Immuno-epidemiology of
malaria
Klaus Dietz
Department of Medical Biometry
University of Tübingen, Germany
DIMACS Worksop
11-13 December 2006
Outline
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What is immuno-epidemiology?
What is malaria?
Why model malaria immunity?
Malaria immunity models: a brief history
A within-host malaria model
Concluding remarks
Serological surveys as
immuno-epidemiological tools
Desowitz RS, Saave JJ, Stein B.
The application of the indirect haemagglutination test in
recent studies on the immuno-epidemiology of human malaria
and the immune response in experimental malaria.
Mil Med.,131:1157-1166 (1966).
Suzuki M. Malaria immuno-epidemiology:
a trial to link field study with basic science.
Gaoxiong Yi Xue Ke Xue Za Zhi.7:224-232 (1991).
.....malaria serological assessment was carried out in
endemic areas in Haiti, Indonesia, Sudan and in Brazil
Amazon. The serological survey was useful in finding
latent foci in a controlled area, for the assessment of past
epidemics,....
A theoretical framework for
immuno-epidemiology
Woolhouse, M.E.J.et al.: Acquired immunology and
epidemiology of Schistosoma haematobium., Nature 351, 757759, 1991 („Acquisition of this immunity seems to be related to
the cumulative effects of repeated infection and provides only
partial protection. These characteristics are consistent with
immuno-epidemiological data for both S. mansoni and S.
haematobium infections of humans.“)
Hellriegel, B.: Immunoepidemiology-bridging the
gap between immunology and epidemiology.
Trends in Parasitology, 17, 102-106, 2001
„Immunoepidemiology combines
individual- and population-oriented
approaches to create new perspectives.
It examines how inter-individual
differences in immune responses affect
the population dynamics of micro- and
macro-parasites to produce the
epidemiological patterns of infection
observed in heterogeneous host
populations.“
A cartoon of
immuno-epidemiological models
Parasite density
Immunity level
Morbidity level
yi yi

  i (t , a, y1 ,...., yn )   i ( y i , zi )
t a
zi zi

  i ( y i , zi )
t a
mi mi

  i  yi , z i 
t
a
i  1,...., n
yi (0, a )  yi (a );i yi (t ,0)  0
zi (0, a )  zi (a );i zi (t ,0)  zi (0)
mi (0, a )  mi (a );i mi (t ,0)  0
STI project on the mathematical modeling of
the impact of malaria vaccines on the clinical
epidemiology and natural history of
Plasmodium falciparum malaria
Thomas A. Smith and team
• Many millions of simulation runs, each in the
order of hours
• Need for supercomputing
Network Computing
Volunteer Computing Project
Malaria cycle
Source:Wellcome Trust
Infected Red Blood Cells (IREs) by asexual (red)
and sexual (green) parasites in Patient G141
n = 54; mean 212 days, median 216 days
Present
geographical distribution of malaria
The challenge of malaria
The President And Mrs. Bush Will Host The White
House Summit On Malaria On December 14, 2006, In
Washington, DC, To Discuss And Highlight Measures
For Combating This Preventable Disease
In June, President Bush announced a new commitment to
combat malaria. His proposal calls for an additional $1.2
billion over the next five years. The money will pay for
insecticide-treated nets, it will allow for indoor spraying
against mosquitoes, and it will provide effective new
combination drugs to treat malaria. Our goal with this new
funding is to reach more than 175 million people in 15
nations. (1.37 $/Person/year)
Growth of the yearly number of malaria
publications
Doubling time: 10 years and 7 months
Why model malaria immunity?
• Not necessary, if one is aiming for
eradication:
• Macdonald, G.: Theory of the
eradication of malaria. Bull. WHO 15,
369-387, 1956.
• WHO global malaria eradication
campaign 1955
Original Eradication Plans
• Interruption of
transmission of main
species infecting
humans by DDT
spraying
• Malaria disappears
spontaneously in
under 3 years
Source: Gabaldon
Pampana: Textbook on malaria
eradication
• If malaria eradication will be achieved it
will be first of all due to the computer
• Macdonald: DDT spraying and mass
drug administration every two months
will interrupt malaria transmission in
Africa
(graph by Martin Eichner)
hypo-
meso-
hyper-
holo-endemic
Cerebral malaria incidence
(per 1000 per year)
(ages 0-9 years)
3.0
Sukuta
(Gambia)
2.5
2.0
Kilifi N
(Kenya)
1.5
Kilifi S
(Kenya)
1.0
0.5
Siaya
(Kenya)
Bakau
(Gambia)
0
0
0.5
1.0
1.5
Force of infection (per year)
2.0
2.5
Snow et al. (1997) The Lancet
Points of attack of potential
malaria vaccines
Smith et al (2006)
Malaria immunity models
• Dietz, K: Mathematical
models for transmission and
control of malaria. 10911133 (1988)
• Molineaux, L and Dietz, K:
Review of intra-host models
of malaria. Parassitologia
41:221-231 (1999)
• McKenzie, FE and Bossert,
WH: An integrated model of
Plasmodium falciparum
dynamic. J Theor. Biology
232, 411-426 (2005)
Ronald Ross (1857-1932)
Second Nobel price in
Medicine in 1902
Infection
without (Ross) and with (Macdonald)
superinfections
Ross („premunition“)
0
1
Macdonald
0
1
k
Age-specific prevalence
  epidemiolo gical inoculaion rate
  recovery rate from one infection


