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Velocity of front propagation in the epidemic model A+B \(\rightarrow\) 2A

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Abstract

We study front propagation in the irreversible epidemic model A+B \(\rightarrow\) 2A in one dimension with initially separated A and B, which diffuse with rates D A and D B respectively and B gets converted by neighbouring A with rate ϵ. We find analytic estimates for the front velocity by writing truncated master equation in the frame moving with the leading A particle. The results obtained are in reasonable agreement with simulation results and are amenable to systematic improvement. We observe a crossover from the linear dependence of front velocity V on D A for smaller values of D A which, for D A ≫ ϵ becomes independent of D A . For D A = D B , macroscopic description for the process is given by Fisher equation and one expects to get mean field dependence (V ~ \(\sqrt{D_A}\)) in the reaction controlled limit, i.e. D A \(\rightarrow\) ∞. However, the observed dependence of V on D A in the limit D A \(\rightarrow\) ∞ rules out such convergence to the naive mean field results.

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Authors and Affiliations

  1. Institute of Physics, Sachivalaya Marg, 751005, Bhubaneswar, India

    Niraj Kumar & Goutam Tripathy

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  1. Niraj Kumar
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  2. Goutam Tripathy
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Correspondence to Niraj Kumar.

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Kumar, N., Tripathy, G. Velocity of front propagation in the epidemic model A+B \(\rightarrow\) 2A. Eur. Phys. J. B 78, 201–205 (2010). https://doi.org/10.1140/epjb/e2010-90977-6

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  • DOI: https://doi.org/10.1140/epjb/e2010-90977-6

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