Modelling Aedes aegypti mosquito control via transgenic and sterile insect techniques: Endemics and emerging outbreaks
Introduction
The history of pest control is as old as human agriculture or disease. The invasion of pest insects often changes or destroys a native ecosystem, and can result in food shortages and disease endemics. As a result, the development of biological control methods has received widespread attention and, in some cases, they have been successful (Benedict and Robinson, 2003, Dyck et al., 2005, Vreysen et al., 2007). However, issues such as the environmental effects of chemical control methods, the economic burden of maintaining control strategies and the risk of pest resistance still remain, and mosquito-borne diseases such as Malaria and Dengue fever prevail in many countries in East Asia, South America and Africa, infecting over 100 million and killing at least half a million in 2010 (WHO, 2012a, WHO, 2012b, WHO, 2012c). Furthermore, repeated invasions are observed in regions where the vector mosquitoes have been eradicated completely in the past. For example, Aedes aegypti and Aedes albopictus are observed in Northern European countries as well as Asia (Hulden and Hulden, 2008, Paupy et al., 2012). Global warming and the human transportation system also promote such situations (Enserink, 2010). As such, continued research into the development of better pest control methods remains vital (Dyck et al., 2005, Pimentel, 2011).
One environmentally friendly alternative for mosquito control is the sterile insect technique, SIT (Knipling, 1955). This species-specific method of insect control relies on the mass rearing, sterilization and release of large numbers of sterile insects, preferably males (Dyck et al., 2005), which, it is hoped, mate with wild-type insects, thereby reducing their reproductive output and, potentially, the pest population abundance (see Black et al., 2011, Wilke et al., 2012 for recent reviews). Mixed-sex sterile releases are avoided where practical as they are generally less efficient and, for species such as mosquitoes, it is only the females that bite. This means that their release could potentially aid disease spread in the short-term (see Alphey et al., 2010 for a recent review).
Other transgenic technologies have recently been developed to improve SIT control (Benedict and Robinson, 2003, Wimmer, 2003, Alphey et al., 2010); these include genetic sexing (Robinson et al., 1999), genetic marking (Peloquin et al., 2000) and genetic female-specific lethality (Seawright et al., 1978). One such transgenic strategy is RIDL, i.e. “Release of Insects carrying a Dominant Lethal” (Thomas et al., 2000, Phuc et al., 2007). Here the released transgenic males are homozygous for a dominant lethal gene that is expressed in both male and female (bisex) progeny that result from mating with wild-type insects. Female-specific RIDL strategies have also been developed (Fu et al., 2010), but here we focus on bisex RIDL control strategies. Hereafter, we use the terms SIT and sterile to refer to early-acting lethality of the progeny of released insects, for example classical SIT using radiation-induced sterility, and the terms RIDL and transgenic to refer to late-acting lethality in both sexes.
We note also that the developmental stage at which the dominant lethal gene is expressed, for instance the embryonic or the larval stages, can have a substantial effect on the control strategy. In particular, late acting genes, which induce death after the density-dependent larval stage, have a significant advantage over SIT strategies because of an additional reduction in pest abundance that arises as a result of larval competition (Atkinson et al., 2007, Phuc et al., 2007, White et al., 2010).
The details of mosquito dispersal behaviour are not completely understood (Reiter et al., 1995, Harrington et al., 2005), though there have been mathematical modelling studies highlighting that Ae. aegypti invasion rates have a critical influence on the success of the control strategy (Lewis and Driessche, 1993, Takahashi et al., 2004, Yakob et al., 2008, Magori et al., 2009, Seirin-Lee et al., 2013). Nonetheless, studies that explore the effects of Ae. aegypti invasive dynamics upon the efficacy of SIT and RIDL control strategies in eliminating mosquitoes are limited to those by Yakob et al. (2008) and Yakob and Bonsall (2009), which consider the interplay of stage structuring and dispersion on a lattice with a small control region that is embedded within an established pest population. These investigations reveal complex dynamics and focus on the differences between SIT and RIDL control strategies for a very limited variation in spatial parameters, other than dispersal rates. However, firstly, it is not clear whether a strategy aimed at eliminating an established pest is appropriate for eradicating an emergent, invading, outbreak. In addition, the influence of systematically varying the size of the region in which control insects are released is an aspect of spatially heterogeneous models that is essentially unexplored and merits detailed study, given the concern that spatial dynamics such as mosquito invasion is becoming a critical issue on global scale (Benedict et al., 2007, Jansen and Beebe, 2010). Furthermore, such detailed investigations are facilitated in the continuum modelling approach considered here, which allows the ready prediction of scaling laws, as illustrated below for the influence of dispersal rates. More generally the continuum approach is typically an appropriate and efficient framework, and thus often advantageous, when the lengthscale and timescale under consideration are large compared to those describing the population's individuals.
Our objective is thus to consider control strategies for two control scenarios via SIT and RIDL: an endemic case and an emerging outbreak for a mosquito vector. In the former case, a mosquito vector is endemic. In contrast, in the latter case invading mosquitoes establish and cause a local outbreak in a previously mosquito-free region; see Fig. 1. An important question is how such differences in the initial scenario induce different responses to variations in control strategies with SIT and RIDL. In particular, we are concerned with how these responses are influenced by spatial parameters such as dispersal rates and especially the lengthscales of the regions in which control insects are released. Thus for the two contrasting scenarios, we investigate how varying the release rate in conjunction with the size of release region influences both the potential for control success and the resources needed to achieve it, in terms of control mosquito numbers, under a range of conditions. We thus discuss the relationships between the size of the control zone, the mosquito dispersal rate and advantageous strategies with respect to reducing control insect numbers and thus improving the strategy costs required to achieve eradication of mosquitoes. Finally, we briefly note that in the emerging outbreak case, we explore release efforts and strategy-costs with a control strategy that can eradicate the wild-type females. This is in distinct contrast to halting the spread of an outbreak using a barrier zone method of our previous study (Seirin-Lee et al., 2013).
Section snippets
Mathematical models
We build upon the temporal model of mosquito population dynamics developed by Dye (1984), which was validated on data for the larval and adult ecology of Ae. aegypti in Wat Samphaya, Bangkok, Thailand, published in Sheppard et al. (1969) and Southwood et al. (1972), and from unpublished reports of the World Health Organization's Aedes Research Unit (ARU) in Bangkok [ibid].
The densities of wild-type female mosquitoes and sterile/transgenic male mosquitoes at time t are respectively denoted by N(t
Endemic outbreaks and the local release strategy
We consider the local release strategy, asking two main questions: (i) To what extent does the dispersal rate affect the potential for eradicating female mosquitoes? (ii) If the local release strategy is effective, what is the minimal release region and how does it relate to the release rate ratio and dispersal rate? Our simulation results show that for some release regions and rates the local release strategy is not always successful in eradicating female wild-type mosquitoes (see Fig. 2). In
Discussion
When the release region of sterile/transgenic insects is sufficiently large, a temporal model for sterile/transgenic technologies may be enough to understand the potential for controlling pest insect populations. However, in practical situations this requires the release of sterile or transgenic insects over a long lengthscale, and therefore results in a heavy economic burden (Vreysen et al., 2007). Thus we are interested in finding the minimal value of the release region size, the release rate
Acknowledgements
S.S.L. was partially funded by the Japan Society for the Promotion of Science (JSPS Excellent Young Researcher Overseas Visit Program and Grant-in-Aid for JSPS Young Researcher). This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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