control Mode[ing

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Mode[ing onchocerciasis transmission and control

Final report for Technical Service Agreement No. 08/181/85 provided by the

World Health Organization on behalf of the Onchocerciasis Control Programme in West Africa for the period June 1

L993

to December I

¹⁹⁹³

October 1994

Centre for Decision Sciences in Tropical Disease Control (CDTDC) Dept. of Public Health, Erasmus University Rotterdam

P.O. Box 1738, 3000 DR Rotterdam, The

) 'F /:) i'\,/-\ r \rr)

Introduction

The proposed activities

for

the

TSA

1993 were almost exclusively devoted

to

the assessment

of

the effectiveness

of

ivermectin treatment as

a

^means

to

control transmission: either when used alone

or

in addition to vector control.

In

Part

I

^(page

3)

we report the model based analysis

of

the results

of

the community treatment

in

Asubende (Ghana).

We

have attempted

to quantiff the

model-parameters

for

the effects

of

a treatment on the microfilariae and the adult parasite.

An

important question that we tried

to

answer

is

whether the impact on the adult worm is permanent ('macrofilaricide-like') or reversible. This analysis has a value

in

its own and has been submitted as a scientific ^paper.

Part

II

^(page 21) of the report deals with the consequences of the new insights

for

the role

of

ivermectin based strategies. We have tried

to find

those strategies based

on

annual ivermectin treatment and

vector

control

which,

under certain conditions,

will

^lead

to

eradication

of

the parasite from a given area, i.e.

will

give rise to negligible recrudescence risks.

Part

III

^(page 33) comprises some miscellaneous notes which have been sent

to

OCP in

view of

the meeting

of

EAC15.

An

important item

in

these notes concerns the possible use

of

entomological criteria in post-larviciding surveillance.

2

Part I

Irreversible effects of ivermectin on adult ^parasites in onchocerciasis patients

in the Onchocerciasis Control Programme in West Africa

Absffact

Ivermectin (MectizanR) is the drug

of

choice

for

onchocerciasis.

It

eliminates microfilariae from the skin and considerably suppresses their reappearance.

In

this paper

it is

investigated

in

what way

this

suppression

is

associated

with

the fecundity

of

adult Onchocerca volvulus. Predictions based

on

hypotheses about reversible and irreversible effects are compiued

with

post-treatment microfilarial counts

of

114 adult persons

from

Ghana. These persons were followed during five years of annual community treatment by the Onchocerciasis Control Programme in West

Africa. It is

shown that

the trend in

microfilarial counts can only

be

explained when

it is

assumed that ivermectin,

in

addition

to

causing a temporary

fall

in the microfilariae production, also affecs the fecundity

of

the worms irreversibly. Following each treatment, worms recover during a period

of

about 10

to

¹¹ months, and reach a new stablelevel of microfilariaeproduction which is 30% ^less than before treatment.

Key words: Onchocerciasis, Onchocerca volvulus, Ivermectin, Modelling

4

The registration

of

the anthelminthic drug ivermectin (MectizanR)

in

1987 was a landmark

in

the control

of

human onchocerciasis

or

river-blindness,

a

parasitic disease caused

by the

filarial nematode Onchocerca

volvulus. Oral

administration

in a

standard dose

of

150-200p.glkg body weight is followed

by

rapid elimination

of

microfilariae (mf) from the skin and gradual reduction

of ocular mf levels [1].

Side effects

are

generally

mild

and

this

makes ivermectin

a

better therapeutic option than Diethylcarbamazine @EC), which is often accompanied

by

severe Mazotti reactions and ocular damage. Ivermectin outperforms DEC also

in a

longer suppression

of

mf- repopulation

of

the skin

[2,3].

^This additional effect of the drug, which was obvious

in all

studies done thus

far,

has initiated research

on

the effect

of

the drug

on

adult parasites.

Adult

female parasites in treated ^persons showed an interruptionof the normal embryogenesis,

but

after a single treatment this appeared to be reversible

for

most

of

the worms

[4,5].

^Excess worm mortality ^has never been observed after

a

single treatment U,2,61. Irreversible effects

on

worms were found after many treatments

with

short intervals varying between

two

weeks and

six

months [6-11].

These studies revealed significantly more dead and moribund female worms

in

frequently treated patients than

in

not

or only

once treated controls. Furthermore, the reproductive activity

of

the surviving worms was markedly reduced. Since the examinations were done shortly after the last treatment

it

remains unknown

to

what extent the impact on reproduction is transient

or

irrevers- ible. Recent research, however, demonstrates that also one ^and a half year after

five

six-monthly doses the fecundity of female worms is

still

considerably reduced [12].

A

question which

is

important

in

view

of

the limited resources available

to

health services in developing countries

is

whether the findings

for

short treatment intervals are also applicable to regimes

with

intervals

of

one year, which is the current practice

in

nearly

all

control progralnmes

[1a]. In

the present paper

we

address

this

^question

by

analyzing data

from a

large community based study

of

annual treatments

in

a hyperendemic region (Asubende, Ghana), organised

by

the Onchocerciasis Control Programme

in

West

Africa

(OCP)

Il4-17).

^The data consist

of

microfi-

larial (mf)

counts

in

skin-snips

from

^persons who were surveyed

over a

period

of

almost five years

in

order

to

evaluate the

first five

treatments. We have investigated whether the observed trend

in mf

counts can be explained

from

short-term and transient effects

of

ivermectin

only,

or whether long-term and irreversible effects on the adult worms are involved too.

Materials and Methods

Study area and selection

of cohorts.

The Asubende region is located along the lower reaches

of the Pru river

in

Ghana, just _west of Lake Volta. OCP started control

of

the vector (the blackfly Simulium damnosum) in this river basin in January 1986. Flies have been collected since 1979 to assess the vector

biting

rate and the vector infectivity.

A

clinical survey was done

in

September 1987 among 796 persons

living in a

cluster

of

three villages

in the

middle

of the

area. Both entomological and clinical findings revealed that the area was hyperendemic

for

the savanna form

of O.volwlus.

The skin microfilarial densities were among the highest encountered

in

the OCP area [13]. The community

trial of

annual ivermectin treatment was started

in

October 1987. In the

first

round

of

treatment more than 15,000 persons were treated, comprising 6L.5%

of

the study population.

In

the present analysis we use data consisting

of mf

counts

in

skin-snips which have been collected

to

evaluate the

first five

treatments (1987-1991). The organization

of

the

trial,

the trends

in

the skin

mf

densities, and the

joint

effect

of

vector control and ivermectin treatment on the transmission potential

of

the flies have been described elsewhere

II4,l7l.

