∂S(r,t)/∂t= μ-β(t)IS-μS+D_1 ∇^2 S(r,t) (2a)

∂E(r,t)/∂t=β(t)IS-(μ+δ)E+D_2 ∇^2 E(r,t) (2b)

∂I(r,t)/∂t= δE-(γ+μ)I+D_3 ∇^2 I(r,t) (2c)

∂R(r,t)/∂t=γI-μR+D_4 ∇^2 R(r,t) (2d)

Here μ is the death rate per capacity, and 1/δ and 1/γ are
the mean latent and infectious periods, respectively, of the
disease. t is the rate of disease transmission between individuals.
The population can be normalized to S+E+I+R
=1, so all dependent variables represent fractions of the
population.

can i know how to discretize the PDE?beside that how to compute the pattern fromation using mathematica?this is the PDE for model cellular automata for dengue.how to do discetization of partial diffential equationn-spatial-20organization-20and-20evolution-20period-20of-20the-20epidemic-20model-20using-20cellul.pdfClick image for larger version. 

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