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Some methods of statistical mechanics applied to ecological phenomena such as the spread of epidemics and abrupt transitions in bacterial dynamics are explained. They have been developed in close association with observations and have met with palpable success. Tethered random walks and coupled Fisher equations are the primary entities described, and propagation of the Hantavirus epidemic is among the phenomena addressed. Among notable results are certain remakable non-monotonic dependences of the transmission of infection on key parameters and an explanation of the formation of refugia based on bifurcations. Several exact calculations and some strategic approximation procedures characterize this chapter.

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Some Statistical Mechanics Techniques for Ecology: Random Walks for Epidemics Spread and Kinetic Equations for Patchiness

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  • 发表日期：

    2026年

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  • V. M. Kenkre

摘要

Some methods of statistical mechanics applied to ecological phenomena such as the spread of epidemics and abrupt transitions in bacterial dynamics are explained. They have been developed in close association with observations and have met with palpable success. Tethered random walks and coupled Fisher equations are the primary entities described, and propagation of the Hantavirus epidemic is among the phenomena addressed. Among notable results are certain remakable non-monotonic dependences of the transmission of infection on key parameters and an explanation of the formation of refugia based on bifurcations. Several exact calculations and some strategic approximation procedures characterize this chapter.