MODELING/GIS, RISK ASSESSMENT, ECONOMIC IMPACT

Household Model of Chagas Disease Vectors (Hemiptera: Reduviidae)Considering Domestic, Peridomestic, and Sylvatic Vector Populations

L. STEVENS,1,2 D. M. RIZZO,3 D. E. LUCERO,1 AND J. C. PIZARRO4

J. Med. Entomol. 50(4): 907Ð915 (2013); DOI: http://dx.doi.org/10.1603/ME12096

ABSTRACT Disease transmission is difÞcult to model because most vectors and hosts have differentgeneration times. Chagas disease is such a situation, where insect vectors have 1Ð2 generationsannually and mammalian hosts, including humans, can live for decades. The hemataphagous triato-minae vectors (Hemiptera: Reduviidae) of the causative parasite Trypanosoma cruzi (Kinetoplastida:Trypanosomatidae) usually feed on sleeping hosts, making vector infestation of houses, peridomesticareas, and wild animal burrows a central factor in transmission. Because of difÞculties with differentgeneration times, we developed a model considering the dwelling as the unit of infection, changingthe dynamics from an indirect to a direct transmission model. In some regions, vectors only infesthouses; in others, they infest corrals; and in some regions, they also infest wild animal burrows. Weexamined the effect of sylvatic and peridomestic vector populations on household infestation rates.Both sylvatic and peridomestic vectors increase house infestation rates, sylvatic much more thanperidomestic, as measured by the reproductive number R0. The efÞcacy of manipulating parametersin the model to control vector populations was examined. WhenR0� 1, the number of infested housesincreases. The presence of sylvatic vectors increasesR0 by at least an order of magnitude. When thereare no sylvatic vectors, spraying rate is the most inßuential parameter. Spraying rate is relativelyunimportant when there are sylvatic vectors; in this case, community size, especially the ratio of housesto sylvatic burrows, is most important. The application of this modeling approach to other parasitesand enhancements of the model are discussed.

KEY WORDS triatoma, Chagas disease, mathematical model, vector control

Chagas disease or American trypanosomiasis is causedby the parasite Trypanosoma cruzi (Kinetoplastida:Trypanosomatidae) and afßicts up to 10 million peo-ple in Latin America (Hotez et al. 2008). It causespotentially life-threatening disease in up to one-thirdof those infected and is most easily cured during theearly stage of infection by using drugs with consider-able side effects (Andrade et al. 2011). The most ef-fective way to achieve and maintain low prevalence ofChagas disease is to prevent humans from being bittenby infected insect vectors. There are �130 species inthe subfamily Triatominae (Hemiptera: Reduviidae),idiomatically referred to as vinchucas, chinches, andkissing bugs in South, Central, and North America,respectively (Capinera 2008). Interrupting transmis-sion is complicated by the fact that the parasite hasmultiple mammalian hosts and insect vectors. Triato-minae feed on a variety of vertebrate hosts, includingmammals and birds, yet only mammals can becomeinfected. Because vectors feed on a variety of hosts,they have domestic, peridomestic (around the house),

and sylvatic (wild) populations. The ecology of theparasite life cycle varies among regions, being inßu-enced by the local domestic vertebrates, insect vectorspecies, and zoonotic vertebrate hosts. In some re-gions, sylvatic vector populations likely jeopardizecontrol efforts (Noireau 2009). Research to date sug-gests low-cost economic and human behavior strate-gies, in combination with insecticide spraying andhousing improvement, are the most effective way toreduce disease transmission (Bustamante et al. 2009,Monroy et al. 2011, Lucero et al. 2013).

