Optimal barrier zones for stopping the invasion of Aedes aegypti mosquitoes via transgenic or sterile insect techniques

Mathematical modelling and release thresholds of transgenic sterile mosquitoes

We formulate simple differential equation models to study the impact of releases of transgenic sterile mosquitoes carrying a dominant lethal on mosquito control based on the modified sterile insects technique. The early acting bisex, late acting bisex, early acting female-killing, and late acting female-killing lethality strategies are all considered. We determine release thresholds of the transgenic sterile mosquitoes, respectively, for these models by investigating the existence of positive equilibria and their stability. We compare the model dynamics, in particular, the thresholds of the models numerically. The late acting lethality strategies are generally more effective than their corresponding early acting lethality strategies, but the comparison between the late acting bisex and early acting female-killing lethality strategies depends on different parameter settings.

The optimal strategy of incompatible insect technique (IIT) using Wolbachia and the application to malaria control

For decades, techniques to control vector population with low environmental impact have been widely explored in both field and theoretical studies. The incompatible insect technique (IIT) using Wolbachia, based on cytoplasmic incompatibility, is a technique that Wolbachia-infected male mosquitoes are incapable of producing viable offspring after mating with wild-type female mosquitoes. While the IIT method experimentally ensured its effectiveness in several field works, the failure of female mosquito population control by replacement owing to the accidental contamination of Wolbachia-infected female mosquitoes has been a concern and an obstacle in implementing the IIT method in nature. In this study, we develop a population-based IIT mathematical model using cytoplasmic incompatibility and evaluate the effectiveness of the IIT method in scenarios where contamination is present or absent. In addition, by extending the model to assess the disease infection status of the human population with malaria, we evaluate the optimal release strategy and cost for successful disease control. Our study proves that IIT could be a promising method to control mosquito-borne diseases without perfect suppression of vector mosquito population regardless of contamination.

Comparing sterile male releases and other methods for integrated control of the tiger mosquito in temperate and tropical climates

The expansion of mosquito species worldwide is creating a powerful network for the spread of arboviruses. In addition to the destruction of breeding sites (prevention) and mass trapping, methods based on the sterile insect technique (SIT), the autodissemination of pyriproxyfen (ADT), and a fusion of elements from both of these known as boosted SIT (BSIT), are being developed to meet the urgent need for effective vector control. However, the comparative potential of these methods has yet to be explored in different environments. This is needed to propose and integrate informed guidelines into sustainable mosquito management plans. We extended a weather-dependent model of Aedes albopictus population dynamics to assess the effectiveness of these different vector control methods, alone or in combination, in a tropical (Reunion island, southwest Indian Ocean) and a temperate (Montpellier area, southern France) climate. Our results confirm the potential efficiency of SIT in temperate climates when performed early in the year (mid-March for northern hemisphere). In such a climate, the timing of the vector control action was the key factor in its success. In tropical climates, the potential of the combination of methods becomes more relevant. BSIT and the combination of ADT with SIT were twice as effective compared to the use of SIT alone.

Modeling the impact of sterile males on an Aedes aegypti population with optimal control

We use partial differential equations to describe the dynamics of an Aedes aegypti mosquito population on an island, and the effects of a sterile male release. The model includes mosquito movement and an Allee effect to capture extinction events. We apply optimal control theory to identify the release strategy that eliminates the mosquitoes most rapidly, conditional on a limited availability of sterile males. The optimal solution for a single location is to initially release a substantial number of mosquitoes and to subsequently release fewer sterile males proportionally to the decreasing female population. The optimal solution for the whole island is intractable given a constraint on the total daily release of sterile males. The best approximation to the spatial optimal control strategy is to focus on the high mosquito density areas first and then move outwards (in both directions along the periphery of the island), until all areas have been covered, retaining throughout sufficient release intensity to prevent reintroduction in the already cleared areas.

Modelling and analysis of impulsive releases of sterile mosquitoes

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.

Towards the genetic control of invasive species

Invasive species remain one of the greatest threats to global biodiversity. Their control would be enhanced through the development of more effective and sustainable pest management strategies. Recently, a novel form of genetic pest management (GPM) has been developed in which the mating behaviour of insect pests is exploited to introduce genetically engineered DNA sequences into wild conspecific populations. These 'transgenes' work in one or more ways to reduce the damage caused by a particular pest, for example reducing its density, or its ability to vector disease. Although currently being developed for use against economically important insect pests, these technologies would be highly appropriate for application against invasive species that threaten biodiversity. Importantly, these technologies have begun to advance in scope beyond insects to vertebrates, which include some of the world's worst invasives. Here we review the current state of this rapidly progressing field and, using an established set of eradication criteria, discuss the characteristics which make GPM technologies suitable for application against invasive pests.

Resistance to genetic insect control: Modelling the effects of space

Genetic insect control, such as self-limiting RIDL² (Release of Insects Carrying a Dominant Lethal) technology, is a development of the sterile insect technique which is proposed to suppress wild populations of a number of major agricultural and public health insect pests. This is achieved by mass rearing and releasing male insects that are homozygous for a repressible dominant lethal genetic construct, which causes death in progeny when inherited. The released genetically engineered ('GE') insects compete for mates with wild individuals, resulting in population suppression. A previous study modelled the evolution of a hypothetical resistance to the lethal construct using a frequency-dependent population genetic and population dynamic approach. This found that proliferation of resistance is possible but can be diluted by the introgression of susceptible alleles from the released homozygous-susceptible GE males. We develop this approach within a spatial context by modelling the spread of a lethal construct and resistance trait, and the effect on population control, in a two deme metapopulation, with GE release in one deme. Results show that spatial effects can drive an increased or decreased evolution of resistance in both the target and non-target demes, depending on the effectiveness and associated costs of the resistant trait, and on the rate of dispersal. A recurrent theme is the potential for the non-target deme to act as a source of resistant or susceptible alleles for the target deme through dispersal. This can in turn have a major impact on the effectiveness of insect population control.

On an integro-differential model for pest control in a heterogeneous environment

Insect pests pose a major threat to a balanced ecology as it can threaten local species as well as spread human diseases; thus, making the study of pest control extremely important. In practice, the sterile insect release method (SIRM), where a sterile population is introduced into the wild population with the aim of significantly reducing the growth of the population, has been a popular technique used to control pest invasions. In this work we introduce an integro-differential equation to model the propagation of pests in a heterogeneous environment, where this environment is divided into three regions. In one region SIRM is not used making this environment conducive to propagation of the insects. A second region is the eradication zone where there is an intense release of sterile insects, leading to decay of the population in this region. In the final region we explore two scenarios. In the first case, there is a small release of sterile insects and we prove that if the eradication zone is sufficiently large the pests will not invade. In the second case, when SIRM is not used at all in this region we show that invasions always occur regardless of the size of the eradication zone. Finally, we consider the limiting equation of the integro-differential equation and prove that in this case there is a critical length of the eradication zone which separates propagation from obstruction. Moreover, we provide some upper and lower bound for the critical length.

Dispersal of adult culex mosquitoes in an urban west nile virus hotspot: a mark-capture study incorporating stable isotope enrichment of natural larval habitats

Dispersal is a critical life history behavior for mosquitoes and is important for the spread of mosquito-borne disease. We implemented the first stable isotope mark-capture study to measure mosquito dispersal, focusing on Culex pipiens in southwest suburban Chicago, Illinois, a hotspot of West Nile virus (WNV) transmission. We enriched nine catch basins in 2010 and 2011 with ¹⁵N-potassium nitrate and detected dispersal of enriched adult females emerging from these catch basins using CDC light and gravid traps to distances as far as 3 km. We detected 12 isotopically enriched pools of mosquitoes out of 2,442 tested during the two years and calculated a mean dispersal distance of 1.15 km and maximum flight range of 2.48 km. According to a logistic distribution function, 90% of the female Culex mosquitoes stayed within 3 km of their larval habitat, which corresponds with the distance-limited genetic variation of WNV observed in this study region. This study provides new insights on the dispersal of the most important vector of WNV in the eastern United States and demonstrates the utility of stable isotope enrichment for studying the biology of mosquitoes in other disease systems.

The distance and direction of adult mosquitoes movement on the landscape are important processes in the spread of mosquito-borne diseases, and are critical to understand to the development of effective intervention programs. Here we present a novel approach to study adult mosquito dispersal by using stable isotope enrichment of natural larval habitats. We apply this technique in a focal hotspot of West Nile virus (WNV) transmission in suburban, Chicago, USA to measure dispersal of Culex spp. mosquitoes. We enriched larval mosquitoes in residential catch basins using ¹⁵N-potassium nitrate and captured adult mosquitoes in traps surrounding these catch basins. Of 10,817 adult female Culex mosquitoes trapped and tested for stable isotopes, 12 individuals were enriched with ¹⁵N, indicating they originated from the catch basins receiving stable isotope amendments. The mean dispersal distance was 1.15 km and maximum flight range was 2.48 km. Ninety percent of the female Culex mosquitoes stayed within 3 km of their larval habitat, which corresponds with the distance-limited genetic variation of WNV observed in this study region. This study provides new insights on the dispersal of the most important vector of WNV in the eastern United States and demonstrates the utility of stable isotope enrichment for studying the biology of mosquitoes in other disease systems.