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Profile Threshold
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The Profile-Threshold model was introduced in 2017 by Milli et al. [#]_.

The Profile-Threshold model assumes the existence of node profiles that act as preferential schemas for individual tastes but relax the constraints imposed by the Profile model by letting nodes influenceable via peer pressure mechanisms. 

The peer pressure is modeled with a threshold. 

The diffusion process starts from a set of nodes that have already adopted a given behaviour S:

- for each of the susceptible node an unbalanced coin is flipped if the percentage of its neighbors that are already infected excedes its threhosld. As in the Profile Model the coin unbalance is given by the personal profile of the susceptible node;
- if a positive result is obtained the susceptible node will adopt the behaviour, thus becoming infected.
- if the **blocked** status is enabled, after having rejected the adoption with probability ``blocked`` a node becomes immune to the infection.
- every iteration ``adopter_rate`` percentage of nodes spontaneous became infected to endogenous effects.

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Statuses
--------

During the simulation a node can experience the following statuses:

===========  ====
Name         Code
===========  ====
Susceptible  0
Infected     1
Blocked      -1
===========  ====

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Parameters
----------

============  =====  ===============  =======  =========  =====================
Name          Type   Value Type       Default  Mandatory  Description
============  =====  ===============  =======  =========  =====================
threshold     Node   float in [0, 1]   0.1     False      Individual threshold
profile       Node   float in [0, 1]   0.1     False      Node profile
blocked       Model  float in [0, 1]   0       False      Blocked nodes
adopter_rate  Model  float in [0, 1]   0       False      Autonomous adoption
============  =====  ===============  =======  =========  =====================

The initial infection status can be defined via:

    - **fraction_infected**: Model Parameter, float in [0, 1]
    - **Infected**: Status Parameter, set of nodes

The two options are mutually exclusive and the latter takes precedence over the former.


-------
Example
-------

In the code below is shown an example of instantiation and execution of a Profile Threshold model simulation on a random graph: we set the initial infected node set to the 10% of the overall population, assign a profile of 0.25 and a threshold of 0.15 to all the nodes.

.. code-block:: python

    import networkx as nx
    import ndlib.models.ModelConfig as mc
    import ndlib.models.epidemics as ep

    # Network topology
    g = nx.erdos_renyi_graph(1000, 0.1)

    # Model selection
    model = ep.ProfileThresholdModel(g)
    config = mc.Configuration()
    config.add_model_parameter('blocked', 0)
    config.add_model_parameter('adopter_rate', 0)
    config.add_model_parameter('fraction_infected', 0.1)

    # Setting nodes parameters
    threshold = 0.15
    profile = 0.25
    for i in g.nodes():
        config.add_node_configuration("threshold", i, threshold)
        config.add_node_configuration("profile", i, profile)
    
    model.set_initial_status(config)

    # Simulation execution
    iterations = model.iteration_bunch(200)
    
.. [#] Letizia Milli, Giulio Rossetti, Dino Pedreschi, Fosca Giannotti, “Information Diffusion in Complex Networks: The Active/Passive Conundrum,” Proceedings of International Conference on Complex Networks and their Applications, (pp. 305-313). Springer, Cham. 2017