^{Treatment dosage}

varied between 130 and 2ffipglkg body weight.

From the 796 persons examined at the baseline survey

in

1987,

we

selected

the

114 adult persons

()20

years)

who

satisfy

the

inclusion criteria

of

the

following two

cohorts. The first cohort

(n=78)

consists of ^persons who were treated in all five rounds and were re-examined

in

all eight follow-up surveys which were done at 4 and 12 months after the

first two

treatments,

5

and 12 months after the

third,

11 months after the fourth and

6

months after the

fifth

treatment. The second cohort was selected

for

a longer follow-up period

of

a single treatment.

It

consists

of

36 persons who were treated at the

first

but not at the second round, and who were re-examineA 24 months after the

first

treatment. We restricted ourselves

to

adult persons because

it is only

for older ages that one may expect

a

constant infection

level

and, hence, exclude

the

confounding effect

of

ageing

[18].

The dark bars

in

Figure 1 show the frequency distribution

of mf

counts in skin-snips before treatment and at the follow-up surveys.

Modelling the effects

of

ivermectin. Hypotheses on the effect

of

ivermectin have been tested

using

the

stochastic simulation model ONCHOSIM.

This

model describes

the

development

of

O.volvulus

in

man and flies and the transmission

of

the parasite. Elsewhere we explain the model

in full

and report its validation ll9-221. ONCHOSIM allows

for

a detailed simulation

of

control strategies. This enabled us

to

mimic the vector control activities employed

in

the Asubende area, thus accounting

for

the observed fluctuations

in

the transmission potential

of

the

flies [17].

^The microsimulation method,

which is

characterized

by

simulating

the

life-histories

of

individual hypothetical persons

in

a dynamic population (birth, acquisition

of

parasites, accumulation

of

mf,

6

death) and individual parasites (maturation, mating, mf-production, death), allows

for

describing and testing possible effects

of

ivermectin on the level

of

worms and humans. Since the output

of

the calculations

is on

an individual level, we were able

to

select those adult persons

from

the simulated population

for

whom the timing

of

treatments and surveys satisfied

the

same criteria used

for

selecting

the

cohorts, and

for

whom

the

skin-snip count distribution before

the

first treatment was identical to that of the cohorts.

An

assumption used throughout the analysis is that ivermectin treatment eliminates

all mf in

a

person.

Apart from this

immediate effect,

we will

investigate one transient and

two

types

of

irreversible effect on the fecundity

of

adult female worms. The transient effect

is

modelled as a

recovery period during which the mf production rate increases

from

zero

to

a new stable level. In case

of the first

type

of

irreversible effect

of

the drug, called oroductivity reduction,

this

new stable

level will be lower

than before treatment

for all

female

worms. The

second

type of

irreversible effect is the immediate and permanent cessation

of

mf-production

in

a certain fraction of the parasites, be

it

by death or by total loss of fecundity (.fecundity loss), while the other worms recover

to

their pre-treatment productivity. The magnitude

of

differences

in

transient and irrever- sible effects between persons and between treatments

is

called effect

variability

and

is

measured

by

the variation coefficient,

i.e.

quotient of the standard deviation and the mean

of

the effect. We explicitly test whether the increase

in

the mf-production during the recovery period

is

linear or not. In the Annex we give a mathematical description of the assumptions.

Testing of hypotheses. According to the definitions of the model parameters, we

will

test two basic hypotheses

I

^and

II for

the effect

of

ivermectin on adult worms:

I.

Treatment has transient effects

only, i.e.

there

is no

productivity _reduction

or

fecundity

loss; II.

^{Treatment has also}

irreversible effects.

To

check whether the two types

of

irreversible effect

differ in

their explana- tion

of

the data, we

will

also test them separately. Hypothesis

IIa

states that an irreversible effect

is only

caused

by

^permanent productivity reduction;

in

hypothesis

IIb it is only

caused by fecundity loss. When both

effecs

are combined, a fraction

of

worms immediately looses fecun-

dity,

and the remainder eventually reaches a stable mf-production, but

on a

reduced level. Each hypothesis is tested by a x'based comparison of observed and predicted skin-snip distributions for the follow-up surveys

of

each cohort. Some skin-snip count categories shown

in Figure I

^have

been combined

so that the

number

of

individuals

is at

least

5 per

category. Estimation

of

parameters

is

achieved

by

minimizing

X'using

a downhill-simplex method _1231. Apart

from

the parameters directly related to the effect

of

ivermectin, we

will

estimate the mf-lifespan, since ttris parameter is an important determinant

of

the delay between stabilization

of

the mf-production and

stabilization

of the mf{ensity in the skin

(see Annex). Furthermore,

we

always assume 3%

treatment

failure.

Such

failure has

been reported before and

has

been

mainly

ascribed to

mal absorption ^(d iarrhoea, vo mitin E, etc. I24l) ^.

Results

The results

of fitting

the hypotheses about the effect

of

ivermectin to the data

of

the surveys after

five

treatment rounds strongly suggest that the drug affects the mf-production

of

female parasites not only temporarily

(P<0.01)

but also irreversibly

(P>0.1);

see Table 1. The irreversible effect can be quantified as a productivity reduction

of

35%

for all

female worms,

or

as a total loss

of

fecundity (or death)

for

28%

of

the worms. The data are explained

well

by both hypotheses, ^and detailed biological data would be required

to

differentiate between them. The goodness-of-fit did

not

improve significantly

by

combining the

two

types

of

irreversible effect;

they

appear

to

be interchangeable. Lower values

for

productivity reduction have to be compensated

by

higher values

for

total loss

of

fecundity

in

such a way that the combined loss

of

productivity

in

a patient ^equals about3?%.

The

recovery

in

mf-production

is

estimated

to

take 10-l

l

^{months, and}

^the

mf-production accelerates during this period (the associated shape parameter, not shown in the Table, has a value

of

1.5

with

a 95Vo confidence interval

from

1.2

to

1.9). Note that the absence

of

an irreversible effect leads

to

larger values

for

the recovery period and the mf-lifespan,

but

apparently without achieving a sufficiently good explanation of the data.

There appears

to

be a considerable variability between patients in the effect

of

treatment. The values

of 0.52

and

0.54 for the

effect variability

imply

an inter-quartile range,

i.e. a

range

of

values which covers the centre half

of

the patients,

of

6

to

14 months

for

the recovery period,

of

lTVo to 38% for the fecundity loss, and of 20% to 47% for the productivity reduction.

