Continuos time

docs/reference/models/epidemics/SEIR.rst

@@ -1,6 +1,6 @@
-****
-SEIR
-****
+*********
+SEIR (DT)
+*********
 
 
 In the SEIR model [#]_, during the course of an epidemics, a node is allowed to change its status  from **Susceptible** (S) to **Exposed** (E) to **Infected** (I), then to **Removed** (R).
@@ -9,6 +9,7 @@ The model is instantiated on a graph having a non-empty set of infected nodes.
 
 SEIR assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch to removed with probability gamma (the only transition allowed are S→E→I→R).
 
+This implementation assumes discrete time dynamics for the E->I  and I->R transitions.
 
 --------
 Statuses

docs/reference/models/epidemics/SEIR_ct.rst

@@ -0,0 +1,108 @@
+*********
+SEIR (CT)
+*********
+
+
+In the SEIR model [#]_, during the course of an epidemics, a node is allowed to change its status  from **Susceptible** (S) to **Exposed** (E) to **Infected** (I), then to **Removed** (R).
+
+The model is instantiated on a graph having a non-empty set of infected nodes.
+
+SEIR assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch to removed with probability gamma (the only transition allowed are S→E→I→R).
+
+This implementation assumes continuous time dynamics for the E->I and I->R transitions.
+
+--------
+Statuses
+--------
+
+During the simulation a node can experience the following statuses:
+
+===========  ====
+Name         Code
+===========  ====
+Susceptible  0
+Infected     1
+Exposed		 2
+Removed      3
+===========  ====
+
+----------
+Parameters
+----------
+
+=====  =====  ===============  =======  =========  =====================
+Name   Type   Value Type       Default  Mandatory  Description
+=====  =====  ===============  =======  =========  =====================
+beta   Model  float in [0, 1]           True       Infection probability
+gamma  Model  float in [0, 1]           True       Removal probability
+alpha  Model  float in [0, 1]           True       Latent period
+=====  =====  ===============  =======  =========  =====================
+
+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.
+
+-------
+Methods
+-------
+
+The following class methods are made available to configure, describe and execute the simulation:
+
+^^^^^^^^^
+Configure
+^^^^^^^^^
+.. autoclass:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.__init__(graph)
+
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.set_initial_status(self, configuration)
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.reset(self)
+
+^^^^^^^^
+Describe
+^^^^^^^^
+
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.get_info(self)
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.get_status_map(self)
+
+^^^^^^^^^^^^^^^^^^
+Execute Simulation
+^^^^^^^^^^^^^^^^^^
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.iteration(self)
+.. automethod:: ndlib.models.epidemics.SEIR_ct_Model.SEIRctModel.iteration_bunch(self, bunch_size)
+
+
+-------
+Example
+-------
+
+In the code below is shown an example of instantiation and execution of an SEIR simulation on a random graph: we set the initial set of infected nodes as % of the overall population, a probability of infection of 1%, a removal probability of 0.5% and an incubation period of 5% (e.g. 20 iterations).
+
+.. 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.SEIRctModel(g)
+
+    # Model Configuration
+    cfg = mc.Configuration()
+    cfg.add_model_parameter('beta', 0.01)
+    cfg.add_model_parameter('gamma', 0.005)
+    cfg.add_model_parameter('alpha', 0.05)
+    cfg.add_model_parameter("fraction_infected", 0.05)
+    model.set_initial_status(cfg)
+
+    # Simulation execution
+    iterations = model.iteration_bunch(200)
+
+
+
+.. [#] J.L. Aron and I.B. Schwartz. Seasonality and period-doubling bifurcations in an epidemic model. Journal Theoretical Biology, 110:665-679, 1984

docs/reference/models/epidemics/SEIS.rst

@@ -1,6 +1,6 @@
-****
-SEIS
-****
+*********
+SEIS (DT)
+*********
 
 
 In the SEIS model, during the course of an epidemics, a node is allowed to change its status  from **Susceptible** (S) to **Exposed** (E) to **Infected** (I), then again to **Susceptible** (S).
@@ -9,6 +9,7 @@ The model is instantiated on a graph having a non-empty set of infected nodes.
 
 SEIS assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch back to susceptible with probability lambda (the only transition allowed are S→E→I→S).
 
+This implementation assumes discrete time dynamics for the E->I  and I->S transitions.
 
