Characterizing Protection Effects on Network Epidemics driven by Random Walks
Resumo
Protection effects (PFx) denote protective measures taken by individuals (such as to wear masks and wash hands) upon their risk-perception towards an ongoing epidemic outbreak. The holistic force produced may fundamentally change the course of a spreading, with respect to both its reach and duration. This work proposes a model for PFx on network epidemics where nodes are sites mobile-agents may visit. Risk aversion is encoded as random-walks biased to safe sites. Assuming the network is a complete graph, the model is analyzed and framed as a classical SIS. We find a regime under which PFx preclude endemic steady-states upon arbitrarily large rates for both walk and transmissibility. Simulation results support our theoretical findings.
Palavras-chave:
epidemia em redes, efeito de proteção, passeios aleatórios, modelos epidêmicos
Referências
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Cai, Y., Kang, Y., Banerjee, M., and Wang, W. (2015). A stochastic sirsepidemic model with infectious force under intervention strategies.Journal of Differ-ential Equations, 259(12):7463 – 7502.
Capasso, V. and Serio, G. (1978).A generalization of thekermack-mckendrick deterministic epidemic model. Mathematical Biosciences,42(1):43 – 61.
Cauchemez, S., Bhattarai, A., Marchbanks, T., Fagan, R., Ostroff,S., Ferguson, N., and Swerdlow, D. (2011). Role of social networks in shaping disease transmission during a community outbreak of 2009 h1n1 pandemic influenza. PNAS,108:2825–30.
de Souza, R. C. (2020).Simulator for network epidemics with bi-ased random walks as protection effects. https://github.com/rchiesse/randomWalk.
Draief, M. and Ganesh, A. (2011). A random walk model for infection on graphs: Spread of epidemics & rumours with mobile agents. Discrete Event Dynamic Systems, 21(1):41–61.
Eames, K. T. D., Tilston, N. L., Brooks-Pollock, E., and Edmunds, W. J.(2012). Measured dynamic social contact patterns explain the spread of h1n1v influenza. PLOS Computational Biology, 8(3):1–8.
Funk, S., Salathé, M., and Jansen, V. (2010). Modelling the influence of human behaviour on the spread of infectious diseases: A review. Journal of the RoyalSociety, Interface / the Royal Society, 7:1247–56.
Granell, C., Gómez, S., and Arenas, A. (2013). Dynamical interplay between awareness and epidemic spreading in multiplex networks. Phys. Rev. Lett.,111:128701.
Guo, W., Cai, Y., Zhang, Q., and Wang, W. (2018). Stochastic persistence and stationary distribution in an sis epidemic model with media coverage. Physica A: Statistical Mechanics and its Applications, 492:2220 – 2236.
Hyman, J. M. and Li, J. (1997). Behavior changes in sis std models with selective mixing.SIAM Journal on Applied Mathematics, 57(4):1082–1094.
Ibrahim, P. S. Y. (2012). Modelagem e Análise de Epidemias SIS em Redes baseadas em Passeios Aleatórios. Master’s thesis, Federal University of Rio de Janeiro,Brazil.
Lam, H., Liu, Z., Mitzenmacher, M., Sun, X., and Wang, Y. (2012). Information dissemination via random walks in d-dimensional space. SODA ’12, page1612–1622, USA. Society for Industrial and Applied Mathematics.
Lee, S., Rocha, L. E. C., Liljeros, F., and Holme, P. (2012). Exploiting temporal network structures of human interaction to effectively immunize populations.PLOS ONE, 7(5):1–10.
Mao, L. and Yang, Y. (2012). Coupling infectious diseases, human preventive behavior, and networks – a conceptual framework for epidemic modeling. Social Science & Medicine, 74(2):167 – 175.
Newman, M. (2010).Networks: An Introduction. Oxford University Press,Inc., USA.
Ogilvy, K. W., G., M. A., and Thomas, W. G. (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A, 115.
Robinson, S., Everett, M., and Christley, R. (2007). Recent network evolution increases the potential for large epidemics in the british cattle population. Journal of the Royal Society, Interface / the Royal Society, 4:669–74.