Table 1 also gives

95%

confrdence intervals

for

the parameter estimates. Since the recovery period and the mf-lifespan

jointly

_{determine the} speed

of

mf-repopulation

of

the skin, they are to some extend interchangeable, and consequently

fairly

wide confidence intervals were found for these parameters.

The limited

information

on

the lifespan

of

microfilariae

[25)

^{suggests that 4} months

(our lower limit) is highly

unlikely.

This

implies that the associated upper

limit of

16

8

months for the recovery period is possibly ^also too high

Figure I

^compares

^the

^{observed mf-count} frequency distributions

for the

post-treatment surveys

with

the predictions from the hypothesis

of

permanent productivity reduction (Hyp. IIa).

There are no systematic differences between prediction and observations

for

cohort

1 (Fig.

1a).

The lowest and highest mf-count categories are underestimated

for

the follow-up survey

of

cohort

2 ^(Fig.

^1b),

which

suggests that

the

longer-term effect

of

treatment

may vary

more between patients ttran predicted by the ^model.

The fit of the

predictions

to the

survey data

is

summarized

in ^Figure 2. The

data are represented as

a

geometric mean mf-count.

We fitted

an exponential curve

to the

peaks

of

the predicted post-treatment trends, which represent the situation just before a new annual treatment.

The figure clearly shows that disregarding irreversible effects

of

ivermectin leads

to

an underes- timation of the additional effect of each further treatment.

Discussion

Our

analysis

of the

results

of five

consecutive annual treatments provides strong evidence that apart

from killing

microfilariae, ivermectin also has a significant impact on the

viability of

adult female parasites.

A

good explanation

of

the trends

in

mf-counts was obtained

by

assuming that each treatment is followed

by

a period

of

about

l0

months

of

gradually increasing

mf

production

to

a level which

is

30% lower than before treatment. The data

did

not allow us

to

differentiate between the hypothesis that all female parasites

in

a person are affected equally and the ^hypothesis that a fraction looses fecundity completely (or dies) while the others recover to their pre-treatment mf-production level.

The temporary effect is

in

line with the results from earlier studies which showed that in most worms the normal release

of

mf was interrupted after treatment, but that

I0 to

12 months later the percentage

of

worms

with

normal production had increased again significantly 14,5,26). Although none

of

these studies revealed excess mortality

of

worms

by

a single treatment, after one year ^a considerable fraction (40% lsD was not (yet) releasing

mf.

This explains the delay

in

repopulation

of the skin by mf

11,3,27-291. Even after

two

years markedly reduced mf-levels were found [30,31], although most ^persons had become mf-positive again. Also in our cohort

2,the

mean mf-

density after

two yqus

was

still

^less than half the pre-treatment level. These observations suggest a lasting treatment effect. On the other hand, the dashed line in Figure

2

makes clear that one has

to be careful

in

drawing conclusions from visual inspection

of

mf-trends: also without irreversible drug effects the predicted trend shows an, albeit insufficient, decrease

in

the mf-count at the 12- month follow-up surveys (the peaks

of

the curves). This predicted decrease

is

exclusively due to the reduced transmission

of

the parasite as

a

consequence

of

ivermectin treatment and (partial) vector control [17].

Conclusive biological evidence

of

irreversible effects

of

ivermectin was obtained from patients who had received

four to

twelve doses at intervals

of two

weeks

to six

months. More dead or moribund female parasites were found

in

these patients than controls who received no

or

a single treatment [5-7,9,10]. ^Excess worm mortalities

of

25

to

33% were found

in

patients who received eight

to

eleven 3-monthly doses

[9].

^These percentages are about

the

same as

the

irreversible effect

we

found

per

_treatment round.

This

suggests that

this

effect

is

predominantly due

to

a

productivity reduction

for

all female worms and to a much lesser extent due to total fecundity ^loss

or

death. Analogous

to

our results, six months after the last dose (the longest follow-up

in

^most

studies) most female worms had not resumed normal embryogenesis and the percentage

of

viable worms was markedly reduced. Recent investigations suggest that recovery to

full

productivity after this short follow-up period is unlikely or

will

at least take more than two years [12].

Our findings partially rely on the interpretation of entomological data (counts

of

flies and their parasite load). We have taken into account the vector control schedule and the resulting trend in the transmission potential

of

the

flies [7]. ^In

calculating this transmission potential we assumed that the parasite larvae

in flies

originate

from

inhabitants

of

Asubende and

will

again be trans- mitted to them. Such an assumption would not be valid in areas with migration

of

flies. However, Asubende is an isolated focus with a local transmission

[3],

^{and hence ideal to} test the impact

of

ivermectin.

The data on mf-counts enabled us

to

test hypotheses on the effect

of

ivermectin, but do not

allow to draw

inferences

on the exact biological

mechanisms

involved.

Unavoidably, simplifications had

to

be made

in

the model. We

will briefly

discuss

two

simplifications which may be important

for

the interpretation

of our

results.

Firstly,

we disregarded any effect on the adult male worms.

In

some studies

a

significant reduction

of

the number

of

male worms were found

[7,9],

^while

in

others this could not be concluded [5,6,10]. ^Although lower counts

of

^male

l0

wonns may be due

to their ability to

leave nodules

[32], it

^may,

at

least temporarily, lead to reduced mating chances. Hence,

the

transient and irreversible reduction

in

mf-production we found could

partly be

attributed

to

absence

or

reduced

viability of

male

worns.

Secondly, we assume no prophylactic effect

of

ivermectin. Such drug induced protection against (super)infection would lead

to a lower

transmission than expected on the basis

of

fly-infection data.

In

experi- mentally infected chimpanzees

a

^partial prophylactic effect was found

on

L3Jarvae,

but not

on later stages

[33].

^{Since the} L3-stage lasts

for

only 3

to 4

days and ivermectin

is

rapidly cleared from the body, no important prophylactic effects are to be expected.

We have tested several other assumptions and extensions

of

the model,

like

effect-variability between the worms

in

one patient, genetic predisposition

of

treatment effect, etc. None

of

them affected

our

conclusion

on the

transient and irreversible nature

of

treatment effect

or led to

a

significantly different quantification.

It

^is, however, important

to

stress that

our

conclusions have been based on the results

of

annual treatment using a dose

of

l3D-ZDpglkg body weight. Changes in treatment frequencies or doses may lead to other effects per treatment.

Our conclusions have important implications

for

the public health impact

of

strategies based

on

annual ivermectin treatment, which is the currently recommended regimen.

