of a simulation model forOnchocerciasis

D,evelopnent

of a simulation model for

Onchocerciasis transrnission and control

in

O.C.P.

Report 2nd ph.="

Anton Plaisier Gerrit ^van Oortmarssen

Dik Habbera

Ilept.

of

Public Ee-al-th and Social Hedicine Erasmus University Rotterdam

P.O. Box 1738 3000 DR Rotterdam, Ttre Netherlands

tel.

010

-

4634092

January 1987

Ttre model-development

is

carried out on

the basis of

^a

Technical Service Agreemnt

(A),

number 08/18f/85, provided

by the t{orld Health Organisation, on behalf of

^the

Onchocerci-asis Control Progranrne (OCp).

1

COTiITBTTS

I

The model VECPAR

II

Report

on

^rapplied modelling and

itrs utilisation

in the O.C.P. ^I

fII

Proposal

for

a simple transmission model

IV Exarnple

of

input and output

of a simple

transmission model

\tBcPA8l.0

A coqruter prog,rao

for

sinrlatfDs the

llfe-cycles of Stmuliuu dr-osro !.1. end

^Onchocerca

volrnrlus, and

tbeir Lntcractlo.

Antoo

Pleist.r Gerrlt

van Oortarrsen

DIL Eabbera

Teclrrlcal

relnrt (draft)

^prepered

for

^IiEO/OGP

Ilept.

of

Publlc Eealtb and Soclal ]lediclne

Erasrnus

llnlverslty

Rotterda

P.Or Box 1738 3000 DR Botterdqil, The Netherlands

tel.

⁰¹⁰

-

^4634092

Septenber 1986

The developnent

of

the VECPAR prograr ras carried

out

^on

the basis of

a Techninal Serul.ce Agreeuent

(A),

ntuber

08/f8fl85,

provided by the ltorld

Eealth

Organisatlon, on

behalf

of

the Onchocerclasl,s Control Programe ^(OCp).

I

Table

of

contents

1.

Introduction.

Model-descript ion

2.I Summary..

_:

2.2

Detailed description

of

the model

?.2.1

The larvae submodel ^.

2.2.2

The fly-larvae-interaction

3.

Discussion items Users guide

4.1

Starting a session

4.2

Using VECPAR 2

2

3

submodel

4 6

9

4

.12 .

¹³

Appendix 1: Mathematical summary

(draft)

22

appendix

2:

Report on the 4th meeting on applied modelling

in

the

OCP

²⁵

I

Introductlon

Thls

report describes VECPAR1.0, the

first

test-version

of

the model for the analysis

of

vector-parasite interaction

in

river-blindness transmission.

The purpose

of

the document

is to facilitate

testing

of

the model,

and

to

raise

discussion regarding some aspects

of

the model

that

need further improvement. The VECPAR model describes one part

of

the transmlssion cycle

of river

blindness (onchocerciasis). Another model, HUMPAR1.0, describes the human-parasite aspects

of

the disease, and was developed by our

group

ln 1985.

This

model was formerly called ONCHOSIM, we prefer

to reserve

this

name

for

the whole package

of

the computer programs under development. The

aim of these

models

is twofold: first

they should be used as

an aid

in interpretation

of

the data collected by the Onchocerciasis Control Programme

(OCp) conducted

in

Western

Africa;

secondly the two models

are

detailed Precursors

of

corresponding building blocks

of

a

ful1

transmission model of Onchocerciasis

that will

be developed

in

the forthcoming

time. It is

hoped

that

the

full

transmission model

will

^be an important

aid in activities

for the OCP,

e.g.

with respect

to

planning and long-term predictions (migration, recrudescence, devolution) and

in

choosing between

different

policy options.

A

number

of

meetings have been held on the subject

of

modelling

and its

application

in

analysis and planninguin OCP. The most relevant meeting for

the

^{present VECPAR} model was the

4"",

which took place

at

our

institute

in Rotterdam

(dec.

_{16-18, 1985) and}

in

^which

staff

members

of

OCP/VCU, OCp/EpI

and

OCP/STAT

participated. In

the report

of this

meeting (see Appendix 2)

the

provisional

list of

contents

of

the model can be found

that

was agreed

upon by the

participants.

This

list,

and an outline

of the

model, were

discussed

further at

a

visit of dr.

^Remme

to

Rotterdam

(april

18

and

2L,

1986).

The present version

of

the model has been developed along

the

lines

of these

meetings.

The

aspects

that

are

not yet (or onry partially)

implemented are

listed in

the discussion section.

The VECPAR model describes the part

of

the transmission cycle

that

starts with intake

of microfilariae

by Simulium damnosum, and ends when infective

larvae are

released during a subsequent bloodmeal.

fn the

model, two

processes interact:

1.

