4 a cognitive heuristic model of epidemics

A Cognitive Heuristic model for
Epidemics Modelling
A. Guazzini*
Department of Psychology, University of Florence
*: CSDC, Centre for the study of Complex Dynamics,
University of Florence, Italy

Contacts: andrea.guazzini@complexworld.net
emanuele.massaro@complexworld.net
franco.bagnoli@complexworld.net Webpage: http://www.complexworld.net/

A Cognitive Heuristics model for Epidemiology

Summary:

• Infections vs Behavior, the complex interactions that make Epidemics an interesting
problem.
• The Cognitive Skills that make us smart and effective Infection Avoiders
• The Human Cognitive Heuristics: an operative deﬁnition of the module II
• A new operative framework for the modeling of Human Cognitive Heuristics:The
tri-partite model
• The challenge: ....................
• A minimal description of a cognitive inspired agent
• Numerical simulations: the recipe
• Results
• A step forward
• Some Open Problems ....

AWASS 2012
Edinburg 10th-16th June

A Cognitive Heuristic model for Epidemiology

Standard modeling of Epidemics

Epidemic diffusion is usually modeled by means of spreading processes acting
within networks with a given (frequently complex) topology.

Such approaches have proven to be quite effective for the forecasting of
“simple/typical” diseases, such as the seasonal ﬂu.

AWASS 2012


Cognitive Epidemics Modeling
fundamental hypothesis

A- Homogeneous Vs Multilayer/Nested/Multi-scale representation of the Network.

Rigid and Fixed Unweighted Dynamical and Rewiring Weighted
Symmetrical Lattice Like Networks and Asymmetrical Networks
Topology affects:

- Spreading of Viruses, Information, Money and Strategies

- Economical aspects such as the “Value of an Encounter”

- The selection and reproduction of the agents/strategies
Time evolution of number of
infected agents of an classical
“SIR” model on different
networks topologies

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B- “Rigid” and “Passive” nodes Vs “Smart” and “Adapting” agents

Encoding

A coherent and ecological approach to make an
agent cognitive should consider:
Decision
Making
- A bounded memory/knowledge
- An economic principle driving the learning
Environment Action - An evolution/diffusion of the (best) strategies

Learning

Knowledge A Cognitive Agent should provide:

Exp. Gain - Sensitivity to the environmental conditions
Decision Making
- Spontaneous evolution of new strategies
Exp. Risk - Adaptive and coherent behaviors
Encoding
Cognitive
Heuristic

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C- Multiple Time Scaling of the Epidemics Phenomena

- The typical Timescale of the Virus depends on:
- Infectious rate
(v) - Death rate
⌧i - Mutation rate
- Spontaneous infectious rate, etc..

- The Timescale of the Agents
- Learning dynamics,
(a) - Strategies evolution,
⌧i - Reproduction,
- Lifetime, etc ...

- The Timescale of the Network
- Information spreading,
(n)
⌧i - Diffusion rate of the epidemic
- Economical cycles, etc....

AWASS 2012


A new operative framework for the modeling of Human Cognitive Heuristics:
The tri-partite model

Reaction time

Module I Flexibility
Unconscious knowledge
perceptive and attentive processes
Cognitive costs
Relevance Heuristic

Module II
Reasoning
Goal Heuristic
External Recognition Heuristic
Solve Heuristic
Data

Module III
Learning
Behavior
Evaluation Heuristic

The minimal structure of a Self Awareness
cognitive agent

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The Human Cognitive Heuristics: an operative deﬁnition

Using the theoretical tools of the Cognitive Neurosciences, Community Recognition/Deﬁnition and Community
Detection can be designed as the ability of the cognitive system to extract relevant information from the
environment, creating Prototypes (Mental Schemes) of Perceptive/knowledge Information Pattern

