morbidity, according to the degree of infection. This article presents

a simulation of the human immune system using a multiagent system approach. More speciﬁcally, we propose

a simulation study aimed at the acute phase of Chagas’ disease, related to the macrophage-Trypanosoma in-

teraction. The simulation showed that the initial number of T. cruzi inﬂuences in the outcome of infection and

was found a relationship between the escape factor and the total elimination of T. cruzi.

1 INTRODUCTION

Chagas’ disease (CD) was ﬁrst described by Carlos

Ribeiro Justiniano Chagas in 1909, in northern Minas

Gerais (Brazil). Recently, because of the globaliza-

tion, this disease that was endemic only in countries

of Central America and South America is now oc-

curring in other regions of the world such as North

America and Europe (Siqueira-Batista et al., 2007;

Rassi Jr et al., 2012). Trypanosoma cruzi (T. cruzi),

the etiological agent, is capable of causing a sig-

niﬁcant damage in the vertebrate host tissues lead-

ing to serious consequences, according to the de-

gree of infection (Alcantara and Brener, 1980). Af-

ter infection, the individual develops an acute phase

of short duration. At this stage a highly aggressive

form of T. cruzi, the trypomastigotes, is present in

the bloodstream. This causes the immune system re-

sponse via humoral and cellular mechanisms of innate

immunity such as complement-mediated lysis, natu-

ral killer cell cytotoxicity and phagocytosis carried

out by the mononuclear phagocyte system (MPS),

mainly by macrophages (Coura and Borges-Pereira,

2010; Rodrigues et al., 2010). The parasites use

escape mechanisms to survive to the action of the

macrophages and are not completely eliminated lead-

ing to a chronic disease characterized by low par-

asitemias with the prevalence of intracellular para-

sitism of the amastigotes form (Coura and Borges-

Pereira, 2010; Rodrigues et al., 2010). The disease

presents two distinct phases, an acute phase which

is followed by a chronic phase that can be classiﬁed

as indeterminate, cardiac or digestive form (Siqueira-

Batista et al., 2007). Usually, one third of the pa-

tients presenting the indeterminate classiﬁcation de-

velop symptomatic CD some decades after the ini-

tial infection (Siqueira-Batista et al., 2007; Coura and

Borges-Pereira, 2010).

It is believed that the T. cruzi load in the initial in-

fection is a major factor in the development of CD

(Borges-Pereira et al., 1988; Martins et al., 2012).

Cases reporting feces of triatomine with more than

1500 parasites have been described, but it is believed

that the quantities of T. cruzi needed to cause infec-

tion is far less than the inocula used in experimen-

tal infections (Coura and Borges-Pereira, 2010; Ro-

Farago, W., Oliveira, A., Siqueira-Batista, R., Gomes, A., Fietto, J., Cerqueira, F. and Santana, L.

A Multiagent-based Simulation of the Infection of the Macrophage by Trypanosoma Cruzi in the Acute Phase of Chagas’ Disease: Inﬂuence of the Initial Inoculum and Protozoan Escape

Factor.

In Proceedings of the 18th International Conference on Enterprise Information Systems (ICEIS 2016) - Volume 2, pages 29-38

ISBN: 978-989-758-187-8

drigues et al., 2010). Studies report that the vast ma-

jority of cases of acute CD in Brazil are asymptomatic

or mildly symptomatic, possibly due to low inoculum

and/or humoral response (Coura et al., 1983; Coura,

2013). A study encompassing almost three decades

of patients follow-up showed that the cases of more

severe chronic forms originated from cases with se-

vere acute phase. Thus it is possible to deduce that

the initial inoculum and/or the infecting strain of T.

cruzi inﬂuenced the evolution of the disease. Experi-

mental studies have shown that this load is generally

low (Dias, 1982).

