#
Effects of Levy Flights Mobility
Pattern on Epidemic Spreading

Most
of the studies on human and animal mobility pattern including experimental data
and theoretic analysis found that their mobility pattern follows the Levy
flight:

Epidemic spreading processes always follow the mobility of human and animal. In this article,

### Spatial Network Model

__Energy__

The frequency distribution of sum of walk distances in a day for deer and sheep. Both distribution are vary narrow, which represents the energy distribution is homogenous.

__Network Model__

Based on a

__uniform cycle__, each node denotes a small group of people. Given a restriction on total energy, we get a one-dimensional weighted network with a Levy flight spatial structure. According to levi flight pattern (P(d) ~ d

^{alpha}), the weight w

_{ij}on the link between node i and j should be proportional to d

_{ij}

^{alpha}, and for a given network size, the sum of all w

_{ij}d

_{ij}should be a constant which denotes the energy constraint. So, we can get an ensemble network model of these spatial weighted networks generated by many times of realization as:

=>

__Diffusion__

On this weighted network, the infected probability is related with the weight.

where v is the spreading ratio, and I is the set of infected nodes.

##

Randomly choose one node as an infected individual, others are susceptible.

Terminate until all the nodes are infected and register the steps have been taken as T .

##
**SI Model**

Randomly choose one node as an infected individual, others are susceptible. Terminate until all the nodes are infected and register the steps have been taken as T .

__Epidemic spreading speed with different exponents__The figure alongside is for

__n = 1000, V = 0.05.__

The curve has a lowest point when

*alpha*~ 2.

This imples that the mobility pattern will drive the epidemic diffusion.

__Spread ratio under different__*alpha*and various network size nThe dependence of spread ratio on time under different

*alpha*.

A. Spread ratio under

*alpha*= 0 and alpha = −1, respectively.

B. Spread ration under = −2. We can see that when

*alpha*= −2, the spread ratio grows much faster than other cases.

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