In

earlier studies we emphasized the potential

of

the drug

for

reducing the burden

of

blindness [20,34]. ^However, due to lack

of

sufficient follow-up data at that time, an irreversible effect of treatment on the adult worms

could not

demonstrated.

This

was

the

main reason

for

doubts about

the

potential

of

ivermectin

for

transmission control and thus

for

our cautiousness

in

designating

it

as the successor

of

vector

control. Our new

results certainly

merit a

reconsideration

of this point of view. It

should,

for

example, be noted that when each treatment leads

to

an over-all irreversible reduction of the fecundity

of

worms with30Vo, after five treatments this

will

be more than 80% on average

for

those female worms that survive the whole treatment period. Translating

this

figure

to

the impact

of

a long period

(>

10)

of

annual treatment is not straightforward.

Two

complications are that

not

everybody

will

be treated

(a

coverage

of

65-70% would be excellent

in

routine health care) and that transmission

will

continue (albeit

on a lower

level)

so

that new infections

will

occur. Preliminary predictions

with

ONCHOSIM indicate that, although the impact

of

^long term ivermectin strategies is much more pronounced than we concluded earlier, the parasite

will

not be eradicated

within a

period

of

15 years

of

annual treatment

in

an endemic area.

We will

start shortly

with

extensively analyzing the possibilities

of

applying annual ivermectin treatment

to

stop vector control earlier than

originally

planned

in

some areas

of the

OCP.

We will

also further explore the potential

of

the drug

to

control recrudescence

of

infection

if it

occurs after stopping

vector control.

Finally,

the promising

resuls of our

study

will

stimulate the assessment

of

the impact of higher doses on the viability of adult parasites.

Acknowledgement

We would like

to

thank

Dr. E.M.

Samba, Director OCP, and the staff

of

OCP and the National Oncho Team in Ghana for their support of our work.

T2

Annex

If m

denotes

the

mean fraction fecundity loss and

yii the

effectiveness

of

treatment round

! G:1,..,5) ⁱⁿ

^person

j,

then a fraction v;3m

of

the worms

in

^person

j will

permanently cease mf- production immediately after treatment

!. ^vij

is a random variable, which

for

each treatment

!

^and

each person

j is

generated

from

a gamma probability distribution

with

mean

1.0

and a standard deviation equivalent

to

the effect-variability.

For

those female wonns

in

person

j

which

do

not loose fecundity after treatment

!

(a fraction

1:,:d

the mf-productivity

I1r of

^{each worm}

k

^{at time}

I

after treatment is described by:

r,,r(t) = ^r,l.dortr -vfl

= ,,|*(r)r(t -v,d)

for t<vrrTr

for t>v,rTr

"(

)"

⁽¹⁾

t

vrrTr

In this

expression

dg1 is the

mf-productivity

of worm k without

treatment.

This

basic mf- productivity depends on the age and the mating history of the worm. The parameter

d

is the ^mean irreversible productivity reduction,

Tr

is the mean duration

of

the recover), period, _{and S}

is

the shape

of the

recovery.

If _s>1,

then

the

increase

in the

mf-productivity

is initially slow

^and

accelerates by the end of the recovery period.

If g:1,

then this ^increase is linear.

In

the hypothetical case that the random variable ^v13 takes such high values that ^v1i4q and/or v1,d

exceed 1 the products are truncated

to

1. Given the estimates of the effect-variability (around 0.5;

Table 1) these situations are however highly unlikely to occur.

In

case

of

repeated treatment G> 1),

in

the model

it is

not allowed that an ineffective treatment

(which implies a short

recovery

period)

accelerates

the

recovery

of a ^previous

(effective) treatment.

In

case

of

total treatment failure (3Vo

of

treated persons)

v;, is

zero and

no mf

are

killed. It is

assumed that

mf will in

principle be detectable

in the skin

immediately after their release

from the worm. No

provision

is

made

for a

delay due

to

dispersal

in the

body and penetration

of

skin tissues.

Mf

are assumed to have a fixed lifespan CIm).

In

this simple concept,

if

the mf-production rate

of

the worms

in

a person stabilises at time

!,

then the mf-density

in

the skin stabilises at time

t*Tm.

References

1.

^Awadzi

^K,

^Dadzie

^KY,

Schulz-Key

H,

Haddock DRW, Gilles

HM, Aziz MA.

The chemo- therapy

of

onchocerciasis

X. An

assessment

of

four single dose treatment regimes

of

MK-933 (ivermectin) in human onchocerciasis. Ann Trop Med Parasitol 1985;79:63-78.

2.

^Greene

^BM,

^Taylor

^HR,

^Cupp

^EW,

^et

^al.

Comparison

of

ivermectin and diethylcarbamazine in the treatment of onchocerciasis.

N EnglJ

Med 1985;313:133-8.

3.

^Larivibre

^M,

^Vingtain

^{P, Aziz MA,}

^et

^al.

Double-blind study

of

ivermectin and diethylcar- bamazine in African onchocerciasis patients with ocular involvement. Lancet 1985;2:174-7.

4.

Schulz-Key

H,

Klager

S,

Awadzi

K, Diallo S,

Greene

BM,

Larivibre

M, Aziz MA.

Treat- ment

of

human onchocerciasis: the efficacy

of

ivermectin on the parasite.

Trop

Med Parasit 1985;36 Suppl II:20.

5.

^Duke

^BOL,

Zea-Flores

G,

Mufloz

B.

The embryogenesis

of

Onchocerca volvulus over the first year after a single dose

of

ivermectin. Trop Med Parasitol 199l:42:175-80.

6.

^Duke

^BOL,

Zea-Flores

G,

Castro

J,

Cupp

EW,

Muffoz

B.

Comparison

of the

effects

of

a

single dose and

four

six-monthly doses

of

ivermectin

on

adult Onchocerca volvulus.

Am

^J

Trop Med

Hyg

199l;45:132-7.

7.

Duke

BOL,

Zea-Flores

G,

Castro

J,

Cupp

EW,

Muffoz

B. Effecs of

multiple monthly doses

of

ivermectin on adult Onchocerca volvulus. Am J Trop Med

Hyg

1990;43:65744.

8.

^Duke

BOL,

Pacqud

MC,

Mufioz

B,

Greene

BM,

^Taylor

HR. Viability of

adult Onchocerca

volwlus

after six 2-weekly doses

of

ivermectin. Bull Wld Hlth Org 199l;69:163-8.

9.

Duke

BOL,

Zea Flores

G,

Castro

J,

Cupp

EW, MufrozB.

Effects

of

three-month doses

of

ivermectin on adult Onchocerca volvulus. Am J Trop Med

Hyg

1992;46:189-94.