The development

of

larvae

in

the

fly,

through stages LL, Lz and L3, to the

infective

stage.

2. The life-history of

mature

fries

including

biting

behaviour.

The model does not describe the dynanics

of

the

fly-population,

which would

involve modelling

of

the breeding behaviour.

The output of

the model

is

computed and displayed

in

such a way

that it

can be compared

directly

with the results

of

the OCP/VCU catching

sites.

In

addition, the

model can display graphs and tables

of

the

life events

for

flies

and

larvae.

The

latter

output can be useful

in

the formulation

of

^a

concise vector-parasite module

in

the

fuII

transmission model.

Section 2 starts with a

global overview

of the

model

and of

the assumptions made

for

the 2 processes.

Next,

a detailed (more technical) description

is

given

of

the two processes

separately. In

the discussion of

section 4,

aspects

of

the model

that

could be incorporated

or

improved are

presented. _The most,important

point is

probably migration

of flies, that

is not

yet

implemented

in

the present version. An outline

for

an implementation

of

migration

is

presented. _A users guide

for

the ^VECPAR model

is

^presented

in

section 3 and includes technical points regarding the simulation and the performance

of

the model.

In

Appendix 1 a mathematical formulation

of

the model

is

^given.

2

2.

^l{odel descrlptlon

2.1 Sumary

The model

is

confined

to

the vectorial part

of

the transmission,

i.e.

from

intake of

microfilariae from a hurnan host

until

the

release of

infective larvae

to

a human host

at

a subsequent bloodmeal. The goal

of

the model is

to

simulate a

situation similar to

the

field-situation

during a VCU-catching

session; that is:

a

fly

population with a certain

distribution

with respect

to fly-ager

parous

rate

and

larvae-load. It is

assumed

that the fly-

population

is in

an equilibrium

situation, i.e. that

the age-distribution is constant over

time.

Under

this

assumption, the age-distribution

of

the

fly-

population

is directly

related

to

the

life-table.

Consequently,

for

the

equilibrium

situation,

the momentary

situation is

equivalent

to

the weighted

life-events of

a specific cohort

of flies that is

followed

from

maturation

until

death (see

figure below).

This equivalence

is utilized in the

mod,el

and all

results are extracted from the simulation

of

the course

of life

of such a cohort.

fly-

age

4-

+

time catching -

sesston

figuret

'+'denotes ^death

of

the

flies.

For the sake

of simplicity it

assumed

that all flies

die on the same age

1S

In the

model, the

fate of

the

fly-cohort is

determined

by the

following

processes !

1.

Intake of

larvae from the human

host,

possibly followed by death

of

the vector.

2

3

Release of infective

larvae'

during successive

sugar- and bloodmeals.

Development

of the

larvae through intermediate stages

to

the

infective

stage.

Ageing and mortality

of

the

flles.

Migration

of flies

^(not

yet

implemented

in this

version).

Key-variables

in

the model

are:

the length

of

the bloodmeal-intervals and

the possible durations of

the

Iarval

stages

(Ll, L2, L3(B) and

L3(H)-

infective). Other

variables

are:

the natural

fly-mortality, the

larvae- intake by the

flies

and the consequent excess

fly-rnortality, the

mortality

of the larvae in

the

different stages,

and the

proportion of

infective larvae

that is

released during sugar- and blood-meaIs.

A number

of

simplifications have been made

in

the model.

First, it

is

assumed

that larvae

ingested more than two bloodmeals

ago can all

^be considered

as

^I

infectiver

regardless

of

the age

of these larvae. As

^a

consequence,

no provision is

made (thus

far) for

the existence

of

^(L3B)

larvae that

stay

in

the body

of

the

fly

but

never

become

infective.

The second

simplification

concerns the

relation

between human microfilariae-load

and intake

of microfilaria

followed by passage

of

the gut-walI, which

is

not

yet

included

in

the current version

of

the model.

Instead it is -

for

simplicity -

assumed

that

an invariable tintaker

of

Ll-larvae can act

as

^a shortcut.

Finally,

the ^process

of

migration

of flies,

which undoubtely

is

^of

major

importance,

awaits

inclusion

into

the model. The way

we think

to implement

this

process

is

^presented as an item

of

discussion

in this

report.

The output of

the model consists

of

the

distribution of

the

biting fly-

population

over the

number

of

inhabitant larvae

of all types, and

the

distribution of

the number

of

larvae released

at

a bloodmeal. Part

of

the

output is in a

format

that

enables

direct

comparisons

with the

^VCU- tabulations.

