Rates of Convergence for the Three State Contact Process in One Dimension
- 111 Downloads
The basic contact process with parameter μ altered so that infections of sites that have not been previously infected occur at rate proportional to λ instead is considered. Emergence of an infinite epidemic starting out from a single infected site is not possible for μ less than the contact process’ critical value, whereas it is possible for μ greater than that value. In the former case the space and time infected regions are shown to decay exponentially; in the latter case and for λ greater than μ, the ratio of the endmost infected site’s velocity to that of the contact process is shown to be at most λ/μ.
KeywordsContact processes Immunization
- 2.Andjel, E., Chabot, N., Saada, E.: A shape theorem for an epidemic model in dimension d≥3. arXiv:1110.0801 (2011)
- 5.Durrett, R.: Ten Lectures on Particle Systems. Lecture Notes in Math., vol. 1608. Springer, New York (1995) Google Scholar
- 17.Tzioufas, A.: Contact processes on the integers. Ph.D. Thesis, Heriot-Watt University (2011) Google Scholar
- 18.Tzioufas, A., Zachary, S.: Unpublished manuscript (2007) Google Scholar