Infection in the vertebrate host occurs when theparasite enters the body through mucous membranes,a break in the skin, or the ingestion of infected vectors.The blood-sucking vectors live in houses, moving fromdiurnal hiding places to feed at night. Scratching theitching insect bite transmits the parasite into the bloodof the mammalian host. The parasite can also be trans-mitted to humans by blood transfusion, and maternalÐfetal transmission occurs. Severe acute symptoms oc-cur in �1% of cases. Chronic symptoms develop inabout one-third of those infected and occur some10Ð20 yr after initial infection (Andrade et al. 2011).The disease affects the heart in 25% of those infected,the esophagus and colon in 6%, and the peripheralnervous system in 3%.

Three initiatives have been developed to reduce theprevalence of Chagas disease in Latin America. The

1 Department of Biology, University of Vermont, 321 Marsh LifeScience Building, Burlington, VT 05405.

2 Corresponding author, e-mail: lori.stevens@uvm.edu.3 Facultad de Bioquõmica, Universidad Mayor Real y PontiÞcia de

San Francisco Xavier de Chuquisaca, Sucre, Bolivia.4 School of Engineering, University of Vermont, 220 Votey Building,

Burlington, VT 05405.

0022-2585/13/0907Ð0915$04.00/0 � 2013 Entomological Society of America

Southern Cone Initiative was implemented in 1991 inArgentina, Bolivia, Brazil, Chile, Paraguay, and Uru-guay to reduce Chagas disease by targeting transmis-sion by insect vectors and blood transfusion. Five ofthe six countries reduced prevalence by 60Ð90%, sothat rates of infection in 2000 ranged from a low of0.06% in Uruguay to a high of 3.9% in Paraguay (Mon-cayo and Silveira 2009). Despite this success, someregions, especially the Department of Chuquisaca,Bolivia, retain a high rate of infection. In regionswhere the Triatoma infestans (Reduviidae, Triatomi-nae) is solely domestic, vector control is simpliÞed.Genetic evidence suggests the Andes region is possi-bly the geographic origin of the species (Giordano etal. 2005); however, the Gran Chaco has not been ruledout (Perez de Rosas et al. 2011, Piccinali et al. 2011,Quisberth et al. 2011). Within Chuquisaca, in theProvince of Oropeza, 35% of children aged �5 yr wereseropositive in 2002 (SEDES-Chiquisaca 2006). T. in-festans, the major vector of Chagas disease in the South-ern Cone countries, has been increasingly reported fromsylvatichabitats(Buitragoetal. 2010;Waleckxetal. 2011,2012). Since 1997, the Andean (Colombia, Ecuador,Peru, and Venezuela) and Central American (Belize,Costa Rica, El Salvador, Guatemala, Honduras, Mexico,Nicaragua, and Panama) initiatives have focused on vec-tor control in these regions where there are domestic,peridomestic, and sylvatic populations.

Although vectors feed on a variety of hosts andpotentially have domestic, peridomestic, and sylvaticpopulations, most triatomine species are strictly in-habitants of wild ecotopes and never invade houses. Asmall number are domesticated, and along with a num-ber of sylvatic species that intermittently invadehouses, these transmit the parasite to humans anddomestic mammals. Vector control is central to re-ducing transmission because home infestation ratescan be high and 100s of triatomines can be found in asingle house (Pizarro et al. 1996). The main domesticspecies (T. infestans, Triatoma brasiliensis, Triatomadimidiata, Triatoma sordida, Panstrongylus megistus,and Rhodnius prolixus) are responsible for �80% ofhuman Chagas disease (Stevens et al. 2011).

Chagas disease has been modeled as a vector-trans-mitted disease by using indirect transmission models(Anderson and May 1991) by several authors (Velas-coÐHernandez 1994, Cohen and Gurtler 2001, Inabaand Sekine 2004, Spagnuolo et al. 2011, CruzÐPachecoet al. 2012). These models consider the transmissiondynamics between the mammalian host and the insectvectors. The more recent models have focused on theeffect of various control measures, including the effectof insecticide spraying on vector control (Spagnuoloet al. 2011, CruzÐPacheco et al. 2012), and consideredtransmission dynamics among various populations suchas humans, domestic animals (e.g., dogs), peridomesticanimals (e.g., chickens), and vectors. One of the maindifÞcultieswhenmodelingvector-transmitteddiseases isthat the time scales of the host and vector populationcycles are very different. Human life expectancy is �70yr in many of these countries, but vector life cycles aretypically of the order of months.