2.2 bXaTled description

of

the nodel

2.2.L The larvae-subnnodel

In

the larvae submodel, the input-data on the

life-history of

the larvae are transformed

into

a reference table

that

gives,

for

any day since intake, the status

of

the

larvae.

This table

will

be consulted

during

calculations

with the fly-larvae

submodel. Four developmental stages

of larvae

^are

distinguished: Ll-

(immediately

after

intake and passage

of

the gut wall), L2-

and L3-larvae in the

body

of the f1y (L3B) and

L3-larvae (morphologically

identical to

L3B-larvae)

in

the proboscis

(L3H). Only

the L3H-larvae

are infective and

can be transmitted

during a

sugar-

or

^a

bloodmeal.

The

submodel deals with the development

of the larvae, starting

from

4 5

4

intake until

^{the moment}

at

which a larvae becomes

infective

^{(reaches stage}

L3H).

The L3H-larvae are not treated

further in this

submodel,

but

^are

recorded

in

the

fly-larvae

interaction model. For the

first

three stages the

possible

durations ^(program equivalents:

durst!!,

dusrtl2

iespectively; in aays)

^together

with [E-p*lr6lFti""

L3-body : o.030 i 1 0.0000

1.0000 z

Results parasite-submodel (reference table) ^:

L1 LZ L3 L3-head

and durstl3body

( robdurstLl

proportion of larvae, en-

gorged at day 0, ttrat is in each of the stages at ^a

given age (ttprevaleneerr) proportion of larvae, en-

gorged at day 0, entering the fly-head at given age (Itincidencerr ₎

probdurstl2 and probdurstl3body respectively) on these durations should be

given. The life-history of

the larvae

is further

influenced

by

daily

mortality

which should be stated

for

each stage

(Ll, L2,

^L3B) separately.

Starting from these basic data

all

possible life-history-paths

of

the larvae

are calculated and

ultimately summarized

into the

reference-table. An

individual

life-history-path

ends when the larva dies

or

^when

the

L3H-stage has been reached. From

that

moment the

fate of

the

(infective)

larva

will

be

managed

by the

f1y-larvae-submodel.

An

example

of input and

output (reference

table) for this

submodel looks

like:

Input-variables parasite-submodel :

Stage Daily

mortality ^Stagedurations (days)

Probabi-

lities

L1 : o. 100 1

2i

^0.00001.0000

L2: ^0.070 I

2 3

0.0000 0.8000 0.2000

\

Age Stage

I

2 3 4 5 6 7I

0.900 0.810

0.544 0.654 0. 123

Column L1-L3

Colum L3-head 0.753

0.701 0.130

0.501 o. 116

The result

should

be

read as

follows: At day 5

13.02

of the

larvae

originally

taken

in at

day 0

is in

the L2-stage and 54.42

in the

L3B-stage.

The remainder 100-(13.0+54.4)=32.62 died during rhe

first

4

days. At

day 7

12.32

is in

the L3B-stage while 50.12

just

entered the L3H-stage. This 50.12 L3H-larvae

is further

processed

in

the f1y-larvae- submodel. This means that the 11.62 L3[-larvae on day 8 represents the

shift

from the L3B-

to

the L3H-

stage

at that

day only

1

z

3

4 5

2.2.2

lhe

fly-larvae-interactlon ^subuodel

In simulating the life-history of

^a

specific fly-cohort the initial

population consists

of

nulliparous

flies that

have the

first

bloodmeal. ^The

output for

^the equilibrium-population should be based

on sinulated

events

for all fly-ages.

Therefore,

the

number

of

days simulated should be

sufficiently

^large

to

^guarantee

that at

the end only a negligible proportion

of

the cohort

is still

alive.

It is

^assumed

that at

any given moment an individual

fly

can be completely characterized by:

The number

of

larvae engorged

at

the

last

bloodmeal ^(NLN) The time (days) since the

last

bloodmeal ^(TL)

The number

of

larvae enBorged

at

the

last

but one bloodmeal ^(NLP) The time-lag between the

last

and

last

but one bloodmeal ^(TP) The number

of

L3H-larvae ^(NLH)

In

order

to

^account

for all

^possible combinations

of

the

5

characteristics

(although,

_depending on the

input,

not

all

combinations are

possible) all calculations are

performed

in

a S-dimensional

state-matrix. In the

state matrix, the fly-frequency

is

^recorded

for

each combination (NLN,..rNLH). The

state-matrix

is

^updated

in

simulating the changes

in

the

fly-population

^day

by day. The simulation

starts with

10000 nulliparous

flies at

the

first

f1y-

age (A) that, after

emerging from pupae, the

flies

can take

a

^bloodmeal

(depends

on the values in

probcvclelenRth,

see variables

below and

discussion-items). The start-population

fits in celt

^(NLN=0, TL=A, NLP=0,

TP=A, NLH=0)

of

the state

matrix.