Among the cells of the mononuclear phagocytic

system, the macrophage presents a key role in the

host response to T. cruzi. These cells have trypanoci-

dal and tripanostatic capacity and often determine the

degree of susceptibility of the infected host (Russo

and Starobinas, 1991). Activation of macrophages

in the acute phase of CD has long been described in

the literature. Activated macrophages are able to kill

the parasite. However, the resident macrophages do

not perform this action. The relevance of this try-

panocidal activity is not yet fully known (Celentano

and Gonz´alez Cappa, 1993). Macrophages phago-

cyte epimastigotes and trypomastigotes. The ﬁrst

kind is digested, while the latter kind escapes from

the vacuole and is transformed into amastigotes that

multiply inside the macrophages. This phenomenon

occurs in the region where the penetration of try-

pomastigotes takes place, initiating the intracellular

stage of the parasite. Each amastigote by binary ﬁs-

sion yields dozens of new amastigotes that after four

to six days are transformed into tripomastigotes that

disrupt the cell and reach other tissues. A simple bi-

nary division of amastigote is repeated every twelve

hours and produces about nine generations of para-

sites that disrupt the macrophage (Rey, 2008). Acti-

vation of macrophages leads to activation of T lym-

phocytes that secrete interferon γ, which in turn in-

duces macrophages to produce interleukin 1 (IL 1),

tumor necrosis factor (TNF), and nitric oxide (NO)

(Siqueira-Batista and Geller, 2008). The NO is ex-

tremely toxic for the T. cruzi and seems to be respon-

sible for tripanolitic action exerted by macrophages

(Rey, 2008). More detailed studies to improve the un-

derstanding of the immune system may contribute to

the treatment and prevention of the disease.

Multiagent system (MAS) has been successfully

applied in many complex systems. It allows the ex-

ploration of macroscopic behavior emerging from mi-

croscopic interactions. For this reason, MAS is con-

sidered by many authors the best approach to model

the immune system. Its main disadvantage, however,

is the high computational cost when a large number

of agents is used (hua Li et al., 2009). The simula-

tion using techniques of multiagent systems (MAS)

has been an important tool in the investigation of the

phenomena of interactions between the various cell

types of the immune system and pathogens such as

viruses, bacteria, and protozoa(Possi et al., 2011; Fol-

cik et al., 2007; Borges, 2012). These studies led to

designs with a bottom-up approach, i.e., the systems

are conceived deﬁning the individual aspects of the

agents, such that the emergency of the collective be-

havior occurs naturally from the interactions of the

agents with themselves and with the environment. As

a result, it is possible to test hypotheses of interest in

a realistic manner, i.e., without programming the de-

sired scenarios directly, but, instead, obtaining them

as a consequence (Possi et al., 2011).

The group of Modeling and Simulation of the Im-

mune System (ModeSimmune) of the XXX Univer-

sity, in a joint effortwith the Departments of Medicine

and Computer Science, is developing a simulator

of the human immune system called AutoSimmune,

based on the simulator initially developed by (Fol-

cik et al., 2007). AutoSimmune has been developed

since 2010 and is now able to perform many simu-

lations of interest, including viral and bacterial in-

fections and events involved in autoimmune condi-

tions (Possi et al., 2011; Bastos et al., 2013). In this

work, the investigations are focused on CD. To sim-

ulate CD regarding the interaction between T. cruzi

and macrophage cells, it was necessary to model and

introduce the T. cruzi agent. Furthermore, we had to

modify the existing pattern of the macrophage agent

in the simulator so that it was able to respond to stim-

uli from T. cruzi as described by (Coura and Borges-

Pereira, 2010). We analyzed whether the initial num-

ber of T. cruzi parasites inﬂuences the outcome of in-

fection and also the relationship between the rate of

escape of the parasite from the macrophage phago-

cytic vacuoleand the ﬁnal number of T. cruzi agent af-

ter an intracellular multiplication cycle of them (Possi

et al., 2011). Assuming that we have a reliable sim-

ulation of the real immune system, the analysis of

the results that we have obtained from our in silico

simulation provide us with strong evidences that new

hypotheses on the investigation of potential therapies

and/or drugs against CD might be of great impact in

this ﬁeld of study.

