A Bayesian Hierarchical Model for Estimation of Abundance and Spatial Density of <i>Aedes aegypti</i>

<div><p>Strategies to minimize dengue transmission commonly rely on vector control, which aims to maintain <i>Ae. aegypti</i> density below a theoretical threshold. Mosquito abundance is traditionally estimated from mark-release-recapture (MRR) experiments, which lack proper analysis regarding accurate vector spatial distribution and population density. Recently proposed strategies to control vector-borne diseases involve replacing the susceptible wild population by genetically modified individuals’ refractory to the infection by the pathogen. Accurate measurements of mosquito abundance in time and space are required to optimize the success of such interventions. In this paper, we present a hierarchical probabilistic model for the estimation of population abundance and spatial distribution from typical mosquito MRR experiments, with direct application to the planning of these new control strategies. We perform a Bayesian analysis using the model and data from two MRR experiments performed in a neighborhood of Rio de Janeiro, Brazil, during both low- and high-dengue transmission seasons. The hierarchical model indicates that mosquito spatial distribution is clustered during the winter (0.99 mosquitoes/premise 95% CI: 0.80–1.23) and more homogeneous during the high abundance period (5.2 mosquitoes/premise 95% CI: 4.3–5.9). The hierarchical model also performed better than the commonly used Fisher-Ford’s method, when using simulated data. The proposed model provides a formal treatment of the sources of uncertainty associated with the estimation of mosquito abundance imposed by the sampling design. Our approach is useful in strategies such as population suppression or the displacement of wild vector populations by refractory <i>Wolbachia</i>-infected mosquitoes, since the invasion dynamics have been shown to follow threshold conditions dictated by mosquito abundance. The presence of spatially distributed abundance hotspots is also formally addressed under this modeling framework and its knowledge deemed crucial to predict the fate of transmission control strategies based on the replacement of vector populations.</p></div

Results from estimation using data from field studies.

<p>Intervals colored in solid red indicate Fisher—Ford estimates. Intervals colored in solid blue indicate estimates from the hierarchical model. Labels ST1 and ST2 indicate studies conducted in September 2012 and March 2013, respectively. The September 2012 study had 4 cohorts given by 4 different colors: blue (b), pink (p), yellow (y) and green (g). Labels ST1 also include which cohorts were used in the analysis by grouping cohorts ({b}, {b+p}, {b+p+y}, { b+p+y+g}). Estimates of population abundance are shown along with both <i>y</i>—axes (different scales), the one on the left side for study ST1 and on the right side for study ST2.</p

Observed (unweighted, dots) and weighted (IPCW-weighted, lines) annual median CD4+ cell counts since start of ART stratified by cohort, age at start of ART, gender and race.

<p>Dashed lines represent important CD4+ cell count thresholds of 200, 350, and 500 cells/μL.</p

Estimates of abundance for the populations of female <i>Aedes aegypti</i> in Z—10, Rio de Janeiro, in Sept 2012 (ST1) and March 2013 (ST2), according to the hierarchical model and the Fisher-Ford model.

<p>Estimation realized using samples from 16000 iterations using data from both studies. The hierarchical model results are obtained using JAGS after running 10000 iterations per chain (first 2000 were discarded) in two Markov chain simulations. Fisher—Ford estimates are obtained using a bootstrap approach (re-sampling <i>R</i>_<i>s</i> = 1000). For the Fisher—Ford estimation the survival rate is assumed to be <i>ϕ</i> = 0.8.</p

Estimates of survival probability for marked population of <i>Ae. aegypti</i> released in Z—10, Rio de Janeiro, according to the hierarchical model.

<p>Estimation realized using samples from 16000 iterations using data from both studies. The hierarchical model results are obtained using JAGS after running 10000 iterations per chain (first 2000 were discarded) in two Markov chain simulations. Fisher—Ford estimates are obtained using a bootstrap approach (re-sampling <i>R</i>_<i>s</i> = 1000).</p

Abundance estimation in simulated scenarios, using the hierarchical and the Fisher-Ford models.

<p>The total number of iterations was 12000 for each of 2 Markov chains. The first 3000 iterations are discarded as burn-in interval. The area of attraction is of size 5 (b5) and also 8 (b8), probability <i>p</i> = 0.5. The number of traps is <i>J</i> = 64. For the Fisher—Ford estimates a number of <i>R</i>_<i>s</i> = 1000 re-sampling was used and the daily survival probability was <i>ϕ</i> = 0.8, same value used in the simulations. For the case (200, 300) with a small attraction area the sample size (2) is very small and no Fisher—Ford estimates are reported. The notation (m,u) refers to the quantity (number of captures, capture ratios) for marked and unmarked mosquitoes, respectively.</p

Observed (unweighted, dots) and weighted (IPCW-weighted, lines) annual median CD4+ cell counts since start of ART stratified by initial ART regimen and pre-treatment HIV RNA viral load.

<p>Dashed lines represent important CD4+ cell count thresholds of 200, 350, and 500 cells/μL.</p

Unstratified and stratified observed and weighted median (interquartile range) CD4+ cell counts for years 1, 4, 7 and 10 after start of antiretroviral therapy and the percentage of patients with weighted CD4+ cell count >500/μL at year 10.

<p>HIV: human immunodeficiency virus, ART: antiretroviral therapy, ADI: AIDS defining illness.</p>a<p>Age at the start of ART.</p>b<p>Reported mode of HIV risk exposure was categorized injection drug users (IDU) and not IDU.</p>c<p>Pre-treatment CD4+ cell count and HIV RNA were defined as the value closest to the date of start of ART up to 6 months prior.</p>d<p>Initial ART regimen was classified as NNRTI-based or PI-based. Integrase inhibitor-based regimens were too few (N = 75) to draw consistent conclusions and were thus excluded.</p>e<p>ADI at the start of ART was defined as the presence of any CDC 1993 condition at six months prior to up to one month after start of ART.</p>f<p>Hepatitis B/C co-infection was defined as having chronic infection at the start of ART.</p

Observed (unweighted, dots) and weighted (IPCW-weighted, lines) annual median CD4+ cell counts since start of ART stratified by injection drug use (IDU), hepatitis C co-infection, and AIDS defining illness at the start of ART.

<p>Dashed lines represent important CD4+ cell count thresholds of 200, 350, and 500 cells/μL.</p

Estimates obtained from MRR data in the simulated scenarios.

<p>The estimated values for abundance are shown along the <i>y</i>–axis (for all cases in the <i>y</i>—axis on the left—hand side, except for the case <i>N</i>₂ = 3000 shown along the <i>y</i>—axis on the right—hand side), whereas each case is shown along the <i>x</i>-axis, described by the number (known value of) of unmarked individuals used in the simulation. The plot on the left—hand side shows results for a small basin of attraction, whereas on the right—hand side results are shown for traps’ basins of attraction that have radiuses 60% greater. Red lines indicate the numbers of unmarked mosquitoes that were used in the simulations for each of the configurations.</p