The

distribution

over the number

of Ll-,

L2-

and

L3(B + H)-larvae can be obtained by combining the state-matrix ^(NLN through

TP) with the

reference table

that is

produced

by the

larvae-

submodel.

Each

day

^(=each fly-age) the

flies

are assumed

to

undergo

a

number of processes resulting

in

^an

alteration of

^the frequencies

in

the state-matrix.

These processes

follow

from the input-specifications

of the

fIy-larvea-

submodel. These specifications are ^(names

of

variables underlined):

Daily mortality

(fraction) of

the

flies

(dailymortSD)

Daily mortality

of lnfective

(L3H-)larvae (dailvmortlH)

Probabilities for

the possible

lengths of the

bloodmeal-cycle (probcvclelength)

Average

fraction

release

of infective

larvae per sugarmeal

(as

a

rule

^preceding a bloodmeal) (propreleaseSugar)

Average fraction release of infective larvae per

bloodmeal

( propreleaseBlood ₎

Proportional rintaker during a

bloodmeal,

of Ll-larvae

in categories

that

must be defined ^(t

lintate)

The

excess

mortality (fraction) to

which

flies

are subjected ^when certain numbers

of

larvae (excessmortsD)

d

b c d e

f

oD

they ^engorge

Some

of

the processes (especially when related

to

larva1 development)

also influenced by the reference-table produced by the larvae-submodel.

The processes

that

the

flies

are assumed

to

undergo

daily

are:

6

are

I

2

3

4

5

6

Fly-mortality resulting from causes other than intake

of larvae.

This

mortality

^{reduces the number}

of flies in

each

cell of

the state-matrix with a glven

fraction

(dailymortSD).

Mortality of infective larvae in

^the

flies.

As

a result of

this

mortality,

characterislic 5 ^(NLH) changes.

In

other words there

will

^be

a shift along

the

5""

dimension

of the state-matrix, following

^a

binomial

distribution

with the fraction

mortality

(dailymortlH) _{and the}

resulting

larvae-load ^(NLH) as the

p- and k-

parameters respectively (see also mathematical summary).

Based

on

the reference-table from

the

larvae-submodel,

larvae

^from previous bloodmeals

that

have reached the L3H-stage are added

to

the pool

of infective

larvae, thus

altering

the frequencies

for

^{dimension 5}

(UtH) through a

shift

toward higher numbers

of

L3H-larvae.

Dependent

on

the time since

last

bloodmeal

(!t)

_and

the

distribution (probcyclelength)

a

^number

of flies will havla

new bloodmeal. ^The

flies

are placed

in

two separate temporary state-matrices

with

equal

structures, one for

the non-biting and one

for

the

biting

population.

Biting flies:

Will release a

number

of infective

larvae

during a

sugarmeal preceding the bloodmeal (on the basis

of

propreleaseSugar), thus reducing

their

L3H-store.

Will release

a number

of infective

larvae

during the

bloodmeal

itself

^(on the basis

of

propreleaseBlood)

Will at

the same time engorge a number

of L1-larvae

^(Llintake)

from the

human host

(to be

generalized

trough a

vector/host submodel, see discussion).

(The processes

a. b.

and

c., that result in

a change

of

the number

of

larvae (NLN,NLP,NLH) are controlled again by the binomial

shift

method)

May

die

as a

result of

an (high) _intake

of larvae. This is

^a

simple proportional

reduction

of

^the content

(nr. of flies)

of each element

of

the state-matrix.

The

consequences

of

having

a

bloodmeal

are reflected in all characteristics.

The existing information

in

^NI.N and TL regarding the

preceding _bloodmeal

is transferred to

NLP-and

TP-(last but

^one bloodmeal)

and

the content

of

NLP

(intakelT last 6It one

bloodmeal)

is -

^dependent on the time since intake and weighted against the larvae reference-table

-

added

to

the L3H

store. Finally,

the time since the

last

bloodmeal

(tl,) is

reset

to

1 day, the intake follows from 4c.

Ageing

of flies that

^did

not

have a bloodmeal. The time

since

last

bloodmeal (TL)

is

increased one day.

The

temporary state-matrices

of biting and non-biting flies

are assembled again

in

the

original

state-matrix.

In the figure below a schematic representation of the simulation ^processes is given.

