Computer models of parasite populations and anthelmintic ... - CSIRO

Computer models of parasite populations and anthelmintic resistance
RJ Dobson and EH Barnes
CSIRO Livestock Industries, F D McMaster Laboratory, Locked Bag 1, Armidale NSW 2350, Australia,
1. Summary
2. Background
2.1. Common Preconceptions about Drug Resistance
2.2. Persistent Drugs and Capsules
2.3. Low Efficacy Drugs
2.4. Drug Combinations
3. Simulation Case study
3.1. Model Assumptions
3.1.1. Table 1. Assumed anthelmintic efficacy against resident worms and incoming larvae
3.2. Management Simulated
3.2.1. Haemonchus control
3.3. Case-study Results
3.3.1. Years to Resistance
3.3.2. Worm Control
3.3.3. Table 3. Mean lamb worm burden during and after drug resistance develops
Table 3a Ostertagia
Table 3b Trichostrongylus
Table 3c Haemonchus
3.4. Acknowledgements
4. References
5. Further Reading
5.1. Flock/Farm Management Software
5.2. Genetic Models
5.3. Parasite and General Models
1. Summary
Computer models of parasite epidemiology can be used to investigate integrated parasite management
programs and their effects on worm control and anthelmintic resistance. Models for Trichostrongylus,
Ostertagia and Haemonchus incorporate worm parasite populations, climate, grazing management, host
immunity, drug use and selection for drug resistance, and can be used to explore how treatment frequency,
pasture rotation, drug persistency and drug efficacy affect levels of parasitism and drench resistance. A
Case Study examining selection by low efficacy drenches is used to demonstrate an application of the
models and highlights the difference between model predictions and conventional recommendations to
delay selection for drug resistance. In Section 5 (Further Reading) information on more general sheep
industry software as well as references to parasite population models can be found.
2. Background
Recommendations to delay selection for anthelmintic resistance have been generally based on theory and
judgement [1, 10,11] rather than supporting experimental evidence. This is because field trials to test
different drug use strategies [16] are conducted on a relatively brief evolutionary time scale and cannot
proceed faster than the rate of selection for anthelmintic resistance in a commercial grazing enterprise.
Selection can be accelerated in laboratory studies [5, 7]; however, extrapolating such results to grazing
systems is difficult because laboratory studies do not account for many aspects of selection. Simulation
models have been used as an adjunct to “field” and “pen” experimentation to help understand the
dynamics of parasite populations and devise strategies for avoiding drug resistance. They have the
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advantage of compressing the time scale and evaluating a range of environmental and management effects
on worm populations and resistance.
Most experiments [5, 7] and models [3, 8, 12] of selection for anthelmintic resistance have studied
survivors of drug treatment and until recently have ignored the potential for selection of incoming larvae
after treatment. The exceptions to this included a model of selection for resistance by a benzimidazole
(BZ) sustained release capsule [2] and models designed specifically to examine persistent drugs [6, 13].
Dobson et al. [6] showed that persistence period (against incoming larvae) and initial efficacy (against
resident worms) were important factors in determining the rate of selection for resistance. Smith et al.
[13] concluded that either high efficacy (against heterozygous resistant genotypes) or relatively low
efficacy against resident worms (susceptible and resistant genotypes) could delay selection for resistance,
and demonstrated that long half life drugs had greater potential for selection than short half life drugs.
Leathwick et al.[9] modelled the behaviour of a 100-day-slow release capsule used under commercial
grazing practices in New Zealand, and concluded that if a single capsule replaced a five-drench
preventative program in lambs, selection for resistance would be delayed provided that adult sheep were
left untreated.
This review will consider practical applications of these models in terms of worm burdens and selection
for drug resistance. The models do not predict loss of wool or meat production associated with failure to
adequately control worms. However, we generally assume the larger the worm populations the greater the
production losses. Unfortunately the objective of ensuring effective worm control conflicts with the
objective of minimising selection for drug resistance, particularly when the former is based around the use
of anthelmintics. There is no best generic advice or compromise to solve this dilemma, because individual
farmers will attach greater importance to one or the other of these objectives depending on their particular
circumstances. The long-term solution is to select lines of sheep that are immune to worms (see
www.csiro.au/nemesis). In the short term to preserve effectiveness of anthelmintics it is necessary to adopt
management practices that will slow the onset of drug resistance but may be associated with production
penalties.
