7 summer solstice2012-a cognitive heuristic model of epidemics

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  • 7 summer solstice2012-a cognitive heuristic model of epidemics

    1. 1. 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 Webpage: http://www.complexworld.net/
    2. 2. A Cognitive Heuristics model for EpidemiologyCompelling features in modeling epidemics • Social structure. • Viral dynamics. • Psychological and Cognitive effects. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    3. 3. A Cognitive Heuristics model for Epidemiology The Classical Modelling of Epidemics• The simplest models of epidemics correspond to percolation problems on a social network.• The two key ingredients are the probability of infections and the viral dynamics.• The simplest viral dynamics are SIS and SIR. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    4. 4. A Cognitive Heuristics model for Epidemiology Are we still alive?• In spite of the scale-free social structure, and long-range connections, we are still alive.• Prophylaxis, fast intervention and education are valid in preventing epidemics.• How can we include these elements in a simple model? Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    5. 5. A Cognitive Heuristics model for Epidemiology Role of Perception, Alarmism and Prejudice (i.e.The cognitive Strategy)• We are able to modify our behavior, either lowering the probability of infection or reducing contacts.• These modifications are triggered by the alarm level and perception of a danger.• Both local and global information became in such scenarios fundamental. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    6. 6. 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. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    7. 7. 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 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    8. 8. 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 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    9. 9. 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.... Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    10. 10. 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 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    11. 11. 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 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    12. 12. 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 ) Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    13. 13. 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 ) 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 ˜t ˜t i The agent strategy is represented by a vector (e.g. Cognitive DNA) where the Pi|j = exp(Mij t t 1 (i) t + H1 2 (i) t + H2 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: Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    14. 14. 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 decreased (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 decreased if i get no the infection, and is increased alternatively (Trustable=0, Untrastable=1) Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    15. 15. 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) Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    16. 16. 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 sons 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) Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    17. 17. A Cognitive Heuristic model for Epidemiology Preliminary Results 5 Final Number of Infected (Seed=10) Final Number of Infected (Seed=4) Final Number of Infected 5 P=1 P=f(M) 100 P=f(H1) P=f(H2) P=f(M,H1,H2) 50Final Number of Infected 25 10 5 0.1 0.2 0.4 0.8 1 P=1 Infectious Rate P=f(M) 100 P=f(H1) Final Number of Infected (Seed=20) 5 P=f(H2) P=f(M,H1,H2) Final Number of Infected 50 P=1 P=f(M) 100 P=f(H1) P=f(H2) 25 P=f(M,H1,H2) 10 5 50 0.1 0.2 0.4 0.8 1 Infectious Rate 25 10 5 Conditions: N=225, K=30, Death Rate=0.1, Tmax=1000 0.1 0.2 0.4 Infectious Rate 0.8 1 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    18. 18. A Cognitive Heuristic model for Epidemiology Preliminary Results 1000 Relaxing Time (Seed=10) Relaxing Time (Seed=4) 1000 Time 500 P=1 200 P=f(M) P=f(H1) P=f(H2) 100 P=f(M,H1,H2) 0.1 0.2 0.4 0.8 1 Infectious RateTime 500 Relaxing Time (Seed=20) 1000 P=1 200 P=f(M) Time P=f(H1) 500 P=f(H2) 100 P=f(M,H1,H2) P=1 0.1 0.2 0.4 0.8 1 200 P=f(M) P=f(H1) Infectious Rate 100 P=f(H2) P=f(M,H1,H2) Conditions: N=225, K=30, Death Rate=0.1, Tmax=1000 0.1 0.2 0.4 Infectious Rate 0.8 1 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    19. 19. A Cognitive Heuristic model for Epidemiology Average Gain (Seed=10) Preliminary Results 20 P=1 P=f(M) P=f(H1) P=f(H2) Average Gain (Seed=4) P=f(M,H1,H2) 20 P=1 Gain 10 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) 4 2 1 0.1 0.2 0.4 0.8 1 Infectious RateGain 10 Average Gain (Seed=20) 20 P=1 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) 4 Gain 10 2 1 0.1 0.2 0.4 0.8 1 4 Infectious Rate 2 1 Conditions: N=225, K=30, Death Rate=0.1, Tmax=1000 0.1 0.2 0.4 Infectious Rate 0.8 1 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    20. 20. A Cognitive Heuristic model for Epidemiology Encounters (Seed=10) Preliminary Results 100 P=1 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) Encounters (Seed=4) 100 Encounters P=1 50 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) 20 10Encounters 0.1 0.2 0.4 0.8 1 Infectious Rate 50 Encounters (Seed=20) 100 P=1 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) Encounters 20 50 10 0.1 0.2 0.4 0.8 1 20 Infectious Rate 10 Conditions: N=225, K=30, Death Rate=0.1, Tmax=1000 0.1 0.2 0.4 0.8 1 Infectious Rate Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    21. 21. A Cognitive Heuristic model for Epidemiology Victims (Seed=10) Preliminary Results 20 P=1 P=f(M) P=f(H1) P=f(H2) Victims (Seed=4) P=f(M,H1,H2) 20 Victims P=1 10 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) 4 2 1 0.1 0.2 0.4 0.8 1Victims Infectious Rate 10 Victims (Seed=20) 20 P=1 P=f(M) P=f(H1) P=f(H2) P=f(M,H1,H2) Victims 4 10 2 1 4 0.1 0.2 0.4 0.8 1 Infectious Rate 2 1 Conditions: N=225, K=30, Death Rate=0.1, Tmax=1000 0.1 0.2 0.4 Infectious Rate 0.8 1 Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    22. 22. 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. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    23. 23. Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June... and thank you for the attention!
    24. 24. A Cognitive Heuristic model for EpidemiologyPreliminary Results Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    25. 25. A Cognitive Heuristic model for EpidemiologyPreliminary Results Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June
    26. 26. A Cognitive Heuristic model for EpidemiologyPreliminary Results Summer Solstice 2012 & Biophys 2012 Arcidosso, 26-29 June

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