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Pattern formation of a spatial epidemic model with nonlinear incidence rate hI^2 S/(1 + αI^2) is investigated. Our results show that strange spatial dynamics, i.e., filament-like pattern, can be obtained by both mathematical analysis and numerical simulation, which are different from the previous results in the spatial epidemic model such as stripe-like or spotted or coexistence of both pattern and so on. The obtained results well extend the finding of pattern formation in the epidemic model and may well explain the distribution of the infected of some epidemic. 相似文献
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This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system. 相似文献
3.
In this article, we have proposed an epidemic model based on the
probability cellular automata theory. The essential mathematical
features are analysed with the help of stability theory. We have
given an alternative modelling approach for the spatiotemporal system
which is more realistic from the practical point of view. A discrete
and spatiotemporal approach is shown by using cellular automata
theory. It is interesting to note that both the size of the endemic
equilibrium and the density of the individuals increase with the
increase of the neighbourhood size and infection rate, but the
infections decrease with the increase of the recovery rate. The
stability of the system around the positive interior equilibrium has
been shown by using a suitable Lyapunov function. Finally,
experimental data simulation for SARS disease in China in 2003 and a
brief discussion are given. 相似文献
4.
In this paper we present a model
with spatial heterogeneity based on cellular automata (CA). In the
model we consider the relevant heterogeneity of host (susceptible)
mixing and the natural birth rate. We divide the susceptible
population into three groups according to the immunity of each
individual based on the classical susceptible--infected--removed
(SIR) epidemic models, and consider the spread of an infectious
disease transmitted by direct contact among humans and vectors
that have not an incubation period to become infectious. We test
the local stability and instability of the disease-free
equilibrium by the spectrum radii of Jacobian. The simulation
shows that the structure of the nearest neighbour size of the cell
(or the degree of the scale-free networks) plays a very important
role in the spread properties of infectious disease. The positive
equilibrium of the infections versus the neighbour size follows
the third power law if an endemic equilibrium point exists.
Finally, we analyse the feature of the infection waves for the
homogeneity and heterogeneous cases respectively. 相似文献
5.
Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems 下载免费PDF全文
It has been reported that the minimal spatially extended
phytoplankton--zooplankton system exhibits both temporal
regular/chaotic behaviour, and spatiotemporal chaos in a patchy
environment. As a further investigation by means of computer
simulations and theoretical analysis, in this paper we observe that
the spiral waves may exist and the spatiotemporal chaos emerge when
the parameters are within the mixed Turing--Hopf bifurcation region,
which arises from the far-field breakup of the spiral waves over a
large range of diffusion coefficients of phytoplankton and
zooplankton. Moreover, the spatiotemporal chaos arising from the
far-field breakup of spiral waves does not gradually invade the
whole space of that region. Our results are confirmed by nonlinear
bifurcation of wave trains. We also discuss ecological implications
of these spatially structured patterns. 相似文献
6.
本文通过分析SEIRS类流行病,建立了该类疾病的二维概率细胞自动机模型。在二维中,每个细胞的状态代表易感者,潜伏者,患者,恢复者(或免疫者)和死亡者五个部分个体之一。我们研究了两种情况下,即对潜伏者和患者隔离与不隔离将对疾病转播的影响。经研究我们发现,如果不隔离疾病将持续流行,而及时的隔离则将会减缓疾病的流行。本模型给出了对具体疾病利用细胞自动进行仿真的算法。我们发现当恢复者的失去免疫力大于时,疾病潜伏者和患者的密度序列将在正平衡点附近振荡。最后,我们用计算机对模型进行了仿真。 相似文献
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