To enable a correct comparison between model-results and catching-point data, the model-output is extracted between steps 4a and 4b, i.e. just

a

b c

d

model slructure

agcng ot ^{fles anc larYa.}

mortality of ^flies

monaltty of L3l-l-hrvae

ncldence of ^L3-+-hrvac

aigarmacl + L3Fl-loeB

bloocfflcal + L3l-t-loss

+

larvae-intake nuillparous pcpulattcrl

+

fly-mortality

before biting.

^This _' information about the example

of

model-input output looks

like:

at

the same

time,

implies

that at this

moment only

biting

part

of

the population

will be displayed.

^An (not

displayed:

the reference table

of

^page

5)

^{and -}

Input-variab les f ly-parasite-suboodel ^: Categories for ^number of tarvae ^:

Proportional Ll-intake in ^category:

Mortality caused by intake ^:

Bloodmeal cycle:

Possible cycle-durations ^(days) Probabilities for durations

0 o.500

I 2.-3 4-6 - ^0.300 - ^0.100

>6

ⁱ

0.200 i

0.200 i

Daily mortality of L3-head larrrae : ^.050 Daily mortality of flies : .I50 Average proportion release of ^L3-head larvae

duringasugarneal : ^.100 duringabloodmeal : ^.400

l1 ³

o.600 4i

0.400 i

2

Results ^f ly-parasite-subnode I

Sirmrlated distributions equilibriuro population:

Parous rate: ^0.530932

Stage Larvae-categories:

01

>6

ⁱ >0 i Nr. Larv.lfly

L1 LZ L3ilI

released ^LH

100.000

7 5.489 91.538 87 .047 90.32L

0.000 2.795 0.343 0.978 0.011 0.000

o.429 2.408 2.227 4.593

o.000 24. 51r 8.462 12.953 9.679

0.000 2.111 o.497 0.852 77.32t

2-3

.000 .723 .901 .380 .280 o 6 2 5

4

4-6

0.000 14.564 7..809 4.369 0.794

Simrlated VCU-table ^:

Total ^number of flies dissected Total number of parous flies Total ^number of nulliparous flies

:2O040 :10640 :9400

Parous flies wit-h : --) | ^no i ^LIandL2 | Llorl2 | ^L1orLZ I andl3 I orl,3 ⁱ

LlorL2 L3only only

L3

I ^larvae

Nr:rnber of flies 0

No. flies/1000 parous Number of larvae

3913 361 .8

6727 632.2

49L2 46L.7 10368.2

337L 316.8 4548.4

3356 315.4

1815 170.6

Results of catching point pC xx

Iotal nunber of flies dissected

Iotal number of parous flies :6304^2L2324

Total ntrmber of nulliparous flies :6OiO Parous flies with : --

Nunber of flies

No. flies/1000 parous Number of larvae

>igo llarrrae landl3 !orl3 lHandlzlLlorl2 lLlorl2 i i - ^m

i ^-- I Llorlz I Llonlv

I only ⁱ

---;;;---

-;;i-

63.6 41.4 s508

87 3.7 zL.3¹³⁴

796 535

84.9 1937 .0

395 62.7 1551.0 726 3

CompariEon

of

^UECPRH results and 0Cp/U[U data date!16- ?-1998

time: g:44:eg

_{UCU catchins}

_site:

pC xr 1ffi7,

807, 607, 407, 207, 07,

PAROU$ [AT[

w7,

Sim ^U(Ll

WWN

L3 and LllX

LAEUAL STAIIJS

$im

^\iCU

TM

AI

I

^Stases

#LAEUf;VPA[[]U:.' FLY

L1

or LI

Li

$im l,ttj _$im

^r/,:l[J

60fr

4fr7,

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07,

0.60 0.50 0.40 0.30 0,20 0,10 0.00

VTN

onls Ll?

lmv LI

onl'J

legend:

L3-only

₌

flies

with only L3(S + H)-larvae

only

L12

₌

flies

with only L1- and/or L2-Iarvae

L3 and LL/LZ =

flies

with L3-rarvae and

either Ll- or

L}-larvae

All

_{stages =}

flies

with

all

larvae-staBes (L1- _and L2- and L3B and/or L3H-larvae

3.

Discusslon items

In this section

some aspects

of the current

model

that might

^be

questionable are discussed, and some proposals ar made

for

implementation of factors

that

are missing

in

the current version.

1.

Comparison

of

simulated data with VCU-data

In

addition

to

comparisons between summarizing

tablesr w€ intend

^to

develop the

tools for

a more comprehensive comparison with the detailed catching-point counts we already received on

floppy. Both from

^the model-results and the counts a crosstable with larvae-1oad combinations can be

extracted.

With such tables

all

^possible comparisons (inctuding the

distribution

tables

in

the example

of

2,3) can be made.