10. Chavasse

DC,

Post

RI, Lemoh PA,

Whitworth

JAG. The effect of

repeated doses

of

ivermectin

on adult female

Onchocerca

volvulus in

Sierra

Leone. Trop Med

Parasitol

t4

1992;43:256-262

11. Chavasse

DC,

Post

RI,

Davies

JB,

Whitworth

JAG.

Absence

of

sperm

from the

seminal receptacle

of

female Onchocerca volvulus following multiple doses

of

ivermectin. Trop Med Parasitol 1993;44:155-8.

12.

Kllger

S, Whitworth JAG, Post

RI,

Chavasse

DC,

Downham

MD.

How long do the effects

of

ivermectin on adult Onchocerca volvulus persist. Trop Med Parsitol 1993;44:305-10.

13. Remme

J, Baker RHA, De Sole G, et al. A

^community

trial of

ivermectin

in

^the

onchocerciasis focus

of

Asubende, Ghana.

I.

^Effect

on

the microfilarial reservoir and the transmission

of

Onchocerca volvulus. Trop Med Parasitol 1989;40:367-74.

14.

World Health

Organization

Expert

Committee

on

onchocerciasis

control. First

report Technical Report Series, in press.

15. De Sole G, Awadzi

K,

Remme J, et al.

A

community trial

of

ivermectin in the onchocerciasis focus of Asubende, Ghana.

II.

Adverse reactions. Trop Med Parasitol 1989;40:375-82.

16. Dadzie

KY,

Remme

J, De

Sole

G.

Changes

in

ocular onchocerciasis after

two

rounds

of

community-based ivermectin treatment in a holo-endemic onchocerciasis focus. Trans Roy Soc Trop Med

Hyg

1991;85:267-71.

17.

Alley

ES, Plaisier AP, Boatin

BA,

Dadzie

KY,

Remme

l,

Zerbo

G,

Samba

EM.

The impact

of five

years

of

annual ivermectin treatment on skin microfilarial loads

in

the onchocerciasis focus of Asubende, Ghana. Trans Roy Soc Trop Med Hyg 1994; in ^press

18. Remme J, Ba O, Dadzie

KY,

Karam

M. A

force-of-infection model for onchocerciasis and its application

in

the epidemiological evaluation

of

the Onchocerciasis Control Programme in the Volta River basin area. Bull Wld Hlth Org 1986;64:667-81.

19. Plaisier

AP, Van

Oortmarssen

GJ,

Habbema

JDF,

Remme

J, Alley ES.

ONCHOSIM: a

model and computer simulation program

for

the transmission and control

of

onchocerciasis.

Comp Meth Prog Biomed 199O;31:43-56.

20.

Habbema

JDF, Alley

ES, Plaisier

AP,

Van Oortmarssen GJ, Remme

JHF.

Epidemiological modelling

for

onchocerciasis control. Parasitol Today 1992;8:99-103.

21.

Habbema

JDF, Van

Oortmarssen GJ, Plaisier

AP.

The ONCHOSIM model and

its

use in decision support

for

river blindness control.

In:

Epidemic models: their structure and relation to data. Cambridge University Press; in ^press.

22.

Plaisier

AP,

Van Oortrnarssen GJ, Remme

J,

^Habbema

JDF. The

reproductive lifespan

of

Onchocerca

volwlus

in West African ^savanna. Acta Trop l99L;48:271-84.

23. Nelder JA, Mead R. A simplex

method

of function minimization.

Computer Journal 1965;7:308-12.

24. De

Sole

G,

Remme

J,

^Awadzi

K, et al.

Adverse reactions

after

large-scale treatment

of

onchocerciasis

with

ivermectin: combined results from eight community

trials. Bull Wld

^Hlth Org 1989;67:707-19.

25. Duke BOL. The

effects

of

drugs

on

Onchocerca

volvulus I.

^Methods

of

assessment, population dynamics of the parasite and the effects of diethylcarbamazine.

Bull Wld Hlth

Org

1968;39:137-46.

26.

Albiez

EI,

Walter G, Kaiser

A,

^Ranque P, Newland HS, White

AT,

Greene

BM,

Taylor HR, Btittner

DW.

Histological examination

of

onchocercomata after therapy

with

ivermectin. Trop Med Parasit 1988;39:93-9.

27

.

^Awadzi

^K,

^Dadzie

^KY,

Schulz-Key

H,

Gilles

HM,

Fulford

N, Aziz MA.

The chemotherapy

of

onchocerciasis

XI. A

double-blind comparative snrdy

of

ivermectin, diethylcarbamazine,

and placebo in ^human

onchocerciasis

in Northern Ghana. Ann Trop Med

Parasit 1,986;80:43342.

28. Taylor HR,

Murphy

RP,

Newland

HS, White AT, D'Anna SA,

Keyvan

Larijani E,

Aziz

MA.

Cupp

EW,

Greene

BM.

Comparison

of

the treatment

of

ocular onchocerciasis with ivermectin and diethylcarbamazine. Arch Opthalmol I 986; ¹ 04:863-7 0.

16

29.

Diallo S,

Aziz MA,

LariviDre

M,

Diallo JS, Diop-Mar

I, N'Dir O,

Badiane S, Py

D,

Schulz-

Key H,

Gaxotte

P,

Victorius

A. A

double-blind comparison

of the

effrcacy and safety

of

ivermectin and diethylcarbamazine

in

a placebo controlled study

of

Senegalese patients with onchocerciasis. Trans Roy ^Soc Trop Med

Hyg

1986;80:921-34

30.

Greene

BM,

White

AT,

Newland HS, Keyvan-Larijani

E,

Dukuly

F,

Gallin

MY, Aziz MA, Williams PN, Taylor HR.

Single dose therapy

with

ivermectin

for

onchocerciasis. Trans Assoc Amer Phys 1987;C:131-8.

31.

Schulz-Key

H,

Soboslay

PT,

Hoffrnann

WH.

Ivermectin-facilitated immunity. Parasitology Today 19921'8:152-53.

32.

Schulz-Key

H,

Karam

M.

Periodic reproduction

of

Onchocerca volvulus. Parasitology Today 1986;2:2844.

33. Taylor HR, Trpis M,

Cupp

EW,

Brotman

B,

Newland

HS,

Soboslay

PT,

Greene BM Ivermectin prophylaxis against experimental Onchocerca

volwlus

infection

in

chimpanzees Am J Trop Med

Hyg

1988;39:86-90.