2.1. Common Preconceptions about Drug Resistance:
. Most worm control programs recommend that to reduce selection for drug resistance you should:
• rotate drench classes annually,
• ensure all animals are drenched and
• use drugs showing maximum efficacy.
Two simulation models [3, 13] in particular have been used to explore some of these common
recommendations. In contrast to the recommendations the models suggest:
• that resistance to two drugs will develop at much the same rate regardless of the drug rotation
strategy adopted [3]. Interestingly, treating with two effective drugs at the same time will
substantially delay selection to both [3, 12].
• The strategy of leaving a few animals untreated to preserve susceptible worms has some risk
associated with it, in relation to worm control, but can delay selection for resistance [3].
• Both models [3, 13] have shown that highly effective drenches (eg using high dose rates in the
hope that heterozygote resistant worms (RS) will be killed) and low dose rate or low efficacy
drenches (which allow some homozygote susceptible (SS) and RS worms to survive) can delay
selection for anthelmintic resistance. The models predict selection for resistance will occur most
rapidly when only RS and homozygote resistant (RR) worms survive treatment.
2.2. Persistent Drugs and Capsules:
Most simulation work has focussed on survival of worms resident in the sheep at the time of treatment and
ignored selection of incoming larvae by drug residue in the host after treatment. For example, if ALL
worms in the host are removed at the time of treatment there is no selection for resistance. However, if the
complete kill is obtained by a persistent drug or sustained release capsule (SRC) then the sheep will
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possibly be reinfected with resistant larvae while susceptible larvae are excluded. The longer the
persistent activity or drug release, the longer resistant larvae will have a survival advantage over SS
genotypes, and eventually the establishment of incoming resistant larvae will outweigh the benefit of
removing resistant adult worms at the time of treatment. The length of this critical persistence time will
vary for species and environment. Unpublished simulation work by Dobson and Barnes suggests that this
critical persistence time varies from 20-35 days. That is, persistent activity that excludes SS larvae (L3)
while allowing RS and RR L3 to establish for 20-35 days will select for resistance at the same rate as a
non-persistent drug that is ineffectual against resident RS and RR worms. Experimental work has
demonstrated “that persistent treatments may not only screen populations for resistant genotypes but may
also reduce the density-dependent population regulation acting on those individuals able to survive
treatment”[15]. As a consequence “this may result in the accumulation of greater than expected numbers
of resistant parasites in animals given prophylactic treatment” [15].
2.3. Low Efficacy Drugs: Modern broad-spectrum drugs are expected to have efficacy greater than 99%,
however, drugs with relatively low efficacy (i.e. efficacy against susceptible resident worms is 80% or
greater) can play a useful role in worm control programs. Using simulation models, the following casestudy
explores low efficacy drugs, i.e. drugs that permit survival of SS genotypes, and their role in control
of Trichostrongylus, Ostertagia and Haemonchus spp. This allows comparison with drugs that display
high efficacy against SS only or SS, RS and RR genotypes. When reduced efficacy (about 85-95%) is
caused by anthelmintic resistance, rapid selection for drug resistance occurs and control failure follows.
However, if the relatively low efficacy permits susceptible worms to survive, for example the use of
naphthalophos against Trichostrongylus, selection for resistance is delayed and worm control is still
effective until drug resistance develops.
2.4. Drug Combinations: Computer modelling has shown that the best way to inhibit the development of
drug resistance is by the simultaneous applications of drugs (i.e. the use of combinations or mixtures)
[3,12]. WARNING, this strategy will fail if all animals are treated and then placed on uncontaminated
pasture such as crop stubble, that is, pastures with no refugia. Under these circumstances there is a high
risk of rapid selection for resistance to all drugs used in the combination because only the worms that
survive drug treatment become the founders of the next generation. For example, we modelled Ostertagia
circumcincta populations in a Mediterranean climate (hot dry summers and wet winters). Selection for
resistance was examined for a single treatment with a macrocyclic lactone (ML) when moving the flock to
crop stubble. This imposed intense selection for drug resistance, resulting in up to a 10-fold increase in
ML-R allele frequency from a single treatment. Strategies examined to avoid rapid selection for resistance
under this regimen were leaving 1-2% of sheep untreated and including a combination treatment of
benzimidazole (BZ) plus levamisole (LV) with the ML. Substantial resistance to BZ and LV was assumed
to be present as initial resistance allele frequencies for ML, BZ and LV were set at 2%, 50% and 50%
respectively. The efficacy of ivermectin (IVM), abamectin (ABM) and moxidectin (MOX) against MLresistant
genotypes was assumed to be poor, high and very high respectively. If 1% and 2% of the flock
were untreated, resistance was delayed by 2 and 3-fold, respectively. A combination of BZ+LV included
with the ML did not delay resistance if 100% of the flock were treated but gave approximately additional 5
and 8 fold delays in resistance when 1% and 2% of sheep, respectively, were left untreated. The net effect
was that resistance was inhibited by 7, 32 and 48-fold when IVM, ABA and MOX, respectively, were used
in combination with BZ+LV and 2% of the flock remained untreated. The important message is that
treating sheep when there is no refugia is a very high-risk strategy. Using combinations does not reduce
this risk, but using combinations and leaving a small proportion of the flock untreated can greatly reduce
the risk.