 --------
 Statuses

docs/reference/models/epidemics/SEIS_ct.rst

@@ -0,0 +1,106 @@
+*********
+SEIS (CT)
+*********
+
+
+In the SEIS model, during the course of an epidemics, a node is allowed to change its status  from **Susceptible** (S) to **Exposed** (E) to **Infected** (I), then again to **Susceptible** (S).
+
+The model is instantiated on a graph having a non-empty set of infected nodes.
+
+SEIS assumes that if, during a generic iteration, a susceptible node comes into contact with an infected one, it becomes infected after an exposition period with probability beta, than it can switch back to susceptible with probability lambda (the only transition allowed are S→E→I→S).
+
+This implementation assumes continuous time dynamics for the E->I  and I->S transitions.
+
+--------
+Statuses
+--------
+
+During the simulation a node can experience the following statuses:
+
+===========  ====
+Name         Code
+===========  ====
+Susceptible  0
+Infected     1
+Exposed		 2
+===========  ====
+
+----------
+Parameters
+----------
+
+======  =====  ===============  =======  =========  =====================
+Name    Type   Value Type       Default  Mandatory  Description
+======  =====  ===============  =======  =========  =====================
+beta    Model  float in [0, 1]           True       Infection probability
+lambda  Model  float in [0, 1]           True       Removal probability
+alpha   Model  float in [0, 1]           True       Latent period
+======  =====  ===============  =======  =========  =====================
+
+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.
+
+-------
+Methods
+-------
+
+The following class methods are made available to configure, describe and execute the simulation:
+
+^^^^^^^^^
+Configure
+^^^^^^^^^
+.. autoclass:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.__init__(graph)
+
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.set_initial_status(self, configuration)
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.reset(self)
+
+^^^^^^^^
+Describe
+^^^^^^^^
+
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.get_info(self)
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.get_status_map(self)
+
+^^^^^^^^^^^^^^^^^^
+Execute Simulation
+^^^^^^^^^^^^^^^^^^
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.iteration(self)
+.. automethod:: ndlib.models.epidemics.SEIS_ct_Model.SEISctModel.iteration_bunch(self, bunch_size)
+
+
+-------
+Example
+-------
+
+In the code below is shown an example of instantiation and execution of an SEIS simulation on a random graph:
+we set the initial set of infected nodes as 5% of the overall population, a probability of infection of 1%, a removal probability of 0.5% and an latent period of 5% (e.g. 20 iterations).
+
+.. 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.SEISctModel(g)
+
+    # Model Configuration
+    cfg = mc.Configuration()
+    cfg.add_model_parameter('beta', 0.01)
+    cfg.add_model_parameter('lambda', 0.005)
+    cfg.add_model_parameter('alpha', 0.05)
+    cfg.add_model_parameter("fraction_infected", 0.05)
+    model.set_initial_status(cfg)
+
+    # Simulation execution
+    iterations = model.iteration_bunch(200)
+
+

docs/reference/reference.rst

@@ -39,7 +39,9 @@ In ``NDlib`` are implemented the following **Epidemic** models:
    models/epidemics/SIS.rst
    models/epidemics/SIR.rst
    models/epidemics/SEIR.rst
+   models/epidemics/SEIR_ct.rst
    models/epidemics/SEIS.rst
+   models/epidemics/SEIS_ct.rst
    models/epidemics/SWIR.rst
    models/epidemics/Threshold.rst
    models/epidemics/GeneralisedThreshold.rst

ndlib/models/epidemics/SEIRModel.py

@@ -46,8 +46,6 @@ def __init__(self, graph, seed=None):
             "edges": {},
         }
 
-        self.progress = {}
-
     def iteration(self, node_status=True):
         self.clean_initial_status(self.available_statuses.values())
 
@@ -79,18 +77,15 @@ def iteration(self, node_status=True):
                 if self.params['model']['tp_rate'] == 1:
                     if eventp < 1 - (1 - self.params['model']['beta']) ** len(infected_neighbors):
                         actual_status[u] = 2  # Exposed
-                        self.progress[u] =  self.actual_iteration # save time of exposure t_i
                 else:
                     if eventp < self.params['model']['beta'] * triggered:
                         actual_status[u] = 2  # Exposed
-                        self.progress[u] =  self.actual_iteration # save time of exposure t_i
 
             elif u_status == 2:
 
                 # apply prob. of infection, after (t - t_i) 
-                if eventp < 1 - np.exp(- (self.actual_iteration - self.progress[u]) * self.params['model']['alpha']): 
+                if eventp < self.params['model']['alpha']:
                     actual_status[u] = 1  # Infected
-                    del self.progress[u]
 
             elif u_status == 1:
                 if eventp < self.params['model']['gamma']: