Table 1 A survey of SIT modelling literature

[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.