34. Remme

J, De

Sole

G,

Dadzie

KY,

Alley ES, Baker

RHA,

Habbema JDF, Plaisier

AP,

Van Oortmarssen

GJ,

Samba

EM.

Large scale ivermectin distribution

and its

epidemiological consequences. Acta Leiden 1990;59: 177-91.

Table ^1: Estimates

of

^{parameter values}

for the

different hypotheses*

on the working of

ivermectin on the adult worm.

Parameter

Hypothesis

I

(only transient)

IIa

(also irreversible) IIb

productivity reduction total fecundity ^loss recovery period (months) effect-variability

(coeffi cient of variation) mfJifespan (months)

goodness-of-fit (P-value

ty'l)

357" (26%40V")

10.4 (7-16) 0.s4 (0.4-0.7)

28Vo Q2Vo-35%\

10.7 0.52 19.0

0.87

l4

0.0013 _[39]

e (4-12) 10

0.68 [11.9] 0.42

[ls.s]

Values in brackets represent the 95% confidence interval for these estimates.

A '-'

means that this parameter is not considered and thus has the value 0.

* In

Hypothesis

I

^{the drug has only} transient effects.

In

Hypothesis

IIa

treatment results

in

an irreversible productivity _reduction

in

each parasite. Under Hypothesis

IIb,

treatment causes ^a certain fraction of the parasites to loose fecundity totally.

18

Fig. 1

Frequency distributions

of

microfilarial counts

for

the pre-treatment survey and the post- treatment surveys

of

cohorts 1 (a) and

2 O).

^Dark bars represent the observations. The white bars denote the predictions

for the

assumption that treatment causes

a

^permanent productivity reduction

of

^357o (Hypothesis

IIa

of Table 1). The numbers at the horizontal il(es represent the lower boundaries

of

skin-snip count classes. The numbers in the graphs of

Fig. la

(1 to 8) correspond to those in Fig. 2.

pre-treatmenl cohort 1

o 2 4 0 i6 32 64 124256 No. ol ml ^per skin snip

prs-lroatmenl cohorl 2

4-5 months alter treatment

1 1-12 monlhs alter treatmenl

o o.5 2 I a

tr€atment round

round 1

round 2

round 3

round 4/5 2

Eo

sJ

oo a.

!

=o

so 50 40 30 20 'to o

50 40 30 20 10 o

40 30 20 10 o

40 30 20 10 o

o O5 2 .t 6 16 32 64124 o o.5 2 4 A 16 32 6112A

o o.5 2 I a

o o5 2

3

16 32 64 124

5

8

4

16 32 64 128

6

co

!J

oo

o E

=o o

s

40 30 20 10

o o.5 2 4 A 16 32 61129 o o.5 2 4 A 18 32 6412e

o 05 2 I a 16 32 64 126 7

50 40 30 20 10 o 50 40 30

10 o 2

No. ol ml per skin snip

co gJ eo e

!f o o

a o 16 32 64 12a256 24 months

arter lreatment

t9

.g

Eq

c

=

^an

L

o

o- E c;

c c

(I,

o

=

Fig.

2

Observed (dots) and predicted (ines) geometric mean skin-snip counts

of

study cohort 1.

The solid lines represent predictions ^based on the hypothesis

of

a productivity reduction

of

35Vo

(Hyp.IIa). The

dashed

line is

based

on the

hypothesis

of no

irreversible effects

(Hyp.I).

The peaks

in

the predicted trends (excluding the pre-treatment survey) have ^been connected

with

an exponential curve

$=a.e-b'*).

^{The times}

of

the

five

treatments are in- dicated below the horizontal axis

100 95

30

20

10

0

\

^'88

T1

\

^'89

\

^'90

\

^'91

\ ^'92

T2

T3

^T4

Calendar year

T5

8

20

5

Part II

Eradication of onchocerciasis infection by vector control and annual ivermectin ^treatment.

Introduction

The objective

of

the Onchocerciasis Control Programme in West

Africa

(OCP) is

to

eliminate onchocerciasis as a public health problem in the area covered by the progralnme and to ensure that no recrudescence

of

the infection ^and the disease

will

occur.

Initially,

the only measure

of

control was aerial larviciding

of

the

river

basins, the breeding places

of

Simulium damnosum ssp., in order

to

eradicate the vector and block the transmission

of

Onchocercavolvulus. Since the vector control operations are extremely costly, an important question is after how many years they could

be

ceased

without

running unacceptable

risks of fatal

transmission levels when

the

blackflies return.

In

a previous study, we have applied the ONCHOSIM simulation model

to

^assess the risk

of

recrudescence after several years

of

successful larviciding. Taking into account the differences

in

pre-control endemicity

of the

disease and several

risk

factors favouring recrudescence, we concluded that 14 years should be suffrcient

to

reduce the risk

to

less than l Vo even

in

the most afflicted areas @laisier

et al.,

L99la).

This

has since been adopted :rs

a

general guideline. In developing

this

guideline,

it

was assumed

that,

given

the limited

treatment coverage and the presumed limited impact on the adult parasites, the microfilaricidal drug ivermectin

-

registred in 1987

-

would not play a significant role

in

controlling the transmission and that eradication

of

the parasite should be accomplished

by

vector control alone.

In

large parts

of

the original OCP area (where larviciding started between ¹⁹⁷⁵ and 1977) OCP has discontinued large scale larviciding and replaced

it by a

programme

of

entomological and epidemiological surveillance

in

order to detect unforflrnate occurrences of recrudescence

of

infection.

For two reasons, the initially adopted guideline has to be reconsidered

for

the extension arqm

of

OCP where vector control started later as

well

as

the

areas where

vector

control was ^less sucessful during the

first

years. The first reason is that financial resources become more and more limited, pressing OCP to speed up the ^process

of

devolution, i.e. the transfer

of

responsibilities to the participating countries. The second - forfirnate

-

reason is the growing evidence that ivermectin

is

not only

a very

effective microfilaricide,

but

also has considerable

effecs on

the

viability of

female worms @uke

et al.,

^{1992; Kager et}

al.,

1993).

In

a recent model-based analysis

of

^data

from a

community

trial of

annual treatments

in

the Asubende area (Ghana)

we

have found that,

22

\l

following each treatment, female worms are considerably delayed

in

their mf-production and that the ultimate fecundity

level

stabilizes around 70%

of

pre-treatment @laisier

et al.,

submitted).

Such strong effects

put a

new

light on the

potential

of

community treatment

for

controlling transmission and, hence,

for

shortening the required duration of vector control.

