Modeling the dynamics of VL and its vectors
The task of the mathematical modeling
group at the Gertner
Institute will be to combine mathematical modeling, analyses
of spatiotemporal data patterns with laboratory work to better
understand the ecology, epidemiology and evolution of visceral
leishmaniasis in Ethiopian foci. Integrating mathematical modeling with
rigorous statistical methods, will facilitate accurate estimation of
key parameters relevant to transmission and of putative
importance in controlling the disease. The primary focus of the initial
operational phase of the project will be to apply mathematical modeling
to facilitate the formulation of hypotheses, to guide rational
datacollection strategies and determine sample sizes required for
discriminating between competing hypotheses. For example, one of the
first modeling tasks will be to try and verify or reject the working
hypothesis that VL in Ethiopia is primarily anthroponotic, the role of
zoonotic transmission being relatively minor. Combined with empirical
data to be obtained during the project, such information will assist in
designing optimal control strategies for reducing the burden of
disease. The ultimate goal of this effort is to formulate a set of
measurable criteria that will dictate experimental design and provide
the optimal monitoring criteria for its effectiveness (e.g. minimum
number of infected individuals or infectious sand fly bites per unit
time required to sustain transmission). The starting point of the
modeling effort will be in the spirit of Ronald Ross, who developed the
first mathematical model for malaria. The modeling will be based upon
stylized models designed to provide basic insights into epidemiological
theory. The development of successful control programs requires basic
theoretical foundations for the understanding of the basic principles
and theoretical mechanisms that govern endemic/epidemic behavior. The
core of the modeling which we intend to rely upon is the classical
SIRmodel
Being a "strategic model" that is
deliberately not made unduly complicated, it is possible to determine
the system's equilibria and investigate their stability. The stability
of the "infectionfree" equilibrium state, usually gives many insights
into the disease's "reproductive number" R0, a key epidemiological
parameter. R0 indicates the number of secondary infections produced by
a single infectee in a sea of susceptibles. If R0>1, the
infectionfree equilibrium is unstable and VL can invade the systems.
If R0>1, in the model this is supportive evidence for anthroponotic
transmission of VL in Ethiopia. If R0<1, VL will be unable to
invade. In such a case the model might be missing a crucial component
or the data is not sufficient to parameterize the model, or that the
anthroponotic transmission on its own is not enough to sustain the
disease (i.e. there is an indication for adding a zoonotic component
into the model).
Project personnel
Amit Huppert,
PhD (Project Leader) amit.huppert@gmail.com
Huppert Amit: holds a Ph.D. in Mathematical Biology from Tel Aviv
University. He specializes in interdisciplinary research,
encompassing epidemiology, epidemic modeling, ecology, climate,
statistics and mathematics. Dr. Huppert has substantial research and
modeling experience working with a wide range of mathematical models
some of them at the interface of infectious disease and climate
interactions.
Ezer Miller,
PhD (Post Doctoral Fellow) email: miller@agri.huji.ac.il)
Selected Publications
Huppert, A. and L.
Stone. 1998. Chaos in the Pacific’s coral reef bleaching cycle: a
model. The American Naturalist 152:447459.
Stone, L., P. I. Saparin, A.
Huppert and C. Price. 1998. El Ni?o chaos: The role of noise
and stochastic resonance on the ENSO cycle. Geophysical Research
Letters, 25:175178.
Price, C., L. Stone, A. Huppert,
B. Rajagopalan and P. Alpert. 1998. A Possible link between El Ni?o and
precipitation in Israel. Geophysical Research Letters 25:39633966(21).
Huppert, A., L. Stone,
B. Rajagopalan and Y. Loya. 1998. The Pacific’s coral reef
bleaching cycle  An outcome of increased El Ni?o activity and
interdecadal climate change? Israel Journal Of Zoology
(Abstracts), 44:7576.
Blasius, B., A. Huppert
and L. Stone. 1999. Complex dynamics and phase synchronization in
spatially extended ecological systems. Nature 339:354359(6734).
Stone, L., A. Huppert,
B. Rajagopalan, H. Bhasin and Y. Loya. 1999. The Pacific’s coral
reef bleaching cycle  An outcome of increased El Ni?o activity and
interdecadal climate change? Ecology Letters 2:325330 (5).
Huppert, A,. B. Blasius
and L. Stone, 2002. A model of phytoplankton blooms. The American
Naturalist 159:156171.
Stone. L., R. Olinky, B. Blasius, A.
Huppert and B. Cazelles, 2002 Complex synchronization
phenomena inecological systems. in S. Boccaletti, J. Kurths,
L.M. Pecora, M.L. Spano, ed., 6th Experimenal Chaos Conference,
American Institute of Physics, 622: 476488.
Solow, A. R. and A. Huppert.
2003. On nonstationarity of ENSO. Geophysical Research Letters
30:19101913(17).
Huppert, A., B. Blasius
and L. Stone, 2004. What minimal models can tell.
A reply to van Nes and Scheffer. , The American Naturalist. 163:
927929.
Huppert, A. and A.R.
Solow. 2004 Comment on “Deconvolving the seawater component from subseasonal coral and Sr/Ca at Rarotonga in the southwestern
subtropical Pacific for the period 1726 to 1997”. Geochim.
Cosmochim. Acta. 68 (14): 31373138.
Huppert, A., R. Olinky and L., Stone.
2004. BottomUp excitable models of phytoplankton blooms. The Bulletin
of Mathematical Biology. 66 (4): 865878.
Huppert, A. and A.R.
Solow. 2004. A method for reconstructing climate from fossil beetle
assemblages. Proceedings of the Royal Society London B. 271:
11251128.
Solow, A. R. and A. Huppert,
2004. A potential bias in coral reconstruction of sea surface
temperature. Geophysical Research Letters. 31 (6): Art. No. L06308.
Solow, A. R. and Huppert, A.
2004. Optimal multiproxy reconstruction of sea surface temperature
from corals. Paleoceanography.19 (4): Art. No. PA4004.
Huppert, A., B.
Blasius, R. Olinky and L., Stone. 2005. A seasonally forced
phytoplankton bloom model. Journal of Theoretical Biology.
236(3): 276290.
Huppert, A. and A.R.
Solow. 2005. Reassessing US coral reefs. Science. 308: 17401740.
(short comment)
Stone , L.,* Olinky, R*., and Huppert*,
A. 2007 Seasonal dynamics of recurrent epidemics. Nature
446: 533536. *Authors contributed equally.
Olinky, R., Huppert, A.,
and Stone , L. 2008. Seasonal dynamics and
thresholds governing recurrent epidemics. Journal of Mathematical
Biology 56:827839.
Huppert A., Katriel H.,
Yaari R., Barnea O., Roll U., Stern E., Balicer R. and Stone L. 2010,
Mathematical Models as a Tool for Studying and Developing Strategies in
the Case of a Pandemic Influenza Outbreak. Harefuah, 149:48 (in
Hebrew, English abstract).
