Amit Huppert

Complex dynamics and phase synchronization in spatially extended ecological systems.

Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual ‘4- and 10-year cycle’ of wildlife are often found. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance—twin realistic features that are not found in standard ecological models. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale ‘phase synchronization’,, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.

Seasonal dynamics of recurrent epidemics

Seasonality is a driving force that has a major effect on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases (such as influenza, measles, chickenpox and pertussis), and is of great relevance for host–parasite relationships in general. Here we gain further insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR (susceptible, infectious or recovered) epidemic model. Our analysis differs from other modelling studies in that the focus is more on post-epidemic dynamics than the outbreak itself. Despite the mathematical intractability of the forced SIR model, we identify a new threshold effect and give clear analytical conditions for predicting the occurrence of either a future epidemic outbreak, or a ‘skip’—a year in which an epidemic fails to initiate. The threshold is determined by the population’s susceptibility measured after the last outbreak and the rate at which new susceptible individuals are recruited into the population. Moreover, the time of occurrence (that is, the phase) of an outbreak proves to be a useful parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-peaking diseases (that is, those having high phase) from spreading widely, thereby increasing population susceptibility, and controlling the triggering and intensity of future epidemics. These principles yield forecasting tools that should have relevance for the study of newly emerging and re-emerging diseases controlled by seasonal vectors.

A possible link between El Niño and precipitation in Israel

Various data sets related to precipitation in Israel have been analysed to see whether any statistical relationships exist between the El Nino phenomenon and weather in Israel. An understanding of patterns of precipitation in Israel is extremely important given the limited water resources in the Middle East. The authors have analysed seasonal rainfall, streamflow, snowfall and lake level data, and all of these data sets indicate enhanced precipitation during the winter seasons associated with El Nino years. One intriguing finding is that the statistically significant correlations appear only in the last 25 years.

A Model of Phytoplankton Blooms

A simple model that describes the dynamics of nutrient‐driven phytoplankton blooms is presented. Apart from complicated simulation studies, very few models reported in the literature have taken this “bottom‐up” approach. Yet, as discussed and justified from a theoretical standpoint, many blooms are strongly controlled by nutrients rather than by higher trophic levels. The analysis identifies an important threshold effect: a bloom will only be triggered when nutrients exceed a certain defined level. This threshold effect should be generic to both natural blooms and most simulation models. Furthermore, predictions are given as to how the peak of the bloom \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

The effects of host diversity on vector-borne disease: the conditions under which diversity will amplify or dilute the disease risk.

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Modeling and statistical analysis of the spatio-temporal patterns of seasonal influenza in Israel

\end{document} is determined by initial conditions. A number of counterintuitive results are found. In particular, it is shown that increasing initial nutrient or phytoplankton levels can act to decrease \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Mathematical modelling and prediction in infectious disease epidemiology

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