2.

The

life-cvcle of

_{the lLg}

The user

is

offered the opportunity

to

look

at

the age

specific life-

events

of

the

flies

^(see 2.1 and the menu

in rstart

simulation'

in

4.).

Until

now we did not ^make an attempt

to

interpret

this

interim-results, though such

an

interpretation may be important with

respect to

the implementation

of a

vector-parasite module

in a

fuI1-transmission model, and therefore suggestions about

this

matter are welcome.

3.

Migratioln

In

the current version, migration

of flies is

not implemented. However, we

think that

a

fairly

simple migration option can be

built in

^without

too

much

trouble.

This option

is

an addition

to

the simulation

of

^a

local fly-population. A

second,

distant

population

of flies

is simulated

from

which

flies will

migrate

to the local population.

^A

simple submodel

for

migration would involve the following steps:

The simulation will be started with a local and a distant fly population at day 1 (= fly-age A, see page 6)

The life histories of both populations will be followed simul- taneously (the local population proceeds in the way implemented now).

The simulated part of the distant population consists of those flies that will fly to the 1ocal population

At the first bloodmeal in the distant population, the intake of microfilariae may be different from the loca1 population

A11 distant flies depart after the first bloodmeal

The duration of the flight should be specified. This duration is defined as the time between the last rdistantt bloodmeal, and the next (first tlocalt) _bloodmeal.

Upon arrival, the distant flies ^(and their characteristics) are

mixed with the 1ocal flies. The toriginr of flies in the loca1

population is not recorded.

Points of discussion:

The excess mortality is not modelled explicitly in this approach.

Excess mortality before arrival in the local population could ^be

taken into

account by incorporating

it in

the size

of

the distant population, and

in

the

distribution of

the

flight

duration. Excess

mortality (from

exhaustion)

after arrival is

^neglected

in

this

approach.

Only flies

departing

directly after the first

bloodmeal are considered.

Only

one distant population

ls

considered. This

one

population' however, could be considered as the sum

of

a number

of

populations

with average

distribution for

intake and

flight

duration.

4.

Intake submodel

As already mentioned

in 2.1, in

the current version

of

the model we use

an

imaginary ^I

intake' of

Ll-larvae as

a shortcut for the

^chain:

Microfilaria-intake -

^passing the gut-wall

of

the

fly

and becoming an

Ll-larvae.

Technically

it will

be a rather simple operation

to

^include

this

chain

in

the model, but as long as no data are available

on

^the

exact nature

of this chain,

a

linear

relation

will

be asumed, r*hich is

in fact

no more than an extended

shortcut; or in other words:

[Lt-

intakel will

be rplaced by lMF-intake

x

passaBe-factor], which

is

no

real

amelioration.

At this

^{point we} would

like

too receive suggestions.

Strongly related to this

item

is the

excess

fly-mortality

^which probably

is

the

result of

a high intake

of microfilariae.

This ^excess

mortality is

now

related to the Ll-intake classes, which is

^a

simplification.

The way

in

which the

relation

between MF-intake and

this

mortality may be included

in

the model depends on the solution for

the

^t intaket -item mentioned above.

5.

PersistinR L3B-larvae, remigrating L3H-larvae

An item that

might be a

restriction in

the current model

is the

fact

that

L3B-larvae can

either

become an L3H-larvae

or die.

Once being an

LH(infective)-larvae there

is

no way

back.

Some

field

observations,

however,

(H.

Remme,

pers.

^comm.

)

^{point out}

that

an L3B-larvae can

persist in

^{the body and never become}

infective (tsticking in a leg').

In addition, it

may be possible

for

an

infective

larvae

to

re-invade

the body.

Depending

on

the significance

of

one

or both options

^an

adaptation

of

the model may be necessary.

6.

Binomial draw

Throughout the model, where processes with larvae-numbers (intake, incidence, release) are concerned, it is assumed that these processes

can be described by a binomial draw with the given proportions and the resulting numbers as p- and k-parameters respectively. However, the question is whether a binomial draw is a ^proper description of these

processes. It is imaginable that another distribution would be

preferable.

7. Constant or age dependent mortality

At the

moment, the

(aaify)

_mortality

of

the

fties is

independent of

age. An option that will

be added

in

the next

version is that

^the mortality can change over age. Two options are possible:

l.

The mortality rates follow a

linear trend

^between user-supplied

10

?

mortallty-rates

at

selected days.

The

mortality rates follow

^some

function, e.B.

Gompertz or Weibull.

8.