3. Simulation Case study
The model of Trichostrongylus epidemiology [2] was used to simulate selection with low efficacy, shortpersistency
drugs. Other unpublished versions of this model, which account for survival and development
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of free-living stages and host regulation of Haemonchus and Ostertagia populations, were used to simulate
drug selection in these species.
3.1. Model Assumptions: Table 1 gives the assumptions for the activity of a low-efficacy and short-acting
oral anthelmintic against each worm and larval genotype. Note that the only difference between the 2
drugs is the efficacy against resident worms on the day of treatment; exclusion of larvae following
treatment is presumed to be the same for both drugs. The frequency of the gene for drug resistance was
initially set at 0.01% for all simulations; this yields an approximate efficacy of 80% and 99% for the lowefficacy
and short-acting oral anthelmintics, respectively. SS, RS and RR represent susceptible
homozygous, heterozygous and resistant homozygous genotypes, respectively and assumes a single gene
determines resistance [5,6]. For the short-acting oral drench drug resistance was assumed to be a dominant
trait [3,6,14] in Haemonchus and Ostertagia simulations and a co-dominant trait for Trichostrongylus
simulations. For all species, resistance to the low-efficacy oral drug in parasitic stage worms was assumed
to be dominant. Selection for drug resistance was simulated and evaluated by determining increases in this
gene frequency in larvae on pasture and in grazing sheep.
Table 1. Assumed anthelmintic efficacy against resident worms and incoming larvae.
Drug efficacy (%) against resident worms at the time of treatment.
Worm Species: Trichostrongylus Ostertagia-Haemonchus
Worm genotype: SS RS RR SS RS RR
Treatment type
Low-efficacy oral 80 0 0 80 0 0
Short-acting oral 99 50 0 99 4 2
Drug efficacy (%) against incoming larvae (L3) for 3 days post treatment.
Worm Species: Trichostrongylus Ostertagia-Haemonchus
L3 genotype: SS RS RR SS RS RR
Treatment type
Low-efficacy oral 99 50 0 99 0 0
Short-acting oral 99 50 0 99 0 0
3.2. Management Simulated: Frequency and timing of broad-spectrum treatment used in the two worm
control programs were Wormkill [4] for the summer rainfall environment (Armidale, NSW, Australia) and
“summer drenching” for a winter rainfall environment (Kybybolite, South Australia) which experiences a
hot dry summer. In both environments lambs are treated at weaning and moved to a safe pasture.
Trichostrongylus and Ostertagia populations were simulated in both environments. Haemonchus was not
simulated at Kybybolite as it is not a problem species in this area. At Kybybolite a weaning drench
(12/10) and move to safe pastures combined with a single summer treatment (17/11) was sufficient for
good parasite control, ewes also received a treatment on 17/11. Under Wormkill lambs were drenched on
22/12, 22/2 and 1/5 while ewes only received one broad-spectrum drench on the 22/12.
3.2.1. Haemonchus control: For Haemonchus the simulations included treatments with Closantel (CLS) as
recommended by the Wormkill program (2/11, 22/12 and 22/2 for both ewes and lambs). Two levels were
chosen for CLS efficacy as resistance to CLS occurs in this region. CLS efficacy was set at 80% or 99%
for Haemonchus simulations, however, the evolution of CLS resistance was not modelled in these
simulations, that is, CLS efficacy remained at these levels throughout the simulations. CLS was assumed
to have persistent activity against incoming larvae for 30 days. In the absence of CLS resistance, CLS
treatment excluded 99%, 90% and 60% of L3 for days 1-10, 11-20 and 21-30 respectively after treatment.
