Introduction
Biological observation
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Model notes
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[38] Foster et al. 1988 | Modelled EBS and female-killing of a | Computational model that works on |
hypothetical insect population at various | discrete generations comparing each male | |
migrations, release rates, incomplete sterilities, | genotype with each female genotype. | |
and number of mutated alleles. Under most, | ||
but not all scenarios, EBS achieves better | ||
control than female-killing. | ||
[39] Schliekelman and Gould 2000a
| The authors model a hypothetical transgenic | The model uses combinatorics to determine |
implementation in hypothetical insects | a population’s genetic make-up as inherited | |
whereby there are multiple lethal genes | from parents. Lethality is operational in a | |
in released insects and these lethal genes | population subset with the correct allele | |
are conditional, killing only when certain | active in their genotype. | |
conditions are met and otherwise propagate. Found that under ideal conditions, this | ||
implementation can be far more effective | ||
than traditional EBS. | ||
[40] Schliekelman and Gould 2000b
| Modelled transgenic implementation whereby | This model maintains 20 population signals, |
2–20 lethal genes were engineered into a | one for each possible active allele. | |
hypothetical insect. As the number of lethal | Inheritance is captured as generations | |
genes per released animal increases, there is a | inherit their genetic makeup from the | |
greater chance any one progeny will inherit a | previous generation. | |
lethal gene. Found under ideal conditions, | ||
control could be achieved at rates several | ||
orders of magnitude more effectively than | ||
single gene EBS. | ||
[41] Barclay 2001 | Modelled EBS in hypothetical insects, with | The analysis is performed with a discrete- |
special regard to incomplete sterility and lack | time population model. The paper reports | |
of competitive mating ability, which cause | on many factors including equilibrium | |
decreased levels of control success. | female population with regards to | |
incomplete fertility. | ||
[42] Esteva and Yang 2005 | Models EBS implementation in males | Equation-based population model with |
engineered to have no sperm. Release | density dependent mortality. | |
proportion is important. | ||
[22] Phuc et al. 2007 | Compared EBS to LBS. They found that EBS at | Time-delayed difference equation model |
low release ratios can increase equilibrium size | with a density-dependent mortality in the | |
of adult population, but LBS can result in | aquatic life-stage and based on [43]. The | |
eradication. At high release ratio EBS works but | difference between EBS and LBS was | |
LBS works better. | characterized in population suppression. | |
[44] Kean et al. 2008 | Frequent small releases of EBS moths may be | Discrete-time population model with |
more effective than less frequent releases. They | overlapping generations. This model takes | |
also compared how competitiveness of | into account an over flooding parameter | |
irradiated males effected control. Models doses | and incomplete sterility. | |
of radiation which result in reduced, but not | ||
complete sterilisation of males to the benefit of | ||
increased mating competitiveness. | ||
[45] Yakob et al. 2009 | Modelled LBS, EBS, EFK, and LFK of a | Time-delayed difference equation model |
hypothetical insect population at various | representing the mosquito’s lifecycle with | |
release proportions, migrations, density | adult and larval mortality terms. | |
dependancies, and fecundities. Found bisex | ||
lethal could be preferred over female killing | ||
under certain scenarios. | ||
[46] White et al. 2010 | Models Ae. aegypti, EBS and LBS releases. Found | Population dynamics are modelled with |
control is more effective with fewer males | a time-delayed difference equation model | |
released more often than many males released | extended from [43]. EBS and LBS are | |
less frequently. | modelled and the dynamics of injected pulses of mosquitoes are reported. | |
[47] Deredec et al. 2011 | Models an An. gambiae EFK implementation | This work extends a population model |
where the X chromosome in sperm is targeted | by adding HEG dynamics and focuses on | |
(and two other transgenic techniques that are | reducing the intrinsic reproductive rate of | |
outside the scope of this paper) by release | the female population. Density dependent | |
of mosquitoes carrying homing endonuclease | mortality is considered for larvae. | |
genes (HEG). Determined the number of | ||
individual HEGs targeting essential mosquito | ||
genes required at various mosquito | ||
reproductive numbers with various homing | ||
rates to eliminate a mosquito population. | ||
[37] Thailayil et al. 2011 | Models release size of spermless An. gambiae
| Differential equation model with no explicit |
(EBS) males required at differing rates of | time latency between generations. The | |
occurrences where females mate more than | adult female population separated into | |
once. Very low levels of remating events were | females who have not mated; mated and | |
found to have significant negative effects on | fertile; mated; and infertile. Population | |
the ability to control the mosquito population. | persistence was described in terms of the model coefficients. | |
[48] Dumont and Tchuenche 2011 | Found it more effective to have small and | Extensive system of equations which |
frequent releases of EBS males over large | captures population and compartmental | |
infrequent releases. Also EBS works better | dynamics. | |
when carried out with a larval habitat control | ||
program (mechanical control). | ||
[49] Lee et al. 2013 | Modelled EBS & LBS in Ae. aegypti mosquitoes | Difference equation model similar to [22] |
under endemic and emerging outbreak | but look at an endemic case and emerging | |
scenarios. Evaluated various release and | outbreak of mosquito populations. | |
intervention-region sizes. Found EBS was | ||
always more effective than EBS, though the the | ||
magnitude varied by situation. |
Methods
State
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Duration
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Exit condition
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Note
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Egg
| 1 day + H
t
| None | Reflects incubation and hatch time. |
Larva
| about 12 days | Nighttime | Larval mortality is density dependent and favours |
older larvae. | |||
Pupa
| 1 day + H
t
| Nighttime | Adult emergence from pupae occurs (6 P.M. to 6 A.M. |
in the simulation). | |||
Immature Adult
| 53 hours | None | |
Mate Seeking
| - | 6 P.M. & Female | Mating is 100% successful and mate is assigned randomly. |
Bloodmeal Seeking
| - | Meal Success & Nighttime | Females have a 25% chance of finding a host each hour. |
Bloodmeals take less than 1 hour. | |||
Bloodmeal Digesting
| 36 hours | Nighttime | Agents seek to lay eggs in larval habitats only at night. |
Gravid
| - | Empty Egg Clutch & Nighttime | Agents complete gonotrophic cycles until death. |
Simulated SIT Campaigns
Results
Initial effects
Final effects
Release proportion
Early-acting versus late-acting
Mating competitiveness
Female-killing versus bisex lethality
Discussion
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Population suppression is dependent on the number of released males in a campaign for any cell-lethal gene to a point. After a certain release proportion, the additional males appear to have diminishing returns on population suppression likely due to saturation of the cell-lethal gene. This result is congruent with previous results [44,46,48] but this work shows the dynamic is present with all four cell-lethal implementations tested and using an agent-based modelling technique.
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Late-acting cell-lethality is highly preferred over early-acting because of its ability to exploit density-dependent mortality in the aquatic habitat. A large portion of population suppression occurs within 50 days of the campaign’s beginning. Late-acting genes maintained a higher larval mortality leading to greater population suppression by the end of a simulated year-long campaign. These results are also congruent with previous modelling literature [22,53] but they are demonstrated in an Anopheline simulation.
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Late-acting bisex genes are preferred because these genes lead to mosquito elimination with the fewest number of released males. This is a dynamic in SIT systems and may be counterintuitive though presented in [38]. Female-killing methods are thought to be more efficient because the heterozygous male population is an additional reservoir for the cell-lethal gene. However, the converse is that this population can also serve as a reservoir for wild-types and cause a population to persist (this is illustrated in Figure 6).