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Licensed Unlicensed Requires Authentication Published by De Gruyter November 20, 2020

A real-time search strategy for finding urban disease vector infestations

Erica Billig Rose, Jason A. Roy, Ricardo Castillo-Neyra, Michelle E. Ross, Carlos Condori-Pino, Jennifer K. Peterson, Cesar Naquira-Velarde and Michael Z. Levy ORCID logo
From the journal Epidemiologic Methods

Abstract

Objectives

Containing domestic vector infestation requires the ability to swiftly locate and treat infested homes. In urban settings where vectors are heterogeneously distributed throughout a dense housing matrix, the task of locating infestations can be challenging. Here, we present a novel stochastic compartmental model developed to help locate infested homes in urban areas. We designed the model using infestation data for the Chagas disease vector species Triatoma infestans in Arequipa, Peru.

Methods

Our approach incorporates disease vector counts at each observed house, and the vector’s complex spatial dispersal dynamics. We used a Bayesian method to augment the observed data, estimate the insect population growth and dispersal parameters, and determine posterior infestation probabilities of households. We investigated the properties of the model through simulation studies, followed by field testing in Arequipa.

Results

Simulation studies showed the model to be accurate in its estimates of two parameters of interest: the growth rate of a domestic triatomine bug colony and the probability of a triatomine bug successfully invading a new home after dispersing from an infested home. When testing the model in the field, data collection using model estimates was hindered by low household participation rates, which severely limited the algorithm and in turn, the model’s predictive power.

Conclusions

While future optimization efforts must improve the model’s capabilities when household participation is low, our approach is nonetheless an important step toward integrating data with predictive modeling to carry out evidence-based vector surveillance in cities.


Corresponding authors: Erica Billig Rose, Department of Biostatistics, Epidemiology & Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA, E-mail: ; and Michael Z. Levy, Department of Biostatistics, Epidemiology & Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA; and Zoonotic Disease Research Laboratory, One Health Unit, Facultad de Salud Pública y Administración, Universidad Peruana Cayetano Heredia, Lima, Perú, E-mail:

Funding source: National Institutes of Health

Award Identifier / Grant number: 5R01AI101229, 5R01AI146129, 5T32AI007532

Acknowledgments

We gratefully acknowledge the invaluable contributions of the Ministerio de Salud del Peru (MINSA), the Dirección General de Salud de las Personas (DGSP), the Estrategia Sanitaria Nacional de Prevención y Control de Enfermedades Metaxénicas y Otras Transmitidas por Vectores (ESNPCEMOTVS), the Dirección General de Salud Ambiental (DIGESA), the Gobierno Regional de Arequipa, the Gerencia Regional de Salud de Arequipa (GRSA), and the members of the field and laboratory teams at the Zoonotic Disease Research Laboratory in Arequipa. This study was supported by National Institutes of Health grants 5T32AI007532, 5R01AI146129, and 5R01AI101229. Finally, Dr. Cesar Naquira passed away during the writing of this manuscript. We thank Dr. Naquira for his leadership and everything he taught us over the past 15 years.

  1. Research funding: National Institutes of Health grants 5T32AI007532, 5R01AI146129, and 5R01AI101229.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.

Supporting information

Growth Dynamics

See Figure 4.

Algorithm details

We update the likelihood using the following algorithm:

  1. Initialize β1 and r1.

  2. Initialize infection times I1. Initial infestation Iκ=1 and all other observed infestations initialized at I=2. All other infestations set to I=∞.

  3. Initialize tinsp,i and Ri. If house i has been inspected andor treated, these are set to the respective times. All dates are converted to time since initial infestation, using 90 day intervals. For example, if house i was infested 200 days after the initial infestation, this infestation time is considered Ii=3. If a house has not yet been inspected and treated, tinsp,i=Ri=∞. Tmax is set to the present day.

  4. Initialize insect counts of each infested house given the infestation times I1. This is done using the Beverton-Holt Model:

    • λt=K1+(K1)rt

    • bi,Ii=1

    • bi,tIiPoisson(λtIi)

    • Replace bi,tinsp,i=Bi,tinsp,i, the observed insect counts.

  5. Update rm+1. Propose rNormal(rm,0.05). Update all insect counts bgiven ursing the Beverton-Holt model.

R=min(1,L(r|I,βm,λt)L(rm|Im,βm,λt)p(r)p(rm))

where p is the prior distribution of r. We define pGamma(ar,br).

