Computational models and optimal control strategies for emotion contagion in the human population in emergencies

Emotions play an important role in the decision-making of individuals. Emotional contagion has an influence on individual and group-level behaviors. Particularly, the contagion of negative emotions like panic emotions may result in devastating consequences in the human population in emergencies. This work develops novel computational models of emotion contagion and solves the optimal control problem of emotion contagion in the human population in emergencies. Firstly, by introducing a concept of latent state and considering complicated interactions among individuals, we develop a novel conceptual model of emotion contagion, and further establish a computational model for describing the dynamics of emotion contagion, called the susceptible-latent-infectious-recovered-susceptible (SLIRS) model. Secondly, by considering vaccination, quarantine and treatment as control measures, we expand the SLIRS model into a controlled SLIRS model, and formulate the control problem of emotion contagion as an optimal control problem, so that the total costs of inhibiting emotion contagion are minimized. Finally, we theoretically discuss the existence and uniqueness of the solution of the controlled SLIRS model, and further derive an optimal control solution of the controlled SLIRS model. The simulation results on the synthesis dataset and the real trace dataset show that the optimal control strategies have significant impact on emotion contagion. Especially, the optimal control strategy with a mixture of vaccination, quarantine and treatment can significantly decrease the scale of the outbreak of negative emotions, and incur the lowest total costs of inhibiting emotion contagion. This enables the optimal decision-making for inhibiting emotion contagion under the consideration of limited resources in the human population in emergencies. Hence, this work will make contributions to crisis management and crowd evacuation in emergencies.

[1]  Jiajia Wang,et al.  Sentiment contagion in complex networks , 2014 .

[2]  Alex Gorod,et al.  A Socio-Physical Approach to Systemic Risk Reduction in Emergency Response and Preparedness , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[3]  Michel C. A. Klein,et al.  Modelling collective decision making in groups and crowds: Integrating social contagion and interacting emotions, beliefs and intentions , 2013, Autonomous Agents and Multi-Agent Systems.

[4]  Yi Pan,et al.  Reaction-diffusion modeling of malware propagation in mobile wireless sensor networks , 2013, Science China Information Sciences.

[5]  Hamido Fujita,et al.  Intelligent human interface based on mental cloning-based software , 2009, Knowl. Based Syst..

[6]  Duoyong Sun,et al.  Agent-based simulation research on group emotion evolution of public emergency , 2014, 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2014).

[7]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[8]  Huang Peng.  Study of Panic Behavior Model for Crowd on Pedestrian Bridge in Emergent Event , 2012 .

[9]  Joy Kuri,et al.  How to run a campaign: Optimal control of SIS and SIR information epidemics , 2014, Appl. Math. Comput..

[10]  Ilias Sakellariou,et al.  Experiments with Emotion Contagion in Emergency Evacuation Simulation , 2014, WIMS '14.

[11]  Boris A. Galitsky.  A computational simulation tool for training autistic reasoning about mental attitudes , 2013, Knowl. Based Syst..

[12]  Oluwole Daniel Makinde,et al.  Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives , 2013 .

[13]  Daqing Jiang,et al.  Threshold behaviour of a stochastic SIR model , 2014 .

[14]  Siuming Lo,et al.  Qualitative simulation of the panic spread in large-scale evacuation , 2012, Simul..

[15]  Amit Konar,et al.  General and Interval Type-2 Fuzzy Face-Space Approach to Emotion Recognition , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Carlos Busso,et al.  Iterative Feature Normalization Scheme for Automatic Emotion Detection from Speech , 2013, IEEE Transactions on Affective Computing.

[17]  Xiaofan Yang,et al.  Modeling and analysis of the spread of computer virus , 2012 .

[18]  Michael Inzlicht,et al.  Dispositional mindfulness and the attenuation of neural responses to emotional stimuli. , 2013, Social cognitive and affective neuroscience.

[19]  Hui Lin,et al.  Agent-based simulation of building evacuation: Combining human behavior with predictable spatial accessibility in a fire emergency , 2015, Inf. Sci..

[20]  Vasanthan Raghavan,et al.  Modeling Temporal Activity Patterns in Dynamic Social Networks , 2013, IEEE Transactions on Computational Social Systems.

