Abstract Spatially explicit models have become widely used in today's mathematical ecology and epidemiology to study the persistence of populations. For simplicity, population dynamics is often analysed by using ordinary differential equations (ODEs) or partial differential equations (PDEs) in the one-dimensional (1D) space. An important question is to predict species extinction or persistence rate by mean of computer simulation based on the spatial model. Recently, it has been reported that stable turbulent and regular waves are persistent based on the spatial susceptible--infected--resistant--susceptible (SIRS) model by using the cellular automata (CA) method in the two-dimensional (2D) space [Proc. Natl. Acad. Sci. USA 101, 18246 (2004)]. In this paper, we address other important issues relevant to phase transitions of epidemic persistence. We are interested in assessing the significance of the risk of extinction in 1D space. Our results show that the 2D space can considerably increase the possibility of persistence of spread of epidemics when the degree distribution of the individuals is uniform, i.e. the pattern of 2D spatial persistence corresponding to extinction in a 1D system with the same parameters. The trade-offs of extinction and persistence between the infection period and infection rate are observed in the 1D case. Moreover, near the trade-off (phase transition) line, an independent estimation of the dynamic exponent can be performed, and it is in excellent agreement with the result obtained by using the conjectured relationship of directed percolation. We find that the introduction of a short-range diffusion and a long-range diffusion among the neighbourhoods can enhance the persistence and global disease spread in the space.
Received: 25 March 2008
Revised: 18 September 2008
Accepted manuscript online:
PACS:
87.23.Cc
(Population dynamics and ecological pattern formation)
Zheng Zhi-Zhen(郑智贞) and Wang Ai-Ling(王爱玲) Phase transitions in cellular automata models of spatial susceptible--infected--resistant--susceptible epidemics 2009 Chin. Phys. B 18 489
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
