4 a cognitive heuristic model of epidemics
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4 a cognitive heuristic model of epidemics

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4 a cognitive heuristic model of epidemics 4 a cognitive heuristic model of epidemics Presentation Transcript

  • 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, ItalyContacts: andrea.guazzini@complexworld.net emanuele.massaro@complexworld.net franco.bagnoli@complexworld.net Webpage: http://www.complexworld.net/
  • A Cognitive Heuristics model for EpidemiologySummary: • 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 EpidemiologyStandard modeling of EpidemicsEpidemic 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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology Cognitive Epidemics Modeling fundamental hypothesis A- Homogeneous Vs Multilayer/Nested/Multi-scale representation of the Network. Rigid and Fixed Unweighted Dynamical and Rewiring WeightedSymmetrical 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 AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology Cognitive Epidemics Modeling fundamental hypothesis 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 learningEnvironment 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 behaviorsEncoding Cognitive Heuristic AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology Cognitive Epidemics Modeling fundamental hypothesisC- 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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyA 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 AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyThe 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 HeuristicsWorld 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 Cognitive Heuristic model for Epidemiology A Social Cognition inspired recipe for the epidemics modelingThe 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 AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology 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 ) tEncounter 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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology 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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology A Social Cognition inspired recipe for the The Timescaling: epidemics modeling Ht 1 - H t2 Encounters/Infection PhasePi|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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for Epidemiology 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 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyA Social Cognition inspired recipe Timescales The Timescaling: (A) (SE) (R) (I) for the epidemics modeling > > > ReproductionEvolution PhaseReproduction 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) = RandomDeath (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) AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyPreliminary Results AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyPreliminary Results AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyPreliminary Results AWASS 2012 Edinburg 10th-16th June
  • A Cognitive Heuristic model for EpidemiologyA 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 Edinburg 10th-16th June