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Age-targeted control strategies for schistosomiasis–associated
morbidity and childhood developmental impairment
2674
David Gurarie1 and Charles H. King2
Department; 2Center for Global Health and Diseases, Case University, Cleveland, OH
RESULTS
MODELS: TRANSMISSION-DISEASE-DEVELOPMENT
Age
CHRONIC DISEASE FORMATION
Premises:
4
6
0.05
3
0.1
2
0.2
1
4
3
0.2
2
0
1
0
0
10
20
30
40
50
60
0
10
20
30
40
50
60
Fig.3: Age-specific worm burden (dashed) and chronic damage (solid) with 4
possible disease resolution rates: linear case (left), nonlinear case (right)
Worm
Model Variables: w – (mean) burden; DL;DH – accumulated disease
(for low/high risk groups); H,h – developmental index (weight,
height, etc.) for normal and delayed growth, d=h/H - disability
fraction (d=1 – ‘normal state’).
All variables are functions of age a, and time t. Stationary
transmission and therapy-control drives the system to a stable
(endemic) equilibrium state, that obeys integro-differential
equations:
burden
Low risk
morbidity
High
1.2
0.2
0.15
0.1
0.05
10
20
30
40
50
morbidity
5
0.8
4
0.6
3
0.4
2
0.2
1
60
risk
6
1
0.25
10
20
30
40
50
60
10
20
30
40
50
60
Fig.4: Worm burden (left) and chronic disease prevalence (center/right) for the
3 treatment cohorts of case I (shades of gray) vs. a completely untreated
population (dashed). The low/high risk groups differ by their resolution rates.
Year
 a wa = ha    Treatment  wa ;

Infection + chronic disease
(1)  a Da L = r  wa   n L  D L  ;

H
H
H
 a Da = r  wa   n  D  ;

0.1
1
0.3
Parameters:
5
1
0.35
 a wa = ha    Treatment  wa ;
Infection + early

(2)   d
development
a
=
g
a
f
w

1

f
w
r
a
1

d


         


 d
0.05
Accumulated damage
Stationary human populations and transmission environment
Age-dependent (behavioral) risk factors
Genetic risk factors. Variability in immune response can affect
infection levels, early development, and the accumulation/
resolution of chronic disease. Accordingly, populations are
subdivided into low- and high-risk disease-development cohorts
Child development accounts for natural growth, its inhibition by
infection, and the potential for therapeutic remediation
Age-targeted treatment strategies with complete or partial coverage
of first
treatment
Year
6
6
5
5
20 % efficacy
4
Max morbidity
Schistosomiasis has multiple adverse effects, including longterm chronic disease, and retardation of juvenile growth and
development. W.H.O. advocates control strategy by periodic drug
treatment of affected populations, focusing on school-age children
as the highest risk group for infection. Such control programs have
already began, but important questions remain:
I) Given the nature of infection, its associated diseases,
and the typical patterns of program participation, what are the
optimal strategies for drug delivery to minimize community
burden of disease in a resource-limited setting?
II) What effect could drug treatment have on improving
early childhood development?
We address these problems by mathematical modeling that
accounts for transmission in age-structured populations, the typical
development of acute and chronic diseases, the long term effect of
treatment on chronic disease, as well as the impact on early
childhood development and growth retardation. Our analysis
identifies such optimal control strategies, and shows the potential for
a substantial reduction of both early (developmental) and late-term
morbidity.
Age
Accumulated damage
ABSTRACT
90 % efficacy
3
2
Low risk
1
0
5
15
20
25
treatment
20 % efficacy
90 % efficacy
4
3
2
Low risk
1
10
of first
Max morbidity
1Math.
30
0
5
10
15
20
25
30
Fig.5: Long-term chronic damage as a function of varying the initial treatment age
of strategies II-III (including decreasing adherence), at two different cover levels of
the first cohort: 80% of eligible population (left), and 50% (right). Black curves are
high-risk, gray - low-risk morbidity groups. Two ‘high risk’ curves on each plot
compare the results of risk screening tests at each of two sensitivity levels.
Age
Age
– per capita force of infection (depends on community-wide
160
60
transmission and snail infection)
140
50
ha – age-dependent contact rates (determine worm establishment and
120
40
snail contamination).
100
30
80
r,n - disease accumulation and resolution, can be linear or nonlinear
20
60
10
function of w,D.
g(a), r(a) – natural/ remedial growth rates, based on US (NCHS) data
0
5
10
15
20
0
5
10
15
20
f(w) – infectious inhibition function (0<f<1)
Fig. 6: The US median and 3rd percentile (NCHS) growth curves vs. Kenyan S.
180
US 3rd percentile
US median
Best fit DE
Height, cm
US 3rd percentile
US median
Best fit DE
Weight, kg
70
Treatment:
180
US median height - Boys
US 3rd percentile height
160
Height in cm
Kenya Sh median height
140
120
Programs with risk screening and stratified treatment delivery:
(III) will apportion the treated/untreated fractions among risk groups
based on their predicted risk. We maintain the same overall
coverage rates as case (II), but a larger number of the high-risk
fraction is treated, depending on efficacy of screening.
100
80
4
6
8
10
12
14
16
18
Age in Years
Fig. 2: Abnormal growth curve of male children and teen-age
boys in an
S.haematobium-endemic area
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Methods
The results below combine mathematical analysis / solutions of (1)(2), and numeric codes implemented in Wolfram Mathematica 5.
Age
Age
1
1
0.95
0.98
0.9
0.85
0.8
0.75
Height deficit
EARLY GROWTH RETARDATION
Population is subdivided into treatment cohorts (with different
protocols). We consider two scenarios: (A) blind selection of
treatment cohorts, where both risk groups enter in proportion to
their population fractions; (B) Prescreening to select high-risk
individuals for more intense treatment (Fig. 6).
Treatment strategies and adherence for blind selection:
(I) Follow three realistic limited treatment cohorts: a. 60% of
population treated at ages 6 and 12; b. 20% treated at age 6 only,
c. remaining 20% go untreated
(II) Field compliance levels for multiple treatment: 70% covered by
first treatment go to second, 60% of those to a third one. We allow
2-year gap between sessions (recommended by WHO) and let
timing of initial treatment vary from 1 to 30 years of age.
Weight deficit
Fig. 1: Typical age-prevalence, infection intensity, and chronic
disease formation in S.haematobium-endemic areas
haematobium data (orange dots), and the best-fit DE solutions.
0.96
0.94
0.92
0.7
0.9
0
5
10
15
20
0
5
10
15
20
Fig. 7: The possible effect of ‘near optimal’ treatment regimen on reversing the
height/weight deficiencies associated with infection at 3 different program
efficacies: 20%,50%,90% (orange dots – untreated Kenyan data)
SUMMARY AND CONCLUSIONS
Mathematical models allow us to estimate the effects of agetargeted treatments on both late-term disease formation and
early growth retardation. We find optimal strategies (initial age,
regimen) that yield significant reductions of both. These can
apply to identified high-risk groups or the general population.
Pre-screening for risk produces little effect (over a lifespan)
with high initial coverage, but grows in significance at lower
participation/adherence levels.
1.Medley GF, Bundy DA, Am J Trop Med Hyg 1996;55:149-58.
2.Chan MS, Guyatt HL, Bundy DA., Medley GF, Am J Trop Med Hyg
1996;55:52–62
3.Gurarie D, King CH, Parasitology 2005;130:49-65