Figure 9.4 (a and b)
---------------------------

:download:`Downloadable Source Code <fig9p4.py>` 

.. image:: fig9p4a.png
    :width: 45 %
.. image:: fig9p4b.png
    :width: 45 %

::

    import EoN
    import networkx as nx
    import matplotlib.pyplot as plt
    import random
    import scipy
    
    print("for figure 9.4, we have not yet coded up the system of equations, so this just gives simulations")
    
    r'''We use a large value of N and only a single iteration.  The code is 
    similar to fig 9.2's code, but the loops are structured a little differently.
    
    We loop over graph type first.
    then we loop over kave.
    '''
    
    N = 100000
    n = 10
    gamma = 1./5.5
    tau = 0.55
    iterations = 1
    rho = 0.001
    
    
    def rec_time_fxn(u):
        return 1
        
    def trans_time_fxn(u, v, tau):
        return random.expovariate(tau)
    
    def ER_graph_generation(N, kave):
        return nx.fast_gnp_random_graph(N, kave/(N-1.))
    def regular_graph_generation(N, kave):
        return nx.configuration_model([kave]*N)
        
    display_ts = scipy.linspace(0, 8, 41) #[0, 0.2, 0.4, ..., 7.8, 8]
    for graph_algorithm, filename in ([regular_graph_generation, 'fig9p4a.png'], [ER_graph_generation, 'fig9p4b.png']):
        plt.clf()
        for kave, symbol in ([5, 'o'], [10, 's'], [15, 'd']):
            print(kave)
            G = graph_algorithm(N, kave)    
            t, S, I, R = EoN.fast_nonMarkov_SIR(G, 
                                                    trans_time_fxn=trans_time_fxn,
                                                    trans_time_args=(tau,),
                                                    rec_time_fxn=rec_time_fxn,
                                                    rec_time_args=(),
                                                    rho=rho)
            newI = EoN.subsample(display_ts, t, I)
            plt.plot(display_ts, newI, symbol)
        plt.xlabel('$t$')
        plt.ylabel('Prevalence')
        plt.savefig(filename)