Simplifications

In

the current version

of

the model simplifications are avoided where

possible. The

consequence becomes apparent

in the long

^run-times mentioned

before. In

developing a

faster

programme-version,

it

is possible

to

include a number

of

simplifications. ^Two

of

^{them are:}

1. Instead of

taking

all significant

f1y-ages and

their events

to assemble

the

^rsteady

statet population, it

nay be

sufficient

to

e.g.

take only those

flies that

have had

0, I or

(say) 4 ^preceding

bloodmeals.

2.

Throughout the model a binomial draw

is

used

to

realize a

shift

to

lower

larvae-loads. Applying a binomial draw involves

the

inner

product

between a binomial table and the

state-matrix

mentioned

before. It will

be

clear, that

an lnner product

with

such a large space

is

a time-consuming event and

it

may,

therefore,

be useful

to

replace a binomial draw by a more simple procedure

(see

also

iten

6).

9. Biting

behaviour nulliparous versus parous

flies

In the

current approach,

for

the nulliparous

fly-population, it

is

assumed

that

leaving the pupae on day=age=l

is -

with

respect to

the

timing of the

bloodmeal-cycle

-

equivalent with

having a

^bloodmeal

(without intake).

Consequently,

as

only

the

^parous

population

is

involved in calculations,

a sJ-mulation

starts at

the

earliest

fly-age

that

having a bloodmeal

is

possible (depending on the given duration(s)

of the

bloodmeal

cycle).

However, the question

is

whether

in

the

nulliparous

phase there

exist a

rpre-bloodmealr time-lag analogous to

the

least time lag between subsequent bloodmeals

in

the parous ^phase.

In other words: is it justifyable to

^use the same

distribution

of durations

of

the bloodmealcycle

for

both parous and nulliparous

flies.

11

3

4

4.

Users guide

4.1 Starting a session

The following steps must be undertaken:

1. Insert

^the STARTUP-(system-)floppy

in

drive A: and switch ^{on your P.C.}

2 l,lhen the APl-package has been loaded the MODEL-floppy must

be

^inserted

in A:

followed by pressing ENTER.

(At _{the moment) only when your}

P.C. is

equipped with an IBM CGA (which

is

assumed by the program) using the graphic

tools is

possible. At this point

of

the startup

it is

^{asked whether the P.C. has} a Hercules board.

Be

sure

that

^you give the

right

answer (making graphs with

a

Hercules board can even damage your

P.C.).

When a Hercules board

is

said

to

^be present, using the graphic

tools is

prohibited automatically.

After

termination

of a session,

a new session

can be started

^by entering ^TSTARTT.

Some remarks:

a Both floppyts are 360 Kb formatted.

Donrt write-protect the model-floppy; replacing information

in files

is prohibited then.

When working on hard-disk (recommended):

-

create a subdirectory ^VECPAR

-

copy the contents

of

both floppyrs

(not:

COMMAND.COM, AUTOEXEC.BAT START.BAT and VECPAR.BAT)

in this

subdirectory.

-

copy VECPAR.BAT

to

the root-directory

- start

a session from the root-directory by entering ^TVECPART

b

c

l2

4.2 Ustng ^VBCPAR

The program VECPAR

is written in

APL (SISC APL*PLUS). Each time

the

^APL-

workspace with the model

is

loaded (realized automatically when booting from

the STARTUP-floppy), the

last

values

of

the input variables

of

the prevoius

session

is read from

the

file

FINPLR.ASF

that is

updated

during

that session. Where single choices are involved, the program

is

managed by menus.

The main-menu looks

like:

Each

time

an action

is

terminated during a

session, the

main-menu re- appers

(except, of course,

when the user returns

to

the DOS-environment).

Description

of

the actions from the main menu:

Start si-uulation: With this

choice the next sequence

of actions

is

initiated:

a)

The

fi1e, to

which both input and output

will

be written must be

specified (without

extension,

which is

always

.ASF). If

an

existing filename

is specified,

the user can

either

overwrite the contents

of that file or

choose another name.

b)

The following menu appears: I

Ctroose option

The background of alternatives A ^(and B) and C (and D) is presented in chapter 2.1 and the figure shown there. A simulation- run always debouches into a calculation of the characteristics of a rsteady-stater biting fly-population. The materials for this calculation are, however, the life-events of a cohort followed from birth to death. With option C the intermediate charact.eristics of biting flies of all simulated ages are

calculated and stored in the output-file for inspection afterwards (main-menu: Tabulate output/Draw graphs). With option D this

1

VECTOR-PARASIIE I,IODH.

Anton Plaisier and Gerrit van Oortmarssen Version 1.0 Sept. 1986

Erasus University Rotterdasr

Make choice by using the cursorkeys ^Fl=Help!