This potential

of

the drug is the subject

of

the present paper. We

will

use the ONCHOSIM simulation model

to

investigate the extent to which annual ivermectin treatment can lead

to

earlier cessation

of

vector control. We

will

show how this depends on the attainable treatment ^coverage, the pre-control endemicity in the area, alternative assumptions on the effect

of

ivermectin on adult worms, and the timing of the start of ivermectin treatment.

Methods

Basic assumptions

Vector control operations are assumed

to

be 100% effective,

i.e. to

reduce the biting rate to zero. Flies are assumed to return immediately after cessation

of

larviciding, giving rise to a biting rate equal

to

the pre-control level.

With

respect

to

the effect

of

ivermectin treatment we use the following assumptions: following treatment (1)

all

microfilariae are eliminated,

Q)

female worms recover

from total

loss

of

^fecundity

during,l0.to..11

months and ⁽³⁾ reach

a

new stable mf- production level

rvhich is

permanently 35Vo

lower

than before tr.eatlUgg! (Plaisier

et al.,

sub- mitted). Both the period needed

to

recover and the permanent impact

of

the drug

vary

between persons and between treatments (var. coeff.

a;|!L

^An alternative assumption we test is that the irreversible reduction

of

fecundity is not 35% but only 25Vo per treatment. This lower ^percentage can be justified

from

the confidence interval

for

the estimate

of

this parameter. The coverage

of

treatment (Vo

of

persons getting the drug)

is

one

of

the variables

in

the present analysis. This coverage

is

not equivalent

to

the probability

to

be treated

for

each individual

in

the population:

depending on age and sex and some persons have a higher chance, others a lower.

For

example, children

below 5 are not

treated. Women

in the fertile

ages have

a lower probability

since pregnancy and lactation are exclusion criteria. Furthermore, persons can

differ

considerably in

their

compliance

with

treatment. The age- and sex-specific variation

in

treatment coverage has been taken from the results

of

the Asubende-trial (Alley et

al.,

in press).

In

the Annex we explain

how, ^given a

mean population-coverage,

for

each individual

the probability to be

treated is calculated.

The

assumptions

have been

incorporated

into the

stochastic microsimulation model ONCHOSIM

which

has subsequently been used

to

simulate

the

control strategies.

A

complete description of the model and parameter quantification is provided in Habbema et

al.

(in press). We simulate human populations

of

around 300 persons (natural growth

of

the population

is

compen- sated

by

migration) which show

a

pre-control endemicity level similar

to

the villages Tiercoura and Folonzo (both Burkina Faso)

with a CMFLI of 70

and

30 mf per

skin-snip respectively

@laisier et

al.,

1991b). Observations of pre-control

fly

biting rates are lacking

for

this area. Using observations

in

the Pru-river, close

to

the highly endemic Asubende region

in

Ghana (Remme et

d.,

^{1989) we} estimate the Annual Biting Rate

within

Tiercoura

at27,

(for adult men) and

within

Folonzo

at

I The maximum

$osrre ^to

^fly-bites

is, in

both villages, reached

at the

age

of 15

years. Women

are, on

average, 30% less exposed than

men.

The variation coefficient

of

bites/person

within

a specific age and sex group

is

estimated at 0.39 for Tiercoura and 0.54

for

Folonzo. Since we have previously found that the (age- and sex-indepen- dent) exposure heterogeneity is an important risk factor

for

recrudescence, we

will

also simulate a

'Tiercoura-like' village (called

Tiercoura*)

with an exposure variation coefficient of 0.58.

Simulation of control strategies

A

control strategy

is

completely described

by the

number

of

years

of

(l00Vo successful) vector control

(v), the

number

of

annual ivermectin treatments

(i),

the treatment coverage ^(Vo treated, c) assuming that this

will

be constant

for

the whole period, and the time-lag between the start

of

vector control and the start

of

ivermectin treatment

(d),

assuming that treatment always starts later. We have tested many combinations

of y

_(range:

₀ to

15 years),

i

^{(range: 0-30), c}

(range: 35-75%), and,

d

^(0,

8,

and 16 years). The result

of

each simulated strategy is summarized as 'recrudescence'

(l) or 'no

recrudescence'

(0).

Recrudescence

is

defined as

the

occurence

of

increasing mf-loads after total withdrawal vector control, ivermectin or both

Statistical analysis of simulatton results

The purpose

of

the analysis is

to

estimate the recrudescence risk as a function

of

the strategy- variables. Previously @laisier et

al., l99la)

we have achieved this

by

performing many simula- tions

for

one particular strategy (number

of

years vector control) and counting

the

number

of

simulations resulting

in

recrudescence.

By

choosing an appropriate range

of

durations

of

vector control, those durations where the

risk

approaches zero (e.g. 0.01) could be identified. However,

I

_Community Microfilarial Load; i.e. the geometric mean mf-load in adults 24

-tr.9^?lT:€I!i

logistic regress t----\l

c, and d)[

+

with four

strategy-variables involved

this

approach

is not

suitable: the range

of

vector control- durations where

the risk

changes

from - ¹ to - 0 ^is

^different

^for

^each ivermectin treatment strategy.

In

the present analysis we have applied another method which comprises the following two steps: (1)

for

a large number

of

ivermectin treatment strategies, an iterative procedure is used

to flnd

the duration

of

vector control where the

risk

changes most

rapidly; Q)

the technique

of

ion is applied to estimate the risk

for

^each ftrategy (which is a combination

of v, i,

An

example

of

the iterative procedure is given in

Fig.

1.

In

this example we use the parame-

ters

representative

for

Tiercoura.

The

ivermectin strategy consists

of 10

years

of

treatment, starting

in the

same ye:tr as vector control and covering 65Vo

of the

population.

The

initial duration

of

vector control

is

10 years which results

in

eradication

of the

parasite.

The

initial iteration step is 4 years and hence the next attempt is 6 years vector control. This is (far too) short and results in recrudescence. Now, the iteration step is halved and 8 years vector control is tested.

This is still too short and again

try

¹⁰ years is tested, again resulting

in

eradication. Since we ^are especially interested

in low

recrudescence risks

(e.g.

1%) we take one-third

of

the iteration step when

a "1"

(recrudescence)

is

followed

by a "0"

(eradication). Hence, the new tested value is

9.33 years (nine years and

four

months). Here recrudescence is encountered and we subsequently test

9.67

years (halving

the

interval).

A total of

10 iteration steps

is

done

in this way.

The smallest interval allowed

is

one month. Note that 9.67 years

is

tested three times, successively resulting

in "0", "1",

_and

"0".