If CLS resistance was assumed, CLS treatment excluded 80%, 70% and 50% of L3 for days 1-10, 11-20
and 21-30, respectively, after treatment.
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3.3. Case-study Results
3.3.1. Years to Resistance The times to detection of resistance to the broad-spectrum anthelmintic are
given in Table 2. The time to resistance was defined as the mean of the times taken for the R allele
frequency to reach 10% and 70%. These two points were chosen, as resistance is unlikely to be detected
before R alleles reach 10%, but should have been detected by the time they reach 70%. These data show
the time to resistance for the low-efficacy drug was at least 50% longer than for the short-acting drug in
every environment.
Table 2. Effect of low-efficacy and short acting oral anthelmintics in different environments: years to
detection of drug resistance.
Species Comment Low-efficacy oral Short-acting oral
Ostertagia NSW Wormkill 9 6
Ostertagia SA Summer treatments 6 4
Trichostrongylus NSW Wormkill 13 9
Trichostrongylus SA Summer treatments 19 12
Haemonchus 99%* no CLS resistance 12 7
Haemonchus 80% # CLS resistance 11 6
* indicates 99% CLS efficacy when no resistance to CLS is assumed.
# CLS efficacy of 80% when CLS-resistance is present.
3.3.2. Worm Control: The impact on worm control of low-efficacy versus short-acting treatment is shown
in Tables 3a-c. Table 3 shows:
1) the mean burden of each species of worm in lambs. These were calculated at three times: i)
prior to the detection of drug resistance (ie. when R-allele frequency is at low levels), and when R-allele
frequency is at ii) moderate and iii) high levels.
2)the range of years, from the 20-year simulation, over which each mean was determined, and
3) the initial and final R-allele frequency during those years.
The mean worm burdens in Table 3 are indicators of long term exposure and do not reflect peak worm
exposure that could be responsible for sheep deaths. Predicted sheep mortalities were low for both drug
types despite the increase in drug resistance over time. This result is in large part due to the preparation of
safe pastures for lambs at weaning and may not be applicable to a less severe dry summer environment
(e.g. some Drenchplan areas in NSW and Vic) where summer drenching to reduce pasture contamination
is important for good worm control.
3.3.3. Table 3. Mean lamb worm burden during and after drug resistance develops. Also shown are the
years of the simulations used for calculating the mean worm burdens, and the R-allele frequency at the
start and end of each period. NSW indicates the Armidale summer rainfall environment, and SA indicates
the Kybybolite winter rainfall environment.
Table 3a Ostertagia
DRUG USED Low-Efficacy Oral Short-Acting Oral
RESISTANCE LEVEL low mod. high low mod. high
Ostertagia NSW 834 3879 5878 542 3604 5229
Years 1-8 9-15 16-20 1-6 7-12 13-20
R-allele% 0-34 34-82 82-89 0-44 44-84 84-93
Ostertagia SA 415 1163 4046 282 1242 3927
Years 1-6 7-11 12-20 1-4 5-9 10-20
R-allele% 0-48 48-83 83-93 0-40 40-82 82-94
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Table 3b Trichostrongylus
DRUG USED Low-Efficacy Oral Short-Acting Oral
RESISTANCE LEVEL low mod. high low mod. high
Trichostrongylus NSW 2143 3051 - 1299 2519 3063
Years 1-13 14-20 - 1-9 10-13 14-20
R-allele% 0-44 44-74 - 0-46 46-80 80-96
Trichostrongylus SA 1993 - - 2054 1881 -
Years 1-20 - - 1-13 14-20 -
R-allele% 0-39 - - 0-45 45-71 -
Ostertagia shows the greater increase in worm burdens as R-allele frequency increases. Trichostrongylus
burdens in the summer rainfall zone were most compromised by use of a low-efficacy drench when R-
allele frequency was low. The 65% increase in average worm burden would probably lead to some subclinical
production loss. Trichostrongylus and Ostertagia populations were controlled by the low-efficacy
drug in both environments because preparation of safe pastures for young sheep was assumed (i.e.
drenching was not the sole worm control measure). The more potent short-acting oral drench did control
worms at a lower level than the low-efficacy drug, but selected for resistance at a slightly faster rate. The
results indicate that both drugs can be used to control these species despite having different strengths and
weaknesses.
