Descriptive plots.

<p>Times series (a), autocorrelation function - ACF (b) e partial autocorrelation function - PACF (c) of <i>Ae. aegypti</i> abundance per trap; minimum, average and maximum temperature (d), minimum, average and maximum relative air humidity (e), precipitation (mm) and wind velocity (m/s) (f).</p

Best fitted model.

<p>Estimates of fitted model with climatic variables and interaction term effects on mosquito abundance/week/trap.</p

Interaction Heat Maps.

<p>Heat maps graphs of the <i>Ae. aegypti</i> abundance/week/trap growth with change in values of Minimum Temperature and Minimum Humidity, for LOW (a), MIDDLE (b) and HIGH (c) mosquito abundance in the preceding week. The quadrants formed by the red lines limited by the thresholds (15.7°C and 43.6%) separate the shift effects on mosquito abundance, that can increase (Inc) or decrease (Dec) as the temperature and humidity values increase. Plus sign indicates population growth and minus sign indicates no population growth. The ascending color scale represents the effect on the abundance as the temperature and humidity increase. Blue lines delimit regions where population growth in MIDDLE and HIGH scenarios.</p

Meteorological variables and mosquito abundance Cross Wavelet Spectrums.

<p>Cross wavelet spectrum of <i>Ae. aegypti</i> abundance/week/trap <i>versus</i>: Minimum Temperature (a); Maximum Temperature (c); Average Humidity (e); Precipitation (g). Average Temperature (b); Minimum Humidity (d); Maximum Humidity (f); Wind Velocity (h). Times series were log-transformed and normalized. Colors code for increasing spectrum intensity, from blue to red. Black bolder contours show statistically significant area (threshold of 95% confidence interval). The black curve delimits the cone of influence (region not influenced by edge effects). Period scale is in weeks. The y-axis is on a base 2 logarithmic scale. The black arrows represent the relative phase relationship (anti-clockwise direction starting at the west-east direction). In all graphs, the first series is the mosquito abundance and the second series is a meteorological variable: 0°: both series are in-phase; 45°: the second series is 1/8 of period ahead of the former, 90°: 1/4 of the period ahead; 135°: 3/8 of the period ahead; 180°: the series are out-phase; 225°: the second series is 3/8 of the period behind; 270°: 1/4 of the period behind, 315°: 1/8 of the period behind.</p

Modeling the Non-Stationary Climate Dependent Temporal Dynamics of <i>Aedes aegypti</i>

<div><p>Background</p><p>Temperature and humidity strongly affect the physiology, longevity, fecundity and dispersal behavior of <i>Aedes aegypti</i>, vector of dengue fever. Contrastingly, the statistical associations measured between time series of mosquito abundance and meteorological variables are often weak and contradictory. Here, we investigated the significance of these relationships at different time scales.</p><p>Methods and Findings</p><p>A time series of the adult mosquito abundance from a medium-sized city in Brazil, lasting 109 weeks was analyzed. Meteorological variables included temperature, precipitation, wind velocity and humidity. As analytical tools, generalized linear models (GLM) with time lags and interaction terms were used to identify average effects while the wavelet analysis was complementarily used to identify transient associations. The fitted GLM showed that mosquito abundance is significantly affected by the interaction between lagged temperature and humidity, and also by the mosquito abundance a week earlier. Extreme meteorological variables were the best predictors, and the mosquito population tended to increase at values above and 54% humidity. The wavelet analysis identified non-stationary local effects of these meteorological variables on abundance throughout the study period, with peaks in the spring-summer period. The wavelet detected weak but significant effects for precipitation and wind velocity.</p><p>Conclusion</p><p>Our results support the presence of transient relationships between meteorological variables and mosquito abundance. Such transient association may be explained by the ability of <i>Ae. aegypti</i> to buffer part of its response to climate, for example, by choosing sites with proper microclimate. We also observed enough coupling between the abundance and meteorological variables to develop a model with good predictive power. Extreme values of meteorological variables with time lags, interaction terms and previous mosquito abundance are strong predictors and should be considered when understanding the climate effect on mosquito abundance and population growth.</p></div

Univariate models.

<p>Estimates of individual effects of lagged variables (lag) on mosquito abundance/week/trap according to the generalized linear model.</p

Mosquito Abundance Power Wavelet Spectrum.

<p>Power wavelet spectrum of <i>Ae. aegypti</i> abundance/week/trap. Times series was log-transformed and normalized. Colors code for increasing spectrum intensity, from blue to red. Black bolder contours show statistically significant area (threshold of 95% confidence interval). The black curve delimits the cone of influence (region not influenced by edge effects). Period scale is in weeks. The y-axis is on a base 2 logarithmic scale.</p

Culling Dogs in Scenarios of Imperfect Control: Realistic Impact on the Prevalence of Canine Visceral Leishmaniasis

<div><p>Background</p><p>Visceral leishmaniasis belongs to the list of neglected tropical diseases and is considered a public health problem worldwide. Spatial correlation between the occurrence of the disease in humans and high rates of canine infection suggests that in the presence of the vector, canine visceral leishmaniasis is the key factor for triggering transmission to humans. Despite the control strategies implemented, such as the sacrifice of infected dogs being put down, the incidence of American visceral leishmaniasis remains high in many Latin American countries.</p><p>Methodology/Principal Findings</p><p>Mathematical models were developed to describe the transmission dynamics of canine leishmaniasis and its control by culling. Using these models, imperfect control scenarios were implemented to verify the possible factors which alter the effectiveness of controlling this disease in practice.</p><p>Conclusions/Significance</p><p>A long-term continuous program targeting both asymptomatic and symptomatic dogs should be effective in controlling canine leishmaniasis in areas of low to moderate transmission (R₀ up to 1.4). However, the indiscriminate sacrifice of asymptomatic dogs with positive diagnosis may jeopardize the effectiveness of the control program, if tests with low specificity are used, increasing the chance of generating outrage in the population, and leading to lower adherence to the program. Therefore, culling must be planned accurately and implemented responsibly and never as a mechanical measure in large scale. In areas with higher transmission, culling alone is not an effective control strategy.</p></div

The Canine Leishmaniasis model (SEI₂D).

<p>All dogs are born susceptible (S), and become infected at a rate <b>ßS</b>. Infected dogs go through a latent stage, after which a fraction evolves to an asymptomatic infection (Ia) while the remaining (1-p) evolve into the symptomatic state (Is). A small fraction of asymptomatic dogs may evolve to present signs of clinical disease, which is incorporated into the model through a relapse rate “λ”. The control program screens animals and, if laboratory positive, they move to class Da or Ds, where they remain until culling. Dz class holds those erroneously classified as positive.</p

Sensitivity analysis of parameters in Model SEI₂D.

<p>Box plots comparing parameter values that lead to prediction of successful control (prevalence <1) and failure (prevalence >1) considering a culling program with 4% screening effort and a diagnostic test with 80% sensitivity applied in an area with R₀ = 1.41.</p