Apparently, around this value the

risk is

changing most rapidly.

All

iteration-steps

for all

tested combinations

are

accumulated

in a

^data-file

for use in

the regression analysis. Tentative regression results are used

to

repeat

the

procedure using other starting values and other ^(as a rule smaller) initial iteration intervals.

We have used SPSS

to

calculate logistic regression equations

for

the

risk of

recrudescence

(ref.).

Separate equations are calculated

for

the different area-conditions: Tiercoura,

Tiercoura*,

and Folonzo, as

well

as

for

the different values

for

the delay between the start

of

the two control methods

(d=0, 8, or

16

yqrs;

only

for

Tiercoura) and the effectiveness

of

ivermectin (35% vs.

25% permanent effect; only

for

Tiercoura). The independent variables

of

the regression equations are the duration

of

vector control (v), the number

of

annual treatments

(i),

the treatment coverage

(c),

and

linear,

quadratic and cubic combinations

of v, i

^and

c.

Since neither

i ^{nor c}

^{has a}

meaning

on

its own, they are always combined

in

the regression equations.

In

the procedure for estimating regression coeffrcients we have used a combination

of

backward and forward selection.

Each procedure

is

started

with

the strategy variables

(v

and

i. c)

and

their

linear and ^quadratic combinations (interaction terms,

e.g. i2.c.l).

Coefficients

that are not

significant (P=0.05,

according

to

the Wald-statistic;

ref.)

are eliminated while the significant coefficienS

for

the cubic terms

(e.g. r/;

anA interaction terms

with a

cubic component are included

(e.g. i'C'rl;. ⁿⁿ

example

of

estimated regression coefficients is provided in Table 1. Form the resulting regression equations the risk

of

recrudescence

for

a given

v, i,

^and c can be easily calculated. However, they are

too

complicated

to

calculate the duration

of

vector control which corresponds

with a

given recrudescence

risk

^(given

the

values

of i

^and

c). This is

done iteratively, using

the

routine available in the Borland Quattro-Pro spreadsheet progr:Im.

Results

Fig. 2

shows the trend

in

the recrudescence

risk for

several combinations

of

the number

of

annual ivermectin treatments and the duration

of

vector control

in

a

Tiercouralike

village.

It

^is

assumed that

the

average treatment coverage

is

65% and that both control methods start

at

the same moment.

The

lines

in

the figure represent

'iso-risk'

lines, connecting those strategies that result

in

equal

risks

^(0.01,

0.1, 0.5,

and 0.99). Below (less vector control) and

left of

the line (less annual treatments) the

risk

is higher than indicated, otherwise

it

is lower.

In

the absence

of

ivermectin treatment (points on the Y-axis) approximately 13 years

of

vector control are required

to

reduce

the

recrudescence

risk to

^1%.

This

duration reduces

to

11 years when

ten

years

of

annual ivermectin treatment

is

added. With the same ivermectin strategy the

risk

increases

to

0.1 when vector control is stopped already after 10 years. Recrudescence is certain

(risk >

0.99) with only less than

6.5

years

of

vector control. The iso-risk lines diverge considerably ^as the number

of

treatments increase.

With

16 treatments risks

of

^less than 0.99 are achieved

in

the absence

of

vector control, while

still9.3

^years of vector control are needed to reduce the risk to 0.01.

The effect

of

alternative coveragelevels is shown

in Fig.

3a.

In

this figure only the 0.01 iso-

risk

lines are shown. Especially

for

longer periods

of

treatment the impact

of

higher

or

lower coverages

is

considerably. When treatment is continued

for

15

yqlrs,

then each 10% decrease in coverage corresponds

with

approximately

9

months more vector control

to

maintain

a

recrudes- cence

risk of 0.01; with l0

years

of

treatment the gain

or

loss

is only 2-4

months.

Fig.

^3b

demonstrates

that the

effectiveness

of

control strategies

is highly

dependent

on the

pre-control endemicity

of

the area.

With

a treatment coverage

of

65Vo,

in

a village

like

Folonzo, 20 years

of

annual treatment are sufficient to eradicate the parasite without the help

of

vector control. Shorter periods

of

treatment

(10 - 15

years)

allow

considerable reductions

in the

duration

of

vector control.

26

The predicted implications

of a

delay between the start

of

vector control and

the

start

of

annual treatment is shown

in

Fig.4. The results apply

to

Tiercoura and a coverage level

of

65%.

Up to 20

years

of

^annual treatment,

with a

delay

of 8

years less vector control

is

required to reduce the risk to 0.01 than with an equal start. For example, with a period of ten ^years

of

annual treatment,

[0

years

of

vector control are sufficient; this was almost 11 years when both methods started synchronous. For periods

of

20 years

of

treatment

or

more, a delay

of

8 years is slightly less favourable

in

terms

of

^reducing larviciding. Such long durations correspond

with

less than 8 years

of

larviciding, and this implias a short period without any ^means

of

control (treatment starts after cessation

of

larviciding). This

is

the major problem

with

a long delay

like

16 years. Now treatment always starts when larviciding has stopped, which implies that

in

many cases ivermectin treatment is used

for

the control instead of the prevention of recrudescence.

A

summary

of the

results

is

^provided

in

Table

2. For

each

of the

circumstances and four different coverage levels, the required duration

of

vector control which reduces the recrudescence risk

to l% ue

shown

for four

different durations

of

annual treatment

(5, 10,

15, and 20 years).

The numbers in the table are obtained from the regression equations.

Table 1.

Ivermectin treatment

ixc ix*

ixc

i2xc i3xc

Estimates

of the

coefficients

for the

variables

(row x

^column)

of the

logistic regression equation

for

the recrudescence risk Tiercoura

(d = ^0).

^Prior

^to

^estima-

tion, the variables are transformed as follows:

i =

^no.

of

ivermectin treatments

+

10;

v =

^no.

^of

^{years vector control}

+

10;

c =

coverage (Vo)

+

50. The resulting equation

has the form: tn(r/1-r)=fi.6 + 22.7.v - 28.3.i + ^5.71.i.c

^-

25.1.i. c,v +

..etc., with

r

being the recrudescence risk.

Vector control

v

f

22.71

i

n.s 12.g*

5.71

-t2.5

3.86 n.s.

n.s.

-25.1$

4.47 n.s.

4.86 n.s.

-28.3 13.6

n.s -1.79 -0.576

n.s.+

n.s n.s n.s n.s n.s

* the constant of the equation

t

coeffrcient

for

covariable v

+ not significant

$ coefficient

for

covariable

i.

c. v (interaction term)

28