The next section describes some work related to

the proposed system. Section 3 presents the material

and methods used in the simulation, including a de-

scription of the model. Section 4 shows the results of

running the simulation. Section 5 discusses the results

presented. Finally, section 6 presents the conclusions

of this work.

ICEIS 2016 - 18th International Conference on Enterprise Information Systems

2 RELATED WORK

With regard to novelty, there have been other agent-

based models used to study T. cruzi, including

((Galv˜ao et al., 2008),(Devillers et al., 2008),(Galv˜ao

et al., 2010) and (Rogers et al., 2010)), but none have

focused on the interactions of macrophages and T.

cruzi.

(Galv˜ao et al., 2008) developed of a two-

dimensional agent-based model for chronic chagasic

cardiomyopathy after stem cell transplantation. Their

model included six different types of agents: inﬂam-

matory cell, ﬁbrosis area, cardiomyocyte, proinﬂam-

matory cytokine tumor necrosis factor-α, T. cruzi and

bone marrow stem cell. Although not explicit in the

paper, they have used a model based on cellular au-

tomata.

(Galv˜ao et al., 2010) developed a three-

dimensional multi-agent-based computational model

for the evolution of Chagas’ disease. Their model

included ﬁve different types of agents: inﬂammatory

cell, ﬁbrosis, cardiomyocyte, ﬁbroblast, and T. cruzi.

Note that the macrophages were not modelled. Fi-

brosis was a ﬁxed agent and the other types of agents

could move through the empty space randomly by us-

ing the Moore neighborhood. The aim of the model

was to reproduce the acute and chronic phases of Cha-

gas’ disease and the volume occupied by all different

types of cells in the cardiac tissue.

(Rogers et al., 2010) created a model-based agents

focusing on the T. cruzi vector in the Texas region.

They incorporated data related to the dominant syl-

vatic vector and host species for the T. cruzi in Texas

into an agent-based model using NetLogo.

3 MATERIALS AND METHODS

AutoSimmune is an immune system simulator with

original focus in autoimmunity. In its basic version,

it simulates the bone marrow, thymus, lymph nodes,

blood circulation and parenchymal tissue region. The

regions are simulated as a discrete space in a form

of a two-dimensional grid in which each agent has

a position (i, j). More than one agent can occupy

the same position, which somehow simulates a 3D

space. The movement of the agent is done by chang-

ing its current position to a position in the Moore

neighborhood (Dewri and Chakraborti, 2005). Thus,

an agent cannot “jump” positions, it needs to move

one position at a time. In a cell structure in the form

of a two-dimensional grid, the Moore neighborhood

(of radius one) comprises the eight neighboring cells

to a central cell. If allowed in their speciﬁcation,

an agent can move from one region to another by

means of special elements called portals, as proposed

in (Folcik et al., 2007). The simulation of substances

such as cytokines are performed by means of a layer

of data, named ValueLayer, provided by the Repast

framework

, over which the simulator was built. Sub-

stances, as they are released by cells, undergo a pro-

cess of diffusion, spreading in the surroundings of the

site in which they were released, decreasing its con-

centration, and also undergoing a process of decay,

reducing its amount with time (Possi et al., 2011).

The ValueLayer is an abstract layer of data that, at

the time of its creation, is associated with a region of

the grid. It is possible to combine multiple layers of

data at the same grid. Thus, an agent can know the

concentration of a given substance at that time instant

at position (i, j) (Possi et al., 2011).

The time is modeled using the concept of dis-

crete unit time provided by the framework, called

tick. Each component schedules their execution time,

informing when to start and the invocation interval

(Possi et al., 2011). As a result, all events are properly

synchronized. In the simulator, the afﬁnity (which is

the recognition strength of an antigen by a receptor)

is simulated by the number of matching bits between

two bit sequences: One belonging to a cell receptor

and another belonging to the antigen. The greater

the length of the matching, the greater the afﬁnity.