Prototype of Cognitive Heuristics

World Perception Gate Standard Neural
Cognitive Prototype Reasoning
Network Module (Mental Scheme-A)
I1 P1
w1,1
A1 Relevance/Coherence
Conscious Processing
Assessment
I2 P2 w.,2 A2 K1
w2,1
. Neuro . . K2
. Biology w2,n(K)
. wn(i),2 . .
of wn(a),2
. Encoding . w.,n(a) . Kn(K)
. Pn(i) An(a)
wn(i),n(a)
.
. k1 wn(k),n(a)
The Mental Scheme are
. k2 activated by the inputs and
. changes the representation of
IN Kn(k) the environment

Bounded Knowledge AWASS 2012 Bounded Knowledge
that integrates the Edinburg 10th-16th June that represents the
Input Input


A Social Cognition inspired recipe for the
epidemics modeling
The Environment
- Topology of the network (i.e. Weighted directed Random network)
- Viruses’ Features (e.g. Infectious Rate, Death Rate, Spontaneous Infectious Rate)
- Economical Features (e.g.Value Function, Gain Function)
- Informational Features (e.g. Media!!)

The Agent
- Bounded Knowledge/Memory
- A function of ﬁtness
- Adaptive Cognitive Strategy of decision making

The Timescaling

- Encounters/Infection Phase (i.e Decision Phase)
- Economical Phase (i.e Fitness Estimation Phase)
- Learning/Genetic Phase (i.e Reproduction phase)
Time

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A Social Cognition inspired recipe for the The Environment
epidemics modeling

Topology of the network Viruses’ Features
%% PHASE 0: Network Structure
Topology=rand(N,N); % Virus
Mean_connectivity=30; %N
Topology=Topology<Mean_connectivity/N; SIr=Prob(1); % Spontaneous infectious rate
Ir=Prob(2); % Infectious rate
for i=1:N,
for j=i:N, Dr=Prob(3); % Death rate
Topology(i,j)=Topology(j,i); Itime=#Steps; % Incubation time
end
end Etime=#Steps; % Expression time
Rtime=#Steps; % Resilience time
Weighted undirected Random network with k=30

Economical Features Informational Features
P ⇤ X
i Ci H1 = fA (
t t
Ii )
t
Encounter Value
Function Vet = e P ⇤ i
i ⇥ Ki
Where:
t The state of the subject i at time t
Where:
I i (1 if infected and 0 if sane)
⇤
Ci t t Functions that describe the
e Set the maximum possible gain (here 2) Total number of encounters made by i
fA , gA Media Behavior (Trustability)
Ki Degree of the node (connectivity) t
X X
⇤ ⇤
t⇤ ⇤
⌧ Ci =
Typical economical period (days)
⇤
=t t0 t⇤ =t0 j
Cij t
H2 = gA (Vet
t
)

AWASS 2012


A Social Cognition inspired recipe for the The Agent
epidemics modeling

Fitness Function Bounded Knowledge/Memory
⇤
⇤ Ci t
Mij = t 1
Mij m1 + Ij (1
t
m1 )
Gain Function Gi = Vet
⇤K
i ˜t ˜t
H2 = H2 1
m2 + gA (Vet
t
)(1
⇤
m2 )
if
Where: Encounter X
⇤
˜t ˜t
H 1 = H1 1
m2 + fA (
t
Ii )(1
t
m2 )
Ki Degree of the node (connectivity) Ci Total number of encounters made by i
i
t
X X Iit
⌧ ⇤ Typical economical period (days) Ci =
⇤
t⇤
Cij
The state of the subject i at time t (1 if infected and 0 if sane)
Mij 2 (0, 1)
t
Memory Matrix of past encounters: 0-Safe 1-Dangerous
⇤
= t t0 t⇤ =t0 j m1 , m2 2 (0, 1) Agent Memory Factors (Past Encounters and MEDIA)

Adaptive Cognitive Strategy of decision making
Cognitive
CDNAt

˜1 ˜2
i

The agent strategy is represented by a
vector (e.g. Cognitive DNA) where the
t
Pi|j = exp(Mij 1 (i)
t t
+H t
2 (i)
t
+H t
3 (i))
t
three evolving components weight the
three informational sources.