Table 3c Haemonchus
DRUG USED Low-Efficacy Oral Short-Acting Oral
RESISTANCE LEVEL low mod. high low mod. high
Haemonchus 99%* 130 344 - 102 250 348
Years 1-10 11-20 - 1-6 7-14 15-20
R-allele% 0-49 49-74 - 0-31 31-80 80-86
Haemonchus 80% # 160 464 - 225 153 410
Years 1-10 11-20 - 1-5 6-10 11-20
R-allele% 0-40 40-80 - 0-48 48-82 82-92
* indicates 99% CLS efficacy when no resistance to CLS is assumed.
# CLS efficacy of 80% when CLS-resistance is present.
Haemonchus populations were mainly controlled by CLS even when its efficacy against resident worms
and incoming larvae was reduced by about 20%. Consequently little impact on worm populations of drug
resistance to the broad-spectrum (BS) drenches was observed in these simulations, particularly as BS
treatments are usually accompanied by a CLS treatment. It needs to be emphasised that CLS resistance
remained static in these simulations so that the comparison between low-efficacy and potent BS drenches
could be made. The results (Table 3c) show that Haemonchus can be controlled when CLS is 80%
effective, but in reality this level of resistance would not last. Thus CLS could be relied on to control
Haemonchus when it is 80-90% effective but only as a short-term measure.
3.4. Acknowledgements - We are grateful for financial support from Australian woolgrowers through the
Australian Wool Research and Promotion Organisation in development of these models. The case study
simulation was published in the Proceedings of the Australian Sheep Veterinary Society 1999 AVA
Conference, Hobart 1999 (B. Besier editor) and we wish to thank the ASVS, a Special Interest Group of
the Australian Veterinary Association, for permitting us to reproduce this material.
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4. References
[1] Anthelmintic Resistance. Report of the Working Party for the Animal Health Committee of the
Standing Committee of Agriculture. SCA Technical Report Series-No. 28. Convenor P.J. Waller,
1989, CSIRO, Canberra.
[2] Barnes EH, Dobson RJ. Population dynamics of Trichostrongylus colubriformis in sheep: computer
model to simulate grazing systems and the evolution of anthelmintic resistance. Int. J. Parasitol.
1990; 20:823-31.
[3] Barnes EH, Dobson RJ and Barger IA. Worm control and anthelmintic resistance: adventures with a
model. Parasitol. Today 1995; 11:56-63.
[4] Dash KM. Control of helminthosis in lambs by strategic treatment with closantel and broadspectrum
anthelmintics. Aust. Vet. J. 1986; 63:4-8.
[5] Dobson RJ, Griffiths DA, Donald AD and Waller PJ. A genetic model describing the evolution of
levamisole resistance in Trichostrongylus colubriformis, a nematode parasite of sheep. IMA J Math
Appl. Med. Biol. 1987; 4:279-93.
[6] Dobson RJ, Le Jambre L and Gill JH. Management of anthelmintic resistance: inheritance of
resistance and selection with persistent drugs. Int. J. Parasitol. 1996; 26:993-1000.
[7] Gill JH, Kerr CA, Shoop WL and Lacey E. Evidence of multiple mechanisms of avermectin
resistance in Haemonchus contortus - comparison of selection protocols. Int. J. Parasitol. 1998;
28:783-9.
[8] Leathwick DM, Vlassoff A and Barlow ND. A model for nematodiasis in New Zealand lambs: the
effect of drenching regime and grazing management on the development of anthelmintic resistance.
Int. J. Parasitol. 1995; 25:1479-90
[9] Leathwick DM, Sutherland IA and Vlassof A. Persistent drugs and anthelmintic resistance - Part III.
N Z. J. Zool. 1997; 24:298-9.
[10] Prichard RK, Hall CA, Kelly JD, Martin ICA, and Donald AD. The problem of anthelmintic
resistance in nematodes. Aust. Vet. J. 1980; 56:239-50.
[11] Resistance in Nematodes to Anthelmintic Drugs. Edited by N. Anderson and P.J. Waller, 1985,
CSIRO and Australian Wool Corporation publication. Glebe, N.S.W.
[12] Smith G. A mathematical model for the evolution of anthelmintic resistance in a direct life cycle
nematode parasite. Int. J. Parasitol. 1990; 20:913-21.
