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Stochastic spatial structured model for vertically and horizontally transmitted infection

Author

Listed:
  • Silva, Ana T.C.
  • Assis, Vladimir R.V.
  • Pinho, Suani T.R.
  • Tomé, Tânia
  • de Oliveira, Mário J.

Abstract

We study a space structured stochastic model for vertical and horizontal transmitted infection. By means of simple and pair mean-field approximation as well as Monte Carlo simulations, we construct the phase diagram, which displays four states: healthy (H), infected (I), extinct (E), and coexistent (C). In state H only healthy hosts are present, whereas in state I only infected hosts are present. The state E is characterized by the extinction of the hosts whereas in state C there is a coexistence of infected and healthy hosts. In addition to the usual scenario with continuous transition between the I, C and H phases, we found a different scenario with the suppression of the C phase and a discontinuous phase transition between I and H phases.

Suggested Citation

  • Silva, Ana T.C. & Assis, Vladimir R.V. & Pinho, Suani T.R. & Tomé, Tânia & de Oliveira, Mário J., 2017. "Stochastic spatial structured model for vertically and horizontally transmitted infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 131-138.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:131-138
    DOI: 10.1016/j.physa.2016.10.048
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    References listed on IDEAS

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    1. de Souza, David R. & Tomé, Tânia, 2010. "Stochastic lattice gas model describing the dynamics of the SIRS epidemic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1142-1150.
    2. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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