Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds

Sakisaka, Yukio; Yoshimura, Jin; Takeuchi, Yasuhiro; Sugiura, K.; Tainaka, Kei–ichi

doi:10.1143/jpsj.79.023002

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Thus we lead to the "40% criterion": when the proportion of destroyed site exceeds about 40%, species suddenly faces extinction. This criterion is also observed in other models (Sakisaka et al, 2010).…”

Section: Conclusion and Discussionsupporting

confidence: 83%

Lattice models of habitat destruction in a prey-predator system

2017

Syme, G., Hatton MacDonald, D., Fulton, B. And Piantadosi, J. (Eds) MODSIM2017, 22nd International Congress on Modelling and Si

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In recent decades, species extinction has become one of the most important issues in ecology and conservation biology. Such extinctions are mainly caused by habitat destruction. The destruction has no possibility of recovery for endangered species unless the destroyed habitat is restored. Furthermore, even if the destruction is restricted to a local area, its accumulation increases the risk of extinction. Habitat destruction not only reduces the habitat area but also fragments the habitat. In the present article, we introduce three types of destruction models. i) Bond destruction: the fragmentation occurs, but habitat area is never reduced. ii) Random site destruction: both fragmentation and area loss occur. iii) Rectangular site destruction: the habitat area is reduced, but fragmentation never occurs. We apply a lattice system composed of prey and predator, and compare the effects of the three types of habitat destructions. Simulations reveal that outcomes entirely differ for the different models. The density of prey or predator undergo complicated changes by destructions. The habitat fragmentation is much more serious for species extinction than the area loss of habitat. In our simulation, extinction only occurs for fragmentation models. For the random site destruction, we universally obtain a "40% criterion": when the proportion of destroyed sites exceed percolation transition (40%), the risk of species extinction suddenly increases. Moreover, we find an asymmetric effects on predator and prey. In all destruction models, the steady-state density of predator tends to decrease with the increase of the magnitude (D) of the destruction. In contrast, the effect on prey is rather opposite: prey density usually increases with increasing D.

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Section: Conclusion and Discussionsupporting

confidence: 83%

Lattice models of habitat destruction in a prey-predator system

2017

Syme, G., Hatton MacDonald, D., Fulton, B. And Piantadosi, J. (Eds) MODSIM2017, 22nd International Congress on Modelling and Si

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“…2g , see also Figs. S2 in SI) 17 . Therefore, we cannot expect a significant success by combining the two measures.…”

Section: Discussionmentioning

confidence: 99%

Combined effects of prevention and quarantine on a breakout in SIR model

Kato

Tainaka

Sone

et al. 2011

Sci Rep

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Recent breakouts of several epidemics, such as flu pandemics, are serious threats to human health. The measures of protection against these epidemics are urgent issues in epidemiological studies. Prevention and quarantine are two major approaches against disease spreads. We here investigate the combined effects of these two measures of protection using the SIR model. We use site percolation for prevention and bond percolation for quarantine applying on a lattice model. We find a strong synergistic effect of prevention and quarantine under local interactions. A slight increase in protection measures is extremely effective in the initial disease spreads. Combination of the two measures is more effective than a single protection measure. Our results suggest that the protection policy against epidemics should account for both prevention and quarantine measures simultaneously.

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Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

Soltani

Sadeghnejad

2018

Physica A: Statistical Mechanics and its Applications

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Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds

Cited by 3 publications

References 12 publications

Lattice models of habitat destruction in a prey-predator system

Lattice models of habitat destruction in a prey-predator system

Combined effects of prevention and quarantine on a breakout in SIR model

Scaling and critical behavior of lattice and continuum porous media with different connectivity configurations

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