For the calculation of the afﬁnity we used the method

suggested by (Floreano and Mattiussi, 2008), called

the “length of the longest common subsequence”,

whose goal is to compute, given two patterns of bit

sequences A and B, the size of the largest contigu-

ous subsequence of bits that are contained in A and B

simultaneously, in the same order.

3.1 The Macrophage Agent Model

The software agent that plays the role of macrophages

in the simulator AutoSimmune needed to be im-

proved, since some of its functions that are essential

in the interaction with the T. cruzi were not modeled

and implemented in previous versions. The rules of

this agent are illustrated by the state chart showed in

Fig. 1.

The macrophages in AutoSimmune accomplish

their activities in the tissue, represented in the sim-

ulator by the Tissue zone (based on “Zone 1” deﬁned

by (Folcik et al., 2007)) which represents a slice of

a microscopic generic parenchymal tissue. This agent

migrates to the tissue when they detect the presence of

pro-inﬂammatory cytokines (MK1 group, after (Fol-

cik et al., 2007)) and enter the Tissue zone. The

repast.sourceforge.net

A Multiagent-based Simulation of the Infection of the Macrophage by Trypanosoma Cruzi in the Acute Phase of Chagas’ Disease: Inﬂuence

of the Initial Inoculum and Protozoan Escape Factor

Figure 1: Macrophage state chart.

agent follows the cellular stress signaling substance

until encountering the site of infection ﬂagged by the

necrosis substance released after cellular lysis. In the

presence of necrosis, itcommutes to the macrophage

pro-inﬂammatory state, which produces and releases

cytokine MK1 and phagocytes dead cells, PAMP-

positive pathogens and antigen-antibody complexes,

i.e., antibodies bound to any antigen marking it for

phagocytosis.

Changes in the macrophage behavior when it

phagocytes some foreign particle were inserted in the

AutoSimmune model. In this case, a transition state

called Destroying was created. When a macrophage

phagocytes T. cruzi, it may occur that T. cruzi is

not destroyed and ends up infecting and multiply-

ing inside the macrophage. If the micro-organisms

escape from the parasitophorous vacuole and infect

the macrophage, the macrophage switches to infected

state, continuing with its actions until the number of

parasites is large enough to rupture the macrophage.

After rupture, the cell dies and goes to the Necro-

sis state. At this time, the parasites are released

into the medium and the dispersion of necrosis sub-

stance occurs until the macrophage agent is engulfed

by another cell. When the micro-organisms or par-

ticles are destroyed the agent macrophage processes

it, extracting their antigens and presenting them to

T lymphocytes featuring the Enabled state. Infected

macrophages that destroy any micro-organism will

change to the Infected/Enabled state with the same

functions of the Enabled state, but keeping the inter-

nal proliferation of pathogens.

3.2 The Trypanosoma Cruzi Model

Initially, T. cruzi infects and multiplies in cells of

the mononuclear phagocyte system (MPS), notably

macrophage. Later on, T. cruzi migrates to other

parts of the organism and invades other host cells, es-

pecially smooth muscle, skeletal, cardiac nerve, en-

abling their stay in the host (Siqueira-Batista et al.,

2007; Martins et al., 2012). As we want to sim-

ulate the primary immune response, we inserted T.

cruzi in the Tissue zone. The representative agent

of T. cruzi in AutoSimmune was modeled and imple-

mented according to the parasite’s main functions and

features described in the biological literature, keeping

the highest possible ﬁdelity, so that we could emu-

late its behavior and allow the possibility for poste-

rior in vivo analysis of the immune response towards

the pathogenic agent and its peculiarities. The rules

of this agent are illustrated in Fig. 2.