Time-relatedcomplicationscouldbeavoidedbyusinga different modeling approach, that is, by consideringhouse infestation as the phenomenon to model. In thefollowing model, we consider the dwellings of the mam-mals that suffer the disease to be the “hosts,” that is, hostsinclude human houses, peridomestic structures (e.g.,corrals), and sylvatic dwellings (e.g., animal nests, caves,and rodent burrows). This approach is similar to thatused to model transmission of bovine viral diarrheaamong farm animals (Tinsley et al. 2012).

Recently developed molecular genetic techniquescan be used to estimate vector movement betweenhabitats. Data using microsatellite loci provide infor-mation on the geographic scale at which insects ran-domly mate and can be used to estimate migration(Dorn et al. 2003, Calderon et al. 2004, Pizarro et al.2008). In addition, methods are available to identifythe sources of vertebrate bloodmeals (Pizarro et al.2007, Pizarro and Stevens 2008, Stevens et al. 2012). Byusing these techniques, vector movement can be es-timated, for example, from the number of domesticvectors that contain blood from peridomestic areas(Pizarro and Stevens 2008). We developed a modelthat includes vector movement between domestic andperidomestic or sylvatic habitats, a major concern ofChagas disease transmission. Our model (Fig. 1) isbased on the observation that among rural communi-ties in the Province of Zudanez, Department ofChiquisaca, Bolivia, data from 2002 show a signiÞcantcorrelation between the percent of houses infestedand Chagas disease prevalence in children aged �5 yr(r2 � 0.88; P � 0.02), whereas no correlation existsbetween the percent of infected triatomines and dis-easeprevalence(P�0.50)(SEDES-Chiquisaca2006).With this model, we ask: what is the effect of perido-mestic or sylvatic vector populations on the number ofinfested houses? In addition, we perform a sensitivityanalysis (i.e., examination of how the dynamics of thesystem change as parameter values vary) to provideinformation on the most effective methods for con-trolling vector populations.

Materials and Methods

Model Development. The direct transmissionmodel considers susceptible (uninfested), infested,and resistant (insecticide-treated) houses. With thisapproach, we proceed to model transmission as it isdone for macroparasitic diseases, that is, following thevector burden of each house or corral: the greater thevector burden, the higher the infestation of the dwell-ing. The model assumes mass action, which impliesthat vectors are equally mobile throughout the area,and has two groups of vectors based on the habitatwhere they feed and reproduce. One habitat is houses;the other comprises peridomestic structures (i.e., cor-rals or other structures where livestock are kept, orsylvatic dwellings such as wild animal burrows). Themodel includes the common control method for Cha-gas disease vectors, periodic spraying of residual in-secticides, and there may or may not exist differencesin application to the houses and peridomestic areas.

908 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 50, no. 4

For our model, the reproduction number representsthe number of structures a single infested house caninfest. In the following text, we describe the model,calculate the reproduction number, and examinehouse infestation under a variety of conditions.

Movement between houses and peridomestic areasis modeled such that vectors residing in houses (group1) spend, on average, 1/�1 units of time in corrals orburrows, and (group 2) likewise, vectors in corrals orburrows spend, on average, 1/�2 units of time inhouses. The equations describing the interaction be-tween house and peridomestic vectors are:

dSi

dt� �iNi � �iSi��1 � �i�

Ii

Ni* � �j

Ij

Ni*�� ��i � �i�Si � iTi

dTi

dt� �i�Ii � Si� � i�iTi� �1 � �i�

Ii

Ni* � �j

Ij

Ni*�

� �i � �i�Ti

dIi

dt� �i�Si � iTi�� �1 � �i�

Ii

Ni* � �j

Ij

Ni*�

� ��i � �i�Ii

where for i, j� 1, 2 and i� j; Si, Ii and Ti represent thenumber of susceptible, infested, and insecticide-treated dwellings in each group (1 � houses, 2 �corrals or sylvatic), respectively; and Ni� Si� Ti� Ii(Fig. 2). The parameters �i and �i represent the dwell-ing infestation and replacement rates, respectively. Inaddition, let:

�i ��i

�i � �i

andNi

* � �1 � �i�Ni � �jNj

represent the fraction of their lives that vectors ingroup i spend in group j, and the weighted effectivepopulation size in each group when receiving nonlocalvectors (“visitors” of the other group), respectively.The vaccination or insecticide spraying-related pa-rameters for each subgroup are �i, i, and i,which arethe spraying rate, insecticide waning rate, and spray-ing efÞcacy coefÞcients, respectively (Fig. 2). Dwell-ings, whether infested or not, are sprayed periodicallyat the same rate (�i). Waning (i) represents theamount of time after application that the insecticide iseffective.As sprayingmaynotalwayskill all the insectsin a dwelling, i is the proportion of dwellings that isinsect-free after spraying and (1-i) is the proportionof dwellings that is still infested after spraying.

We used MATLAB (version 7.10.0 R2010A, Natick,MA) to determine that if the total number of dwellingsis constant, the model reduces to:

dTi

dt� �i�Ii � Si� � i�iTi� �1 � �i�

Ii

Ni* � �j

Ij

Ni*�

� �i � �i�Ti

dIi

dt� �i�Si � iTi�� �1 � �i�

Ii

Ni* � �j

Ij

Ni*�� ��i � �i�Ii.

The basic reproductive number, R0, is the averagenumber of susceptible dwellings successfully infested

Fig. 1. Diagram of household-level direct transmission model with compartments for Susceptible, Infested andTreated houses(indicated by subscript 1) and corrals or sylvatic structures (subscript 2). Arrows show possible transitions of houses betweencompartments, where solid lines indicate movement of vectors among the same type of structure, dashed lines indicate insecticidespraying, and dotted arrows indicate movement between houses and corrals or sylvatic structures and vice versa.

July 2013 STEVENS ET AL.: MODEL OF HOUSE INFESTATION WITH CHAGAS DISEASE VECTORS 909

by each infested dwelling in the absence of insecticidetreatments. We deÞne the parameter RT as the repro-ductive number when insecticides are applied. IfRT�1, the infested houses are increasing. The goal of vec-tor control is to Þnd parameters such that RT � 1. Tocompute the reproduction number, we construct amapping, the next-generation operator, from theoriginal equations. Assuming that at the start of the ep-idemic, Si, the number of susceptible dwellings remainsconstant, we need only consider the dynamics of treatedand infested dwellings,Ti and Ii, that actively engaged invector infestation. Setting the two previous equations tozero and rearranging yields:

�i � �i�Ti � �i�Ii � Si� � i�iTi

� �1 � �i�Ii

Ni* � �j

Ij

Ni*� ,

and

��i � �i�Ii � �i�Si � iTi�� �1 � �i�Ii

Ni* � �j

Ij

Ni*� ,

which, after further rearrangement, yields the Þxedpoint system:

�x� � x

wherex � �T1,I1,T2,I2�,

and

� x�

� ��i�Ii � Si� � i�iTi� �1 � �i�

Ii

Ni* � �j

Ij

Ni*�

�i � �i�Ti

�i�Si � iTi�� �1 � �i�Ii

Ni* � �j

Ij

Ni*�

��i � �i�Ii

�i�Ii � Si� � i�iTi� �1 � �i�Ii

Ni* � �j

Ij

Ni*�

�i � �i�Ti

�i�Si � iTi�� �1 � �i�Ii

Ni* � �j

Ij

Ni*�

��i � �i�Ii

� .