Special keys: EIITR=Confirn choice; Esc= stop without choice

Start simulation Modify Paraoeters Modify VCl,l-data

Shor current input Tabulate output

Draw graphs

Printer setup Enter HELP leve1 Erase files

Return to ^DOS

A:Simulation of an equilibritrn situation B:A + Direct output to screen + printer

C:A + _Store life events by day

D:C + plsgqt output to screen + printer

E:Show current input

output is

automatically

dlsplayed.

with option E

the user

is offered the

(last)

opportunity

to

look

at

the current

input.

After pressing the ESC-key

or

^choosing the (STOP)-option

the

main-menu

returns which may be useful

for

changing the input.

c) Initialisation of

the

run. In this

part the

calculation of

the reference-table

of

the rarvae-submodel (see 2.2.1) takes place. rn

addition

some other simulation-tools are derived from

the

input- variables.

d) The actual

model

run.

unfortunately

this is a

slow-proceeding

event.

To a large exent the speed

can,

however, be influenced by

the

values

of

the input-variables ^(see the remarks

at

the

end

of

this section).

Of course the choice made

at I b) also

^(trighfyl influences the speed

of

the run: calculating

all

intermediate age-

characteristics and printing the the results during

the

calculations prolongs the run-time.

e)

Input and output

of

the run

is

saved

in

the

file

chosen

at

1 a).

2..

l{odify paraneters: The following menu appears:

Choose variable(s) to be changed

The meaning

of most

input-parameters

is

explained

in chapter

z.z (underlined

terms).

About the others:

- Donrt

forget

to

^give a relevant run- and subtitle.

-

maxf

lyage

denotes

the

number

olTry-"gillo-u"

invorved in

calculations to obtain the equilibrium population. As

an

exponential death-rate

of

the population

is

assumed the population

theoretically never

disappears

completely. For that

reason

maxflyage must

-

experimentally stated

-

be taken as large

as

to guarantee inclusion of fly-ages that significantly contribute to the total age-spectrum. In test-runs (see example in Z.Z.Z)

maxf yaqe=25 appeared to be reasonable, but this is, of course,

highry

dependent on the applied death-rate

. rt will be

obvious

that

increasing maxflvaRe prolongs the run-time.

Another important parameter

is

nlarvacategories (see again example

in 2.2.2).

As

it

would lead

to

extremeS, long run-times

at

high

possible

larvae-loads, a

fly will

not be characterized

by

exact numbers

of of larvae,

but by larvae-load-categories. Depending on

nmtitle subtitle

maxflyage nlarvacategories Llintake

excessmortsD daiIynortIJI dailymortSD propreleaseSugar propreleaseBlood probcyclelength durstLl

probdurstLl durstL2 probdurstL2 durstL3body

probdurstL3body dailmortlIL2L3

<STOP=Esc>

TIILE FOR RT'N

L4

the

expected larvae-loads the user can determine

both the

^range

and the precision

of

the categories.

In

nlarvacateRories the lower boundaries

of

the categories are given. Some remarks:

-

The upper boundary

of

the

last

^category

is

derived

from

the

size

of

the

last

but one category increased by

one;

the size

of

the

last

category

is

set

to at

least 4.

- As

during calculations

at

^{some points}

(a.o.

when the output

is calculated)

the exact number

of

larvae

rather than

the

categories

is

needed, the contents

of the

categories is

spread evenly over the numbers within the

categories. fn

the

last

category the weights decrease 1inearly.

Some restrictions:

-

The

first

category must comprise only 0 ^(zero)

-

The number

of

categories may not exceed ⁶

-

The

last

upper boundary may not exceed 20 larvae.

An example:

catgories ntrmbers in categories

weights

0 1.0000

1

0

1 I .0000

2 2

3

0.5000 0.5000

4 4

5 6

0. 3333 0.3333 0. 3333

o .437 5 0 . 3125 0. 187s 0.0625

7 7

8 9 10

In

selecting the variable

to

be changed, a short explanation appears at

the bottom of the screen. For changing data the

cursor-, (forward)delete-

and

backspace-keys can be

used.

For entering arrayrs

only

commars

can be

used

to

separate

the elements. After

each

modification the values of the

input-parameters

are

checked,

inconsistencies and impossibilities are traced

and,

when an

error

is located, the modification-menu returns and the

error

can be

rectified.

3.

Ilodify VCU-data: Mediated by the following ^menu,

Ctrange data of selected VCU-catching site

the user is

offered the

possibility to give values to

^parameters

concerning the results

of

VCU-catching

points.

These values serve as a nrparousflies

nrnullipar nrlarvae

csN (STOP=Esc>