Initially, the agent is in trypomastigote form and

randomly moves looking for other agents, which is

called Circling state. When it meets another agent, T.

cruzi checks if there is some afﬁnity with it. If afﬁnity

exists, this is a possible host cell and so the parasite

invades it. After invading the cell, T. cruzi turns into

amastigote and initiates a cycle of multiplications by

successive binary divisions with nine ﬁssions mostly

producing 50-500 parasites depending on the strain of

T. cruzi and the host cell (Rey, 2008; Siqueira-Batista

et al., 2007). After this step, still inside the parasitized

cell, T. cruzi undergoes further transformation into the

trypomastigote form and is released from the cell in

order to penetrate into other cells and tissues.

ICEIS 2016 - 18th International Conference on Enterprise Information Systems

Figure 2: Trypanosoma cruzi state chart.

3.3 Deﬁnition of Variables

The environment for the interactions between agents

in the simulations was the Tissue zone with grid size

150 by 150 units of space. To further analyze the in-

teraction of the parasite with the immune system, a

period of 1825 ticks was ﬁxed. The proposed value

for the tick in this study corresponds to six months of

infection. In this simulated environment, according to

the modeling decisions, the immune reaction should

not happen effectively, since the secondary immune

response has not been triggered yet and it is central to

restrain the levels of parasites (Siqueira-Batista et al.,

2007). During the simulations the following parame-

ters were evaluated:

• Tick: Unit of time provided by the framework.

The relationship between computational tick and

real time required for analysis and interpretation

of the simulations was based on the multiplica-

tion of T. cruzi. Amastigotes multiply by binary

ﬁssion every 12 hours in vivo, according to Rey

(2008), and in AutoSimmune the same process

occurred within 5 ticks, so we deﬁned that a tick

corresponds to 2 hours and 24 minutes.

• Initial number of T. cruzi:Total number of T. cruzi

inserted in the Tissue zone two ticks after the be-

ginning of the simulation. This inoculated para-

site load was set to 300 in the ﬁrst series of simu-

lations and 3000 in the second series.

• Initial number of macrophages: Number of

macrophages present in the Tissue zone before the

parasite load being inserted.

• Escape factor: Deﬁnes the chance of T. cruzi es-

caping from the phagocytic system and multiply-

ing within the macrophage. It can vary from zero

to one hundred percent of chance.

• Active infection: It is the active entry with energy

expenditure of T. cruzi into macrophages. As the

main mechanism of invasion occurs by phagocy-

tosis, the chance of occurring active infection has

been ﬁxed at 0.10 percent.

• Breach number: The maximum number of para-

sites within the macrophage after multiplication

cycle. When the number of T. cruzi reaches this

limit, the cell breaks downand the parasites are re-

leased. In this work, we follow what is described

by (Rey, 2008), i.e., after invading macrophage,

T. cruzi multiplies through a series of binary divi-

sions, about nine, generating approximately 500

strains.

• Tick when the numberof T. cruzi is zero: The time

when the number of parasites reaches zero.

• Maximum number of T. cruzi: It is the maximum

number of parasites in the Tissue zone area at a

given time. Generally,in vivo, this moment occurs

in the acute phase of the disease during the ﬁrst

weeks of infection.

• Maximum number of macrophages: The highest

occurrence of macrophages in the Tissue zone.

Although initially there is a ﬁxed number of

macrophages, when the parasites are introduced,

infecting and destroying cells, more macrophages

are recruited to the site of infection. The amount

depends on how the infection spreads through

the Tissue zone and not necessarily on existent

amount of T. cruzi.

A Multiagent-based Simulation of the Infection of the Macrophage by Trypanosoma Cruzi in the Acute Phase of Chagas’ Disease: Inﬂuence

of the Initial Inoculum and Protozoan Escape Factor

• Number of T. cruzi at the end:Amount of T. cruzi

in Tissue zone at the end of 1825 ticks.

• Number of Macrophage at the end: Amount of

macrophages in the Tissue zone at the end of 1825

ticks.

4 RESULTS

In order to validate the modeling and to study the in-

teractions between T. cruzi infection and the immune

system, two sequences of simulations varying the es-

cape factor were performed, one with initial number

of T. cruzi equal to 300 and another with this pa-

rameter equal to 3000. These values were based on

(Borges, 2012; Coura and Borges-Pereira, 2010) re-

view to investigate the variation of inoculums in vivo.

The values chosen for the escape factor were based on

its relationship with the number of T. cruzi at the end.

Each experiment has an increment of 0.1 or 0.01 in the

value of the escape factor of the previous experiment.

The range of 0.01 was used when the results showed

a random pattern. On the other hand, the value of 0.1

was used when the experiments behaved with a more

predictable pattern. Values above 1% were not simu-

lated because it has been observed that in such cases,

it is difﬁcult for the macrophages to restrain the infec-

tion.

The purpose was to investigate three important is-

sues in the study of CD: Whether there is a situation of

aggression and inﬂammation in response to the para-

site, as described in the literature by (Siqueira-Batista

et al., 2007; Rochitte et al., 2007); Whether the ini-

tial number of T. cruzi inﬂuences the outcome of in-

fection, as demonstrated experimentally in (Borges,

2012); and what is the relationship between the es-

cape factor and the total elimination of T. cruzi. Ta-

bles 1 and 2 show the results obtained after 104 simu-

lations, 52 for initial number of T. cruzi equal to 300,

and the remaining for initial number of T. cruzi equal

to 3000, respectively.

With inoculum of 300 T. cruzi agents, the

macrophages eliminated all of them in 20 simulations

with maximum escape factor up to 0.52%. For the in-

oculum of 3000 in 52 simulations, this phenomenon

occurred 13 times with maximum escape factor of

0.37%.

In simulations with inoculum of 3000 T. cruzi

agents, the lowest escape factor where the number of

T. cruzi at the end did not reach zero was 0.24% and

the highest escape factor where the number of T. cruzi

at the end zeroed was 0.37%. This is a narrow range

(around 0.13%) where the outcome of the infection

varies.

Table 1: Simulations with inoculum equal to 300.

escape Tick max. T. cruzi Mφ max.

factor(%) T. cruzi=0 T. cruzi tick 1825 tick 1825 Mφ

0.00 248 1001 0 364 369

0.10 166 1020 0 438 440

0.20 208 1000 0 348 352

0.21 259 3779 0 396 403

0.22 208 830 0 340 342

0.23 123 813 0 353 354

0.24 345 1000 0 343 348

0.25 316 1115 0 374 376

0.26 195 804 0 336 337

0.27 - 6526 6 373 399

0.28 121 799 0 349 349

0.29 419 1269 0 330 339

0.30 - 23064 7 1395 1396

0.31 - 4330 14 854 854

0.32 279 1555 0 426 430

0.33 1205 1221 0 475 477

0.34 1766 2085 0 489 494

0.35 322 832 0 424 430

0.36 - 25272 3655 2230 2248

0.37 1757 1204 0 443 446

0.38 - 33981 8406 1526 1537

0.39 - 95795 30648 1086 1479

0.40 - 34447 3782 1674 1674

0.41 723 1556 0 419 426

0.42 - 124231 38481 3078 3097

0.43 - 88893 26064 1020 1471

0.44 144 798 0 308 310

0.45 - 95426 11837 1267 1267

0.46 425 868 0 287 300

0.47 - 20003 3433 1804 1804

0.48 - 85131 17386 1092 1515

0.49 - 11000 427 1221 1236

0.50 - 122758 60693 2659 3030

0.51 - 61358 15387 1928 2069

0.52 358 799 0 310 311

0.53 - 105997 22354 2842 3627

0.54 - 132487 30863 1870 2698

0.55 - 186631 101125 4574 5874

0.56 - 91251 39787 2590 2590

0.57 - 132072 47724 4837 5743

0.58 - 60626 18765 1128 1194

0.59 - 67964 24631 746 1531

0.60 - 6432 1425 823 831

0.61 - 2206 47 602 608

0.62 - 149570 90749 2478 3332

0.63 - 59905 27439 3927 3966

0.64 - 117307 15611 678 2239

0.65 - 9386 3829 1474 1474

0.70 - 174423 32523 3182 3589

0.80 - 107358 46055 2627 2900

0.90 - 147222 68838 3034 3806

1.00 - 148243 133889 4332 5149

There is a greater tendency showing that the

largest the escape factor the largest the probability of

T. cruzi to multiply leading to an increasing number

of parasites in the environment, as observed in chart 3.