pR (a) 
1  e      a 

 
 a 
pM a   1  exp   1  e 
 


p R ( ) 

pM    1  exp  
 1  p R ( ) 
Prevalence by age

  4.6 per year ;   1.8 per year ;  2.6

Implications of unrealistic assumptions
about the strength of immunity
• Underestimating the strength of immunity
leads to an
• underestimate of the basic reproduction
number and consequently an
• underestimate of the necessary eradication
efforts and an
• overestimate of the expected control effects
Garki Model (Dietz, Molineaux, Thomas, 1974)
Garki Book (Molineaux L and Gramiccia G, 1980
http://whqlibdoc.who.int/publications)
Garki Data:
http://www.sti.ch/de/forschung/biostatistics/downloads.html
y1
y1
x1
y2
y2
y3
x2
Garki model fit
Fit to Garki data of the
STI project
Prevalence by vectorial capacity
Gupta, S. and Day, K.P.: A theoretical framework for the
immunoepidemiology of Plasmodium falciparum malaria.
Parasite Immunology, 16, 361-370 (1994)
n 1
n
0
1
n k 
n  2
2
R0  3.25
n  40;30;20
k
n
n  20
R0  7.5; 5; 3.25
„Might malaria yield to mathematics“
(Economist, March 12th 1994)
„Recent epidemiological work
suggests that there may be a
stronger chance of
controlinling malaria than
was once thought likely…
Comparing the distribution of
the strains among people by
age with the spread
produced by their* model,
they found a very close
match if the average number
of secondary cases caused
by a single case was
between six and seven.“
*Gupta, Anderson, Day
and Trenholme
Innate and adaptive immunity
Stevenson and Riley (2004)
• Research on the immunology of malaria has tended
to focus on adaptive immunity
• Accumulating evidence…indicates a crucial role for
innate immune responses in protective immunity to
malaria
• Innate responses are essential to limit the initial
phase of parasite replication, controlling the first
wave of parasitemia and allowing the host time to
develop specific adaptive responses that will enable
the infection to be cleared
Fig 1A
Fig 1B
Fig 1C
Correlations between innate immunity threshold,
parasite growth rate and peak density
Correlation between innate and adaptive
immunity thresholds and between two
parameters for adaptive immunity
Feverthresholds
Vaccine effect on initial multiplication
factor
Fig 3
B
A
4
3
2
1
0
Vaccine efficacy
Conclusions from the within-host
model for the first wave
• The 800 data points for 100 patients could well be
described by a simple model with four interpretable
parameters per patient.
• All parameters show large variation.
• The maximum parasitaemia is mainly controlled by
innate immunity.
• The benefit of a vaccine targetting the asexual blood
stages is expected to be strongly host dependent.
• At low immunogenicity the expected vaccine efficacy
against severe malaria is much higher than against
fever.
Concluding remarks
• Historic data (neurosyphilis patients, Garki
project) are still relevant today and in the
future because new data about the natural
course of malaria can for ethical reasons
no longer be collected.
• Estimates for basic reproduction numbers
are model dependent.
• In spite of the fact that malaria is probably
the disease with the largest number of
models there is still no generally
acceptable model.
Acknowledgements
• Louis Molineaux, Geneva
• Tom Smith and his team at the STI,
Basle
• Martin Eichner, Günter Raddatz,
Tübingen