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Wilson renormalization of a reaction–diffusion process

Author

Listed:
  • van Wijland, F.
  • Oerding, K.
  • Hilhorst, H.J.

Abstract

Healthy and sick individuals (A and B particles) diffuse independently with diffusion constants DA and DB. Sick individuals upon encounter infect healthy ones (at rate k), but may also spontaneously recover (at rate 1/τ). The propagation of the epidemic therefore couples to the fluctuations in the total population density. Global extinction occurs below a critical value ρc of the spatially averaged total density. The epidemic evolves as the diffusion–reaction–decay process A+B→2B,B→A, for which we write down the field theory. The stationary-state properties of this theory when DA=DB were obtained by Kree et al. The critical behavior for DADB remains unsolved.

Suggested Citation

  • van Wijland, F. & Oerding, K. & Hilhorst, H.J., 1998. "Wilson renormalization of a reaction–diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(1), pages 179-201.
    • Handle: RePEc:eee:phsmap:v:251:y:1998:i:1:p:179-201
    DOI: 10.1016/S0378-4371(97)00603-1
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    Cited by:

    1. Ilnytskyi, Jaroslav & Pikuta, Piotr & Ilnytskyi, Hryhoriy, 2018. "Stationary states and spatial patterning in the cellular automaton SEIS epidemiology model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 241-255.
    2. dos Santos, Renato Vieira & da Silva, Linaena Méricy, 2015. "Discreteness induced extinction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 17-25.
    3. Ren, F. & Zheng, B. & Lin, H. & Wen, L.Y. & Trimper, S., 2005. "Persistence probabilities of the German DAX and Shanghai Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 439-450.

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