Table 1. Parameter values used in the simulations of the direct transmission model

ParameterControl: no movementbetween houses and

corrals

Case 1: vectors movebetween houses and

corrals

Case 2: vectors movebetween houses and

sylvaticDeÞnition

�i 0/0 0.20/0.20 0.10/0.50 Fraction of their life vectors of group i spend ingroup j

Ni 100/100 100/100 50 of each Total no. of dwellings�i 0.05/0.05 0.05/0.05 0.05 Natural mortality rate of dwellings�i 1/2 1/2 0.01/0.12 Infestation rate of dwellings�i 1/1 1/1 Annually Spraying ratei 2/12 2/12 3 mo inside Waning ratei 0.10/0.80 0.10/0.80 0.10/0 Spraying efÞcacy (percent infested after spraying)

Each row lists a parameter, the values used in the different model cases studied, and the parameter deÞnition. For each case, the values inhouses and corrals or sylvatic areas are shown, separated by the shilling (/) symbol.

Fig. 2. Parameterization of the household transmission model determines rates of transition among compartments.Included are parameters, deÞned in Table 1, for Susceptible, Infested, and Treated houses, as shown in Fig. 1. Ni � Si � Ti� Ii, where i � 1 refers to the houses, two refers to corrals or sylvatic structures.

910 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 50, no. 4

Finding the Þxed points of this map is equivalent toÞnding the equilibrium points of the original differ-ential equation system. Linearizing around the infes-tation-free Þxed point and computing the spectralradius of the linearized map, we obtain the reproduc-tion number:

R0 �1

2��1 � �1��1c1T1

a1b1N1

��1 � �2��2c2T2

a2b2N2

� � �4�1�2T1T2�1�2c1c2

a1a2b1b2N1N2

� ��1 � �1��1c1T1

a1b1N1

��1 � �2��2c2T2

a2b2N2�2�.

where ai � (�i � �i), bi � (�i � �i � i) and ci �(�i � �ii � i).Model Parameterization and Sensitivity Analysis.

Simulations and sensitivity analyses were performedunder several assumptions and are illustrated over atime horizon of 10 yr, a reasonable timeframe to ex-amine the initial effects of different insecticide treat-ment strategies and to observe approach to equilib-rium dynamics.

The parameters and parameter values (Table 1)were estimated for the Department of Chuquisaca,Bolivia, through contacts with local governmenthealth ofÞcials. For example, surveys found vectors in13% of houses after 5 yr of annual spraying (SEDES-Chiquisaca 2006). We provide the model assumptionslater in the study.

Vector movement between houses and peridomes-tic structures is symmetrical, and �20% of vectorsmove between ecotopes. There are 100 houses percommunity. In the model, houses are assumed to havea 20-yr lifespan. In many parts of this region, newcorrals are constructed along with new houses. Inother areas, when people construct a new house, theabandoned structure is used to shelter peridomesticanimals; thus, domestic and peridomestic dwellingsare assumed to be equally abundant, have the same lifespan, and have the same infestation rates (i.e., colo-nizing insects do not distinguish between domesticand peridomestic structures). Sylvatic dwellings are ascommon as houses. Houses and peridomestic struc-tures are sprayed annually; sylvatic dwellings arenever sprayed. Residual insecticides are effective inhouses for�6mo;however, inperidomestic structureswith more exposure to climatic conditions, we assumeimmunity lasts about 1 mo. We assume 90% of sprayedhouses contain no insects, but spraying is assumed tokill all the insects in only 20% of peridomestic struc-tures. After the initial simulations, we did a sensitivityanalysis, examining the effects of a range of parametervalues on RT.

Results

The main conclusion is that insecticide persistenceand spraying frequency have the largest inßuence onhouse infestation. In the following text, we elaborateon the evidence to support this claim.