UUniform(0,1)
Figure 4: Ranking of each house across 3 RJMCMC chains. There were a few houses that changed significantly, but most houses remained within a few rankings between chains. In cases of discrepancies, the median ranking across the chains was used to determine which houses to search.

Figure 4:

Ranking of each house across 3 RJMCMC chains. There were a few houses that changed significantly, but most houses remained within a few rankings between chains. In cases of discrepancies, the median ranking across the chains was used to determine which houses to search.

If U < R then rm+1=r. Else, rm+1=rm.

  1. Update βm+1. Propose βNormal(βm,0.2). The proposal is constrained to (0, 1).

R=min(1,L(β|Im,rm+1,λt)L(βm|Im,rm+1,λt)p(β)p(βm))

where p is the prior distribution of β. We define pBeta(aβ,bβ).

UUniform(0,1)

If U < R then βm+1=β. Else, βm+1=βm.

  1. Propose moving, adding or removing an infestation, each with equal probability.

    To move an infestation:

    1. Update I. Select uniformly from the set of infested houses, NI. If i has not yet been inspected, propose new infestation time IiUniform(Ik+1,Tmax). If i has been inspected but no insects were found at that time, propose new infestation time IiUniform(tinsp,i,Tmax). If i has been inspected and at least one insects was found at that time, propose new infestation time IiUniform(Ik+1,tinsp,i).

R=min(1,L(I|βm+1,rm+1,λt)L(Im|βm+1,rm+1,λt))
UUniform(0,1)

If U < R then Im+1=I. Else, Im+1=Im. If Im+1=I, update bi (all insect counts corresponding to this infestation) so that at Ii, bi1=1.

To add an infestation:

  1. Propose i uniformly from S, the set of susceptible houses.

  2. If i has not yet been inspected, propose IiUniform(Ik+1,Tmax). If i has been inspected, propose IiUniform(tinsp,i,Tmax). Propose biPoisson(λtIi).

R=min(1,L(I|rm,βm,λt)L(Im|rm+1,βm+1,λt)pi(Ii)1q(bi|λtIi))

where pi is the prior probability that house i is infested and q is the proposal distribution of the insect counts bi (Poisson).

UUniform(0,1)

If U < R then Im+1=I. Else, Im+1=Im. If a house is added, the corresponding insect counts but also be added.

To remove an infestation:

  1. Propose i uniformly from the set of occult infestations (previously added, but unobserved, houses).

R=min(1,L(I|rm,βm,λt)L(Im|rm+1,βm+1,λt)1pi(Ii)q(bi|λtIi))

where pi is the prior probability that house i is uninfested and q is the distribution of the insect counts bi (Poisson).

UUniform(0,1)

If U < R then Im+1=I. insect counts corresponding with the removed infestation must also be deleted. Else, Im+1=Im.

  1. Repeat steps (e) – (g) for a total of M iterations.

In the field implementation, r was not estimated, and thus step 5 was omitted. In general, the acceptance rates of parameters ranged from 15% to 60%, including those in the reversible-jump component. Posterior probabilities of infestation ranged from 0% to 20%, but mostly stayed below 10%.

Parameter estimates converged quickly, but it was difficult to assess convergence of posterior probabilities of infestation. We visually assessed convergence by plotting the ranking of each house between chains of the RJMCMC (Figure 5). Rankings were consistent in that top ranked houses were ranked highly across all chains. However, the specific ranking of a given house varied between chains. A typical convergence plot is shown below. A few houses seemed to get stuck at high rankings each chain that did get picked up in other chains. By using the median ranking for each house across chains, we hope to minimize this effect on inspections.

Figure 5: Ranking of each house across 5 potential carrying capacities. There were a few houses that changed significantly, but most houses remained within a few rankings between carrying capacity values.

Figure 5:

Ranking of each house across 5 potential carrying capacities. There were a few houses that changed significantly, but most houses remained within a few rankings between carrying capacity values.

The simulation code is available at

https://github.com/ebillig/Search-Strategy.

Additional details

For all simulations and data applications, we fixed the carrying capacity, K=1000. We did some sensitivity analysis to assess the importance of this assumption. We ran 3 RJMCMC chains on one locality with 5 different carrying capacities, K={100, 500, 800, 1000, 1500}. We obtained the median ranking of each house across the chains for each K, and then plotted the rankings against each other (Figure 5). We can see the heterogeneity in ranking is similar to that between chains within each carrying capacity. Interestingly, the rankings stayed the same between K=1000 and K=1500.

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Received: 2020-01-14
Accepted: 2020-10-27
Published Online: 2020-11-20

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