[13] Smith G, Grenfell BT, Isham V and Cornell S. Anthelmintic resistance revisited: under-dosing,
chemoprophylactic strategies, and mating probabilities. Int. J. Parasitol. 1999; 29:77-91.
[14] Sutherland IA, Leathwick DM, Moen IC and Bisset SA. Resistance to treatment with macrocyclic
lactone anthelmintics in Ostertagia circumcincta. Vet. Parasitol. 2002; 109:91-99.
[15] Sutherland IA, Moen IC and Leathwick DM. Increased burdens of drug-resistant nematodes due to
anthelmintic treatment. Parasitology 2002; 125:375-81.
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[16] Waller PJ, Donald AD, Dobson RJ, Lacey E, Hennessey DR, Allerton GR and Prichard RK.
Changes in the Anthelmintic Resistance Status of Haemonchus contortus and Trichostrongylus
colubriformis exposed to different anthelmintic selection pressures in grazing sheep. Int. J. Parasitol.
1988; 19:99-110.
5. Further Reading
5.1. Flock/Farm Management Software
GRAZPLAN - GrazFeed, GrassGro and LambAlive – Decision support software for the sheep industry.
Ref. Freer M, Moore AD, Donnelly JR. GRAZPLAN: decision support systems for Australian grazing
enterprises. II. The animal biology model for feed intake, production and reproduction and the GrazFeed
DSS. Agricultural Systems 1997; 54:77-126. Clark SG, Donnelly JR, Moore AD. The GrassGro decision
support tool: its effectiveness in simulating pasture and animal production and value in determining
research priorities. Aust J of Exp Agric 2000; 40:247-256. Available through Horizon Technology, PO
Box 598, Roseville NSW 2069. (www.hzn.com.au).
Midas – Model of an Integrated Dryland Agricultural System. “Whole-farm” agricultural and economic
model developed by Agriculture Western Australia for WA’s sheep and wheat growing areas. Ref.
Morrison DA, Young J. Profitability of increasing lambing percentages in the Western Australian
wheatbelt. Aust. J. of Agric. Research 1991; 42:227-241. Contact A D. Bathgate at Agriculture Western
Australia (abathgate@agric.wa.gov.au).
Prograze – an extension package and course in grazing and pasture management and the use of GrazFeed.
A.K. Bell and C.J. Allan. Ref. PROGRAZE – an extension package in grazing and pasture management.
Aust. J. of Exp. Agric. 2000; 40:325-330. McPhee MJ, Bell AK, Graham P, Griffith GR, Meaker GP. PRO
Plus: a whole-farm fodder budgeting decision support system. Aust. J. of Exp. Agric. 2000; 40:621-630.
List of PROGRAZE co-ordinators and their contact phone numbers:
National Co-ordinator Cameron Allan 02 6361 1204
NSW Co-ordinator Alan Bell 02 6763 1254
Vic. Co-ordinator Reg Hill 03 5333 6732
Tas. Co-ordinator Robin Thompson 03 6336 5291
SA Co-ordinator Tim Prance 08 8555 5366
WA Co-ordinator Bill Smart 08 8555 5366
PROGRAZE is not delivered in Queensland
5.2. Genetic Models
Dobson RJ, Griffiths DA, Donald AD, Waller PJ. A Genetic Model Describing the Evolution of
Levamisole Resistance in Trichostrongylus colubriformis, a Nematode Parasite of Sheep. IMA J of
Mathematics Applied in Med & Biol 1987; 4:279-293.
Roush RT, McKenzie JA. Ecological Genetics of Insecticide and Acaricide Resistance. Ann. Rev.
Entomol. 1987; 32:361-380.
Wright S. The Genetical Structure of Populations. Annals of Eugenics 1951; 15:323-354.
5.3. Parasite and General Models
An Introduction to Population Ecology. Hutchinson GE, 1978 Yale University Press, New Haven and
London.
Infectious Diseases of Humans - Dynamics and Control. Anderson RM, May RM, 1991 Oxford University
Press, Oxford, New York and Tokyo.
Parasitic and Infectious Diseases – Epidemiology and Ecology. Edited by Scott ME, Smith G, 1994
Academic Press, New York, London and Sydney.
Roberts MG. A Pocket Guide to Host-Parasite Models. Parasitol. Today 1995; 11:172-177.
Roberts MG, Aubert MFA. A model for the control of Echinococcus multilocularis in France. Vet.
Parasitol. 1995; 56:67-74.
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