The percentages of infested houses were examinedfor three cases: the presence of peridomestic struc-tures, the occurrence of sylvatic populations, and theeffect of different spraying programs. First, we deter-mined the dynamics of infestation by using the directtransmission model with no movement betweenhouses and corrals. We then compared this result withthe case with symmetrical migration between thehouses and peridomestic areas and examined the ef-fect of sylvatic dwellings that are never sprayed. Inaddition to examining house infestation rates, we ex-amined the reproductive rate R0.

We modeled infestation by using the direct trans-mission model with no movement between houses and

Fig. 3. Proportion of houses and peridomestic or sylvaticstructures infested (left) or insecticide-treated (right) overtime for three cases of the model. Initially, all structures areinfested. (A) The results with no movement between housesand corrals as a basis for comparison. (B) The results wherevectors move between houses and corrals. (C) The resultswhen vectors move between houses and sylvatic. The sim-ulations show that the proportion infested changes as a func-tion of vector movement and insecticide spraying rates(sylvatic environments are not sprayed); however, theproportion treated is not affected. Parameter values are inTable 1.

July 2013 STEVENS ET AL.: MODEL OF HOUSE INFESTATION WITH CHAGAS DISEASE VECTORS 911

corrals as the basis for comparison (Fig. 3A). Thesimulation results show that insecticide treatmentdoes indeed reduce infestation; however, even after 10yr, 19% of houses and 46% of peridomestic structuresare infested. When we add migration between thehouses and peridomestic areas (Fig. 3B), house in-festation increases from 19 to 25%, whereas perido-mestic infestation decreases from 46 to 41%. Next weexamine the effect of sylvatic areas that are neversprayed (Fig. 3C); this results in the highest infes-tation rates, 33%, for houses, and almost all burrowsare infested.

In addition to examining house infestation rates, weexamined the reproductive rate R0. First we considerdomestic and peridomestic areas that differ in theinsecticide persistence time and spraying efÞcacy(Fig. 4). For all parameters, except spraying rate, R0

(z-axis) varies from 0 to 2; however, R0 is almost10-fold higher when dwellings are sprayed infre-quently or not at all (z-axis �20 for spraying rate).Overall we see that R0 is most sensitive to sprayingrate, shows intermediate sensitivity to community size(number of houses) and vector mobility, and is leastaffected by infestation rate, insecticide persistence,dwelling longevity, and spraying efÞcacy.

In the case where there are sylvatic vectors (Fig. 5),the reproductive rate R0 is about an order of magni-tude higher than when there are no sylvatic vectorsand shows little sensitivity to house spraying rate. It ismost sensitive to dwelling longevity and the size andmobility of the sylvatic vector population. As with theperidomestic case, there is little effect of insecticidepersistence and spraying efÞcacy, whereas infestationrate has an increased effect.

Fig. 4. R0 over a range of parameters for the case of houses and peridomestic structures.

912 JOURNAL OF MEDICAL ENTOMOLOGY Vol. 50, no. 4

To highlight the effect of spraying efÞciency, argu-ably the most easily manipulated parameter, we showhow R0 varies as a function of spraying efÞciency inhouses and peridomestic habitats (corrals, Fig. 6). If�50% of vectors in corrals are eliminated by spraying,R0 � 1, regardless of spraying efÞcacy in houses, andwhen spraying in corrals kills �90%, R0 � 1.

Discussion

Because eliminating household vectors is the rec-ommended method to reducing Chagas disease prev-

alence, we developed a household model to evaluateintervention strategies, such as spray rate and sprayingefÞciency, and optimize vector control. Our analysissuggests that the presence of a sylvatic or peridomesticcycle that is sprayed differently from houses and dif-fers in insecticide persistence times leads to higherdomestic infestation rates. The sensitivity of RT tovariations in the parameters depends on whethersylvatic vectors are present; speciÞcally, the pres-ence of sylvatic vectors can increase RT by over anorder of magnitude. When there are sylvatic vec-tors, spraying rate is relatively unimportant; com-

Fig. 5. R0 over a range of parameters for the case of houses and sylvatic populations.