!
c
DN At = [ 1;
t
2;
t
3]
t
1 (i), 2 (i), 3 (i) are dynamically evolved by a Montecarlo Method:
i t t t
Where:

AWASS 2012


A Social Cognition inspired recipe for the The Timescaling:
epidemics modeling Ht 1 - H t2 Encounters/Infection Phase

Pi|j = exp(Mij
t t
1 (i)
t ˜t
+ H1 2 (i)
t ˜t
+ H2 3 (i))
t
Pj|i = exp(Mji
t t
1 (j)
t ˜t
+ H1 2 (j)
t ˜t
+ H2 3 (j))
t
IF
t t t
Pi|j Pj|i <
i j
Encounter
t
2 (0, 1)
Possible Cases
(SIR Models)
Uniformly distributed random variable
A- Both the agents are expressing the disease
- The encounter is forbidden (e.g. the Gain is not increased)
- Memory Updating: The trustability factors (Mtij e Mtji) are increased (Trustable=0, Untrastable=1)

B- Both the agents are sane
- The encounter is possible (e.g. the Gain is always increased if the encounter happens)
- Memory Updating: The trustability factors (Mtij e Mtji) are increased (Trustable=0, Untrastable=1)

C- Only one agent is Infective but not Expressing the disease
- The encounter is possible (e.g. the Gain is always increased if the encounter happens)
- Memory Updating: The trustability factor Mtij is decrease if i get no the infection, and is
increased alternatively (Trustable=0, Untrastable=1)

AWASS 2012


A Social Cognition inspired recipe for the The Timescaling:
epidemics modeling Economical Phase
Sane
Infected Every Economical Temporal Step the following recipe is
applied to compute the agents’ “gain”
$
Expressing $

X P ⇤
i Ci
$
Encounter Value
Function Vet = e P ⇤
Resilient i ⇥ Ki
⇤
⇤ Ci
Ki Degree of the node (connectivity)
⇤
Gain Function Gi = Vet
⇤K
⌧ Typical economical period (days)
i
⇤
=t t0
⇤
Ci Total number of encounters made by i
t
X X
Ci =
⇤
t⇤
Cij Finally the agents are sorted with respect to their
t⇤ =t0 j “richness” (i.e. ﬁtness)

AWASS 2012


A Social Cognition inspired recipe Timescales
The Timescaling:
(A) (SE) (R) (I)
for the epidemics modeling > > > ReproductionEvolution Phase
Reproduction Control Parameter: Birthrate R(B) Strategies Evol. Control Parameter: Crossing Over C (O)
(R) (R) (SE) An Uniformly distributed
8(i, j) : G(i,j) > M e(G ) Where Me is the Median 8 #s (i, j)
t
variable C(O) is generated

#s (i, j) = |( (R) ⇥(R(B) ) ) + R | IF (O) 1
t t (B)
C < c
DN A 3
=c DN A S(i,j) i
1 2
(R) Gaussian Noise with Mean=0 and SD=1
3
< C (O) <
3
c
DN AS(i,j) =c DN Aj
Births Standard Deviation
R(B) 2
#t (i, j) Number of son of the couple (i,j) at time t
s
C (O)
>
3
c
DN AS(i,j) = Random

Death (Infection) Control Parameter: Deathrate R(D) Death (Aging) Control Parameter: Critical Age A(C)
t
(I)
8 i Given Ai Age of the agent i

(I) Average time duration
8 i : Ii =1 ⌧ of infection (A) Gaussian Noise with Mean A
(C)
and SD (A(C) )
t t
With probability P1 = R (D) The Agent Dies
IF Ai > (A)
Agent Dies

Where
(A)
= A(C)
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Preliminary Results

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A step forward: Some open problems

- Role of the network topology on the evolution of the system.

- Description of the Strategies evolution dynamics, with particular
attention toward the social segregation and the equilibrium “Mixtures”.

- Role of the Virus parameters on the equilibrium state of the system

- Role of the Media Trustability Functions (f() and g()) on the system
dynamics

- Real Vs Simulated scenarios.

AWASS 2012

4 a cognitive heuristic model of epidemics

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Editor's Notes