Ross, S. (2013). Chapter 7 - the discrete event simulation approach. In Simulation, pages 111 – 134. Academic Press.
Tavares, J. V. B. (2018). Simulação Escalável de Epidemias SIS Baseadas em Passeios Aleatórios com Caracterização de Transições de Fase. Master’s thesis,Federal University of Rio de Janeiro, Brazil.
Tchuenche, J., Dube, N., Bhunu, C., Smith, R., and Bauch, C.(2011). The impact of media coverage on the transmission dynamics of human influenza. BMC public health, 11 Suppl 1:S5.
Volz, E. and Meyers, L. (2007). Susceptible-infected-recovered epidemics in dynamic contact networks. Proceedings. Biological sciences / The RoyalSociety, 274:2925–33.
Wang, Z., Andrews, M. A., Wu, Z.-X., Wang, L., and Bauch, C. T.(2015). Coupled disease–behavior dynamics on complex networks: A review.Physicsof Life Reviews, 15:1 – 29.
Yang, H.-X., Tang, M., and Wang, Z. (2018). Suppressing epidemic spreading by risk-averse migration in dynamical networks. Physica A: Statistical Me-chanics and its Applications, 490:347 – 352.
Zhang, Z., Wang, H., Wang, C., and Fang, H. (2015). Modeling epidemics spreading on social contact networks. IEEE Transactions on Emerging Topicsin Computing, 3(3):410–419.
Zhou, J., Xiao, G., Cheong, S. A., Fu, X., Wong, L., Ma, S., and Cheng,T. H. (2012). Epidemic reemergence in adaptive complex networks.Phys. Rev. E,85:036107.
Cai, Y., Kang, Y., Banerjee, M., and Wang, W. (2015). A stochastic sirsepidemic model with infectious force under intervention strategies.Journal of Differ-ential Equations, 259(12):7463 – 7502.
Capasso, V. and Serio, G. (1978).A generalization of thekermack-mckendrick deterministic epidemic model. Mathematical Biosciences,42(1):43 – 61.
Cauchemez, S., Bhattarai, A., Marchbanks, T., Fagan, R., Ostroff,S., Ferguson, N., and Swerdlow, D. (2011). Role of social networks in shaping disease transmission during a community outbreak of 2009 h1n1 pandemic influenza. PNAS,108:2825–30.
de Souza, R. C. (2020).Simulator for network epidemics with bi-ased random walks as protection effects. https://github.com/rchiesse/randomWalk.
Draief, M. and Ganesh, A. (2011). A random walk model for infection on graphs: Spread of epidemics & rumours with mobile agents. Discrete Event Dynamic Systems, 21(1):41–61.
Eames, K. T. D., Tilston, N. L., Brooks-Pollock, E., and Edmunds, W. J.(2012). Measured dynamic social contact patterns explain the spread of h1n1v influenza. PLOS Computational Biology, 8(3):1–8.
Funk, S., Salathé, M., and Jansen, V. (2010). Modelling the influence of human behaviour on the spread of infectious diseases: A review. Journal of the RoyalSociety, Interface / the Royal Society, 7:1247–56.
Granell, C., Gómez, S., and Arenas, A. (2013). Dynamical interplay between awareness and epidemic spreading in multiplex networks. Phys. Rev. Lett.,111:128701.
Guo, W., Cai, Y., Zhang, Q., and Wang, W. (2018). Stochastic persistence and stationary distribution in an sis epidemic model with media coverage. Physica A: Statistical Mechanics and its Applications, 492:2220 – 2236.
Hyman, J. M. and Li, J. (1997). Behavior changes in sis std models with selective mixing.SIAM Journal on Applied Mathematics, 57(4):1082–1094.
Ibrahim, P. S. Y. (2012). Modelagem e Análise de Epidemias SIS em Redes baseadas em Passeios Aleatórios. Master’s thesis, Federal University of Rio de Janeiro,Brazil.
Lam, H., Liu, Z., Mitzenmacher, M., Sun, X., and Wang, Y. (2012). Information dissemination via random walks in d-dimensional space. SODA ’12, page1612–1622, USA. Society for Industrial and Applied Mathematics.
