ABOUT THE PROJECT

UPDATES ON PROJECT ACTIVITIES

Publications

RESEARCH GROUPS

Structure and management

Endemic Foci of Kala Azar

GALLERY

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 spatio-temporal 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 data-collection 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 SIR-model

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 "infection-free" 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 infection-free 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

Selected Publications

Huppert, A. and L. Stone. 1998. Chaos in the Pacific’s coral reef bleaching cycle: a model.  The American Naturalist 152:447-459.

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, 25:175-178.

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 25:3963-3966(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 inter-decadal climate change? Israel Journal Of Zoology (Abstracts),  44:75-76.

Blasius, B., A. Huppert and L. Stone. 1999. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 339:354-359(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 inter-decadal climate change?  Ecology Letters 2:325-330 (5).

Huppert, A,. B. Blasius and L. Stone, 2002. A model of phytoplankton blooms. The American Naturalist 159:156-171.

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: 476-488.

Solow, A. R. and A. Huppert. 2003. On non-stationarity of ENSO. Geophysical Research Letters 30:1910-1913(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: 927-929.

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): 3137-3138.

Huppert, A., R. Olinky and L., Stone. 2004. Bottom-Up excitable models of phytoplankton blooms. The Bulletin of Mathematical Biology. 66 (4): 865-878.

Huppert, A. and A.R. Solow. 2004. A method for reconstructing climate from fossil beetle assemblages. Proceedings of the  Royal Society London B. 271: 1125-1128. 

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 multi-proxy 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): 276-290.

Huppert, A. and A.R. Solow. 2005. Reassessing US coral reefs. Science. 308: 1740-1740.  (short comment)

Stone , L.,*  Olinky, R*., and  Huppert*, A. 2007  Seasonal dynamics of recurrent epidemics. Nature 446: 533-536. *Authors contributed equally.

Olinky, R., Huppert, A.,  and Stone , L. 2008.  Seasonal dynamics and thresholds governing recurrent epidemics. Journal of Mathematical Biology 56:827-839.

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, 149:4-8 (in Hebrew, English abstract).

Volcani Center, Israel