Longitudinal modelling of

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16 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Longitudinal modelling of
helminth infections

Direct life cycle parasites


Ascaris lumbricoides


Trichuris trichiura


Hookworms (
Ancylostoma duodenale
,
Necator
americanus
)

Each infection has a free living stage affected by
environmental conditions

Life cycle of Ascaris

Compartmental model of Ascaris life cycle

Infective stages

(larvae in eggs)



Worms


W

m
L

m
W

b

l

Environment

Host

L

Basic
Ascaris

life
-
cycle dynamics

d
W =
b
L
-

m
w
W

d
t

d
L

=

l
W

-

b
L
-

m
L
L

d
t

Rate of change of adult
worm population

Rate of change of
infective population

Growth curves in the absence of density dependence

Each population will continue to grow indefinitely due to a lack of constraints

Infective stages

Worms

Time

0

500

1000

1500

2000

2500

1

13

25

37

49

61

73

85

97

0

5

10

15

20

25

30

1

13

25

37

49

61

73

85

97

Time

L

W

Haswell Elkins et al 1986 TRSTMH

A. Lumbricoides

density dependent fecundity

Density dependence

The reproductive potential of each worm
-
pair is limited by the
average number of worms in the host:

f
=
l
e
-

g
W

Where:


f
= number of eggs produced by
each worm
-
pair

g
= density dependence parameter

0

5

10

15

20

25

30

1

12

23

34

45

56

67

78

89

100

Time

W

Host mortality as density dependence

Trichostrongylid parasites of grouse control populations of both hosts and parasites

Untreated

Treated

WHO recommends……

Chemotherapy options are
based on prevalence
estimates.

Mass treatment every year in
high transmission areas….

…twice
p.a.

in high morbidity areas

Children take priority in low
transmission areas.

Use other strategies concurrently.

Model predictions

children

adults

Morbidity = Prevalence of >20 worms. Adults are untreated.

Model validation

Adult worms
M

Miracidia
L1

Susceptible snails
X

Latent snails
Z

Shedding snails
Y

Cercariae
L2

m
1

m
2

m5

m4

m
3

m
3

Human N1

water

Snail N2

b
1

l
1

b
2

l
2

s

Compartmental model of schistosome life cycle

dM/dt =
b
1
L
2
-

m
1
M

Adult worms
M

m
1

Human N1

b
1

Proportion of larvae that
become adults per unit time

Per capita
death rate

Adult worm
population size at
time t

Rate of change of
worm population

Cercariae
L
2


dL
1
/dt = ½

l
1
MN
1
f
-

m
2
L
1
-
b
2
N
2
L
1

Adult worms
M

Human N1

l
1

Miracidia
L
1

m
2

Susceptible snails
X

b
2

No. of eggs hatching
per unit time

Mating function

No. of dead
miracidia per
unit time

Rate of change of
miracidial
population

No. of miracidia that
infect snails per unit
time

Susceptible snails
X

Latent snails
Z

Shedding snails
Y

m4

m
3

m
3

Snail N2

s

dX/dt =
m
3
(X+Z)+u
4
Y
-
b
2
XL
1

Propn of
population that
die per unit time
(recyled into
births)

Propn of susceptible
snails becoming
infected per unit time

Rate of change of
proportion of
snail population
that are
uninfected

b
2

Miracidia
L
1

Susceptible snails
X

Latent snails
Z

Shedding snails
Y

m4

m
3

m
3

Snail N2

s

dZ/dt =
b
2
XL
1



s
Z


m
3
Z

Rate of change of
propn. of snail
population that
are infected but
not shedding

Propn. of snails
becoming infected
per unit time

Propn. of latent
snails that start
shedding

Propn. of
latent snails
that die

dY/dt =
s
Z
-
m
4
Y

Susceptible snails
X

Latent snails
Z

Shedding snails
Y

m4

m
3

m
3

Snail N2

s

Rate of change of
propn. of snail
population that
are shedding

Propn. of
latent snails
that start
shedding

Propn. of
shedding snails
that die

Cercariae
L2

m5

l
2

dL
2
/dt =
l
2
YN
2



m
5
L
2


b
1
N
1
L
2

Rate of change of
cercarial
population

Shedding snails
Y

Total no. of
cercariae
produced per
unit time

No. of
cercariae
dying per
unit time

No. of cercs that
penetrate
definitive host
per unit time

b
1

Human N1

Schistosome model output

Varying snail longevity

5

10

20

30

low fecundity, short worm longevity

Endemic situation

New focus

Mangal
et al
PLoS One. 2008 Jan 16;3(1):e1438

Modelling the impact of long
-
term temperature changes on schistosome transmission

Temperature increases
result in higher mean
worm burdens until about
35 degrees before the
system becomes
‘unstable’

Mangal
et al
PLoS One. 2008 Jan 16;3(1):e1438

Challenges

The social dimension
-

who does what and why?

Population growth / migration


how far will people go to seek prosperity?

Extreme weather events


how frequent, how intense?

Governmental policies


will they offer mitigation or adaptation to climate change?

Evolution



rapid generation times may lead to adaptation of both snails and parasites

Scale



infections act locally, climate change acts globally



Is this the future?