This occurred in the simulations of this study though

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Table 2: Simulations with inoculum equal to 3000.

escape Tick max. T. cruzi Mφ max.

factor(%) T. cruzi=0 T. cruzi tick 1825 tick 1825 Mφ

0.00 179 5502 0 425 425

0.10 211 3869 0 343 343

0.20 471 4019 0 491 507

0.21 1168 4516 0 406 419

0.22 959 5830 0 450 463

0.23 1247 4030 0 319 341

0.24 - 4290 3 518 523

0.25 413 3640 0 386 391

0.26 955 3803 0 525 525

0.27 1174 4601 0 630 650

0.28 1477 4414 0 615 620

0.29 - 11574 10 726 746

0.30 - 18928 1 981 981

0.31 1815 5269 0 629 636

0.32 - 3574 1 498 499

0.33 - 5183 4 607 638

0.34 1624 4503 0 606 624

0.35 - 69472 5421 1345 1424

0.36 - 36352 283 2794 2845

0.37 648 3595 0 408 409

0.38 - 114117 6382 733 1736

0.39 - 123258 64354 2442 3649

0.40 - 9987 334 1917 1917

0.41 - 87750 7292 2533 2533

0.42 - 127525 10635 1755 1755

0.43 - 120302 10790 1148 1696

0.44 - 102800 43675 3173 3471

0.45 - 93822 20017 1319 1514

0.46 - 137813 14931 2579 2591

0.47 - 87098 15687 1420 1585

0.48 - 7586 840 1712 1735

0.49 - 50139 5537 3423 3423

0.50 - 86034 24686 1803 2327

0.51 - 145739 12674 1523 2187

0.52 - 184655 96294 5319 6856

0.53 - 25522 9219 1627 1651

0.54 - 181202 68261 6731 6731

0.55 - 58513 22986 2233 2511

0.56 - 62830 15419 890 1115

0.57 - 156409 60189 2914 4690

0.58 - 127694 25559 930 2776

0.59 - 188053 58005 1406 2919

0.60 - 117632 17953 1412 2113

0.61 - 87890 13474 787 1441

0.62 - 85169 85169 6838 6875

0.63 - 106039 45118 1980 2198

0.64 - 129197 79346 5794 5911

0.65 - 91751 28611 2663 2663

0.70 - 113388 51583 4487 4781

0.80 - 130328 72959 4799 5046

0.90 - 158986 88700 2710 4788

1.00 - 109838 63082 3380 3427

this event did not happen uniformly (charts 4 and 5).

In the simulations with inoculum of 3000, the low-

est maximum number of T. cruzi was 3574 and it oc-

curred for an escape factor of 0.32%, while the high-

est number of T. cruzi was 188053 with an escape fac-

tor of 0.59%.

5 DISCUSSION

We observed that, in the presented simulations, the

results did not differ signiﬁcantly from in vitro stud-

ies. In this work, the initial number of T. cruzi inﬂu-

enced the outcome of infection. Experimental stud-

ies with different species of insects showed that the

number of parasites deposited at the site of infection

and that actively penetrate the host at the time of suc-

tion and defecation by these vectors is variable. After

the contact between infected triatomines and humans,

the outcome will depend on variables that control

the chances of infection (Coura and Borges-Pereira,

2010; Rassi Jr et al., 2012; Coura, 2013) Some stud-

ies report that variables such as the infection rate of

triatomines, the time between the sting and defeca-

tion, the number of evacuations and the quantity dur-

ing this time interval, the number of parasites elimi-

nated, the percentage of infecting forms and their ca-

pacity of penetration, and the intensity of the itching

during the sting are of great relevance to the occur-

rence of the infectious process (Coura and Borges-

Pereira, 2010). (Borges-Pereira et al., 1988) observed

that among eight species of triatomines infected with

T. cruzi, the mean number of parasites per evacuation

was 140. In their study, the authors found an average

of 232 parasites per evacuation among the P. megistus

species. In our simulation study, besides the use of

3000 agents, we also used 300 T. cruzi agents, which

is similar to the study of (Borges-Pereira et al., 1988).