[21]  Boris A. Galitsky.  Exhaustive simulation of consecutive mental states of human agents , 2013, Knowl. Based Syst..

[22]  Emiliano Lorini,et al.  Computational Modeling of Emotion: Toward Improving the Inter- and Intradisciplinary Exchange , 2013, IEEE Transactions on Affective Computing.

[23]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[24]  Ilias Sakellariou,et al.  A Formal Approach to Model Emotional Agents Behaviour in Disaster Management Situations , 2014, SETN.

[25]  Tibor Bosse,et al.  Agent-Based Modeling of Emotion Contagion in Groups , 2015, Cognitive Computation.

[26]  Lijuan Chen,et al.  Global stability and optimal control of an SIRS epidemic model on heterogeneous networks , 2014 .

[27]  Weiguo Song,et al.  Simulation of emotional contagion using modified SIR model: A cellular automaton approach , 2014 .

[28]  N. Bairagi,et al.  Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay☆ , 2014 .

[29]  Chenquan Gan,et al.  A propagation model of computer virus with nonlinear vaccination probability , 2014, Commun. Nonlinear Sci. Numer. Simul..

[30]  Julien Saunier,et al.  Mixed agent/social dynamics for emotion computation , 2014, AAMAS.

[31]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[32]  Donato Trigiante,et al.  Analysis of Hamiltonian Boundary Value Methods (HBVMs): A class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems , 2009, Commun. Nonlinear Sci. Numer. Simul..

[33]  Lamjed Ben Said,et al.  Agent-Based Modeling and Simulation of the Emotional and Behavioral Dynamics of Human Civilians during Emergency Situations , 2014, MATES.

[34]  H. Schättler,et al.  On optimal singular controls for a general SIR-model with vaccination and treatment , 2011 .

[35]  Hans W. Guesgen,et al.  Computational Analysis of Emotion Dynamics , 2013, 2013 Humaine Association Conference on Affective Computing and Intelligent Interaction.

[36]  Ming Chen,et al.  Adaptive BER-constraint-based power allocation for downlink MC-CDMA systems with linear MMSE receiver , 2010, 2010 IEEE 12th International Conference on Communication Technology.

[37]  Xiaofeng Liao,et al.  Dynamical analysis and control strategies on malware propagation model , 2013 .

[38]  Debdipta Goswami,et al.  A Lagrangian Approach to Modeling and Analysis of a Crowd Dynamics , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[39]  S. Lenhart,et al.  OPTIMIZING CHEMOTHERAPY IN AN HIV MODEL , 1998 .

[40]  Shrikanth S. Narayanan,et al.  Fuzzy Logic Models for the Meaning of Emotion Words , 2013, IEEE Computational Intelligence Magazine.

[41]  Milind Tambe,et al.  Empirical evaluation of computational fear contagion models in crowd dispersions , 2013, Autonomous Agents and Multi-Agent Systems.

[42]  Wang,et al.  A Pulse Immunization Model for Inhibiting Malware Propagation in Mobile Wireless Sensor Networks , 2014 .

[43]  M. Petit.  Dynamic optimization. The calculus of variations and optimal control in economics and management : by Morton I. Kamien and Nancy L. Schwartz. Second Edition. North-Holland (Advanced Textbooks in Economics), Amsterdam and New York, 1991. Pp. xvii+377. ISBN0-444- 01609-0 , 1994 .

[44]  R. Vidal.  Dynamic optimization: The calculus of variations and optimal control in economics and management: Morton I. KAMIEN and Nancy L. SCHWARTZ Volume 4 in: Dynamic Economics: Theory and Applications, North-Holland, New York, 1981, xi + 331 pages, Dfl.90.00 , 1982 .

[45]  Zeshui Xu,et al.  Construction of a technology adoption decision-making model and its extension to understanding herd behavior , 2015, Knowl. Based Syst..

[46]  Ahmad Soleimani,et al.  Toward a Computational Model for Collective Emotion Regulation Based on Emotion Contagion Phenomenon , 2014, Canadian Conference on AI.

[47]  Ying Qian,et al.  USEIRS model for the contagion of individual aggressive behavior under emergencies , 2012, Simul..