July 2013 STEVENS ET AL.: MODEL OF HOUSE INFESTATION WITH CHAGAS DISEASE VECTORS 913

munity size, especially the ratio of houses to sylvaticburrows, is most important, followed by vector mo-bility. Infestation rate and spraying efÞcacy are rel-atively unimportant, and dwelling replacement ratehas a large effect if houses persist for more than afew years.

The parameters vary in their facility of manipula-tion. Many, such as community size and house re-placement rate, are intrinsic properties of the localitybeing examined. Others, such as vector movementbetween houses and between the two types of habi-tats, are inßuenced by a combination of human andextrinsic factors. A third group, most amenable tohuman management, includes spraying efÞcacy. Bothease of manipulation and effect on RT need to be con-sidered to help identify the most efÞcient and cost-ef-fective approach to vector control. Further, some ofthese variables will change over time. For example, ef-Þcacy would be altered by the evolution of insecticideresistance or by the quantity of insecticide applied, aswell as insecticide dissemination into refugia such asthatched roofs and cracks and crevices in the walls.

Recently, Lucero et al. (2013) reported that low-cost home improvements (i.e., construction ofchicken coops away from houses and plastering ofwalls) that limit areas of vector refuge within thehome are more effective at keeping infestation lowand increase spraying efÞcacy because there are fewerplaces inside houses for vectors to hide. Our modelsupports these Þndings; Fig. 6 suggests that when theproportion of houses where vectors survive spraying islow, R0� 1, even if efÞcacy in corrals is 50%, but whenthere are many cracks and crevices within homes,vectors survive spraying and efÞcacy in corrals needsto be �90% for R0 �1.

Although developed in the context of Chagas dis-ease, thismodel couldbeapplied toother systems suchas varroa mite infestation in honey bee colonies, aproblem causing millions of dollars of damage eachyear. Mite infestation of hives follows a similar patternto triatominae infestation of houses, and control ef-forts are similar, residual miticide treatments are ap-plied at the level of the hive and on a periodic basis.

In conclusion, our model evaluates how local condi-tionsaffect theChagasvectorcontrol strategyadvocatedby the World Health Organization. Further modelingattempts could include a more complex and stochasticapproach. Although we consider both the ability to ma-nipulatetheparametersandtheireffectonRT,ourmodeldoes not include variation in space or time. In addition,modeldevelopmentcouldalsoconsider thespatial struc-ture using stochastic cellular automata. This model is aÞrst step in developing data-based recommendations forcontrol of Chagas disease vectors.

Acknowledgments

ThisworkwasfundedbytheFulbrightFacultyDevelopmentProgram (JCP), the National Science Foundation (NSF) undercore faculty funding from grant no. NSF Experimental Programto Stimulate Competitive Research (EPS)-0701410, the Na-tional Institutes of Health grant 1R15 A1079672-01A1, and NSFgrant Behavioral and Cognitive Sciences (BCS)-1216193 as partof the joint NSF-National Institutes of HealthÐUnited StatesDepartment of Agriculture Ecology and Evolution of InfectiousDiseases program. Any opinions, Þndings, and conclusions orrecommendations expressed in this material are those of theauthor(s) and do not necessarily reßect the views of the Na-tional Science Foundation.

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Fig. 6. Sensitivity analysis showing the effect of sprayingefÞciency in corrals and houses on reproduction number R0.The dark blue plan is a reference for R0 � 1. When R0 � 1(below the blue plane), vectors will be eliminated. Arrow Ahighlights that if �50% of vectors in corrals are eliminated byspraying, R0� 1, regardless of spraying efÞciency in houses.Arrow B highlights the edge of the teal plane, showing thatR0 � 1 for when spraying in corrals kills �90% of vectors,regardless of efÞcacy in houses.

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Received 25 April 2012; accepted 7 May 2013.

July 2013 STEVENS ET AL.: MODEL OF HOUSE INFESTATION WITH CHAGAS DISEASE VECTORS 915