The results of this study support the assumption

that the escape factor and the total elimination of T.

cruzi are closely linked, since variations of tenths and

even hundredths in escape factor had a signiﬁcant ef-

fect on the outcome of the simulations of the T. cruzi

macrophage interaction in the acute phase of CD.

As might be expected, the secondary immune re-

sponse is very important to prevent infection by the

parasite that causes CD since in most simulations only

the macrophage trypanocidal action was not enough

to halt the progression and action of the parasite. Still,

even not sufﬁcient, the macrophages were able, in

cases where the escape factor was very low, to elim-

inate parasites, and in other cases detain the spread

of infection by stabilizing the amount of parasites. It

shows the macrophage importance in modulating the

immune response to this disease.

As noted by (Possi et al., 2011), AutoSimmune

is still in development. However, the simulator has

been used in an others studies with promising results

(Da Silva et al., 2012; Bastos et al., 2013), which in-

A Multiagent-based Simulation of the Infection of the Macrophage by Trypanosoma Cruzi in the Acute Phase of Chagas’ Disease: Inﬂuence

of the Initial Inoculum and Protozoan Escape Factor

Figure 3: Relationship between escape factor and maximum number of T.cruzi/Number of T. cruzi at the end to inoculum

equal to 300.

Figure 4: Relationship between escape factor and maximum

number of T. cruzi to inoculum equal to 300.

Figure 5: Relationship between escape factor and maximum

number of T. cruzi to inoculum equal to 3000.

creases the expectation that it will be possible to reﬁne

our model, enabling the creation of a tool that sup-

ports hypothesis testing in biology and indicates new

insights for in vitro and in vivo research.

6 CONCLUSION

We conducted a study of an in silico simulation of in-

teractions between T. cruzi parasites and macrophage

cells, in the AutoSimmune. We did not ﬁnd similar

studies in a wide search in PubMed about in silico

simulation of this interaction. The study presented in

this paper showed that the in silico model of the inter-

action between Trypanosoma cruzi and macrophage

is a plausible approximation to what is described in

the medical literature (Siqueira-Batista et al., 2007).

We could observe that the initial number of T. cruzi

parasites inﬂuences in the outcome of infection, as

demonstrated experimentally, and found a relation-

ship between the escape factor and the total elimina-

tion of T. cruzi.

Observing the results for the number of T. cruzi

equal to 300 and 3000, we noticed the importance of

the quantity of inoculated strains on the outcome of

Chagas’ disease. As in (Borges, 2012), it was ob-

served that the tissue parasite load is directly related

to the inoculum used for the infection.

In addition to the results that support the hypoth-

esis about the quantity of inoculated strains on the

outcome of Chagas’ disease and relationship between

the escape factor and the total elimination of T. cruzi,

other important contributions of this research are a

computational model for the acute stage of Chagas’

disease and models of behavior for the macrophage

and T. cruzi.

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As future work, we intend to compare results of

analysis in silico,in vitro and in vivo as well, to obtain

a consensus measure of the value of the escape fac-

tor, and its relation to the activation of the secondary

immune response, due to its importance (Siqueira-

Batista et al., 2007).

ACKNOWLEDGEMENTS

This research is supported in part by the funding agen-

cies FAPEMIG, CNPq, and CAPES. The author Al-

cione de Paiva Oliveira receives a grant from CAPES,

process n.0449/15-6.

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