Optimization of Control Strategies for Non-Domiciliated Triatoma dimidiata, Chagas Disease Vector in the Yucatán Peninsula, Mexico

Background Chagas disease is the most important vector-borne disease in Latin America. Regional initiatives based on residual insecticide spraying have successfully controlled domiciliated vectors in many regions. Non-domiciliated vectors remain responsible for a significant transmission risk, and their control is now a key challenge for disease control. Methodology/Principal Findings A mathematical model was developed to predict the temporal variations in abundance of non-domiciliated vectors inside houses. Demographic parameters were estimated by fitting the model to two years of field data from the Yucatan peninsula, Mexico. The predictive value of the model was tested on an independent data set before simulations examined the efficacy of control strategies based on residual insecticide spraying, insect screens, and bednets. The model accurately fitted and predicted field data in the absence and presence of insecticide spraying. Pyrethroid spraying was found effective when 50 mg/m2 were applied yearly within a two-month period matching the immigration season. The >80% reduction in bug abundance was not improved by larger doses or more frequent interventions, and it decreased drastically for different timing and lower frequencies of intervention. Alternatively, the use of insect screens consistently reduced bug abundance proportionally to the reduction of the vector immigration rate. Conclusion/Significance Control of non-domiciliated vectors can hardly be achieved by insecticide spraying, because it would require yearly application and an accurate understanding of the temporal pattern of immigration. Insect screens appear to offer an effective and sustainable alternative, which may be part of multi-disease interventions for the integrated control of neglected vector-borne diseases.

S A n , τ  = S A T−τ T

Equation 4b
Because we assumed that adults lay eggs regularly, the contribution of individuals immigrating at τ to the production of immature in the next time step equals: where f is the number of eggs per laying. As expected if all individuals are present at the beginning of the time step (τ = 0) and lay all their eggs at this time, the previous Leslie matrix is recovered since S I (n,0) = S I and F(n,0) = f S I . The latter expression corresponds to adult fecundity F, i.e., the product of fertility by the immature survival over the duration of the time step.

The population dynamics model with insecticide spraying
Assuming that natural mortality and mortality due to insecticide acted multiplicatively, the survival probability can be written: where s ins (n,t) accounts for both the variations of the quantity of insecticide present in the house at any time t within the n th time step, and the doseresponse relationship to describe the consequences of insecticide on vector demography. The same relationship holds for adult survival substituting S A to S I .
Fecundity of adults was also decreased as a result of the impact of insecticide on immature and adult survival. The fecundity of adults in the treated houses was then written as: Modelling insecticide spraying only required to evaluate the amount of insecticide present in the domestic habitat at any time, and to calculate the reduction in immature and adult survival probabilities.

Equation for the variations of the amount of insecticide in the house.
To calculate the amount of insecticide q ins (n,t) present in the house at time unit t of any time step n, we considered an exponential decay of the active ingredient and referred to t 1/2 as the insecticide halflife. We allowed for control strategies (Q, P) corresponding to sprays of a quantity Q of insecticide every P time units. We denote n fs the time step of the first spraying and t ins the time unit at which the insecticide is sprayed within the time step. The quantity q ins (n,t) for any couple (n,t) > (n fs , t ins ) can then be written as a sum of the residual quantity of insecticide since the first application. A straightforward calculation leads to: where N = 1 [ n−n fs P ] is the total number of insecticide sprays.

Doseresponse curve to describe the consequences of insecticide on vector demography.
To calculate the reduction in immature and adult survival we used a classical sigmoid dose response described by a logistic equation which applied to ) t , n ( s ins the survival rate to insecticide for 24 hours gives: where LD 50 is the dose that cause the death of 50 % of the population in 24h, and b is the hill slope of the sigmoid. b itself can be expressed with respect to LD 50 and LD 90 , the dose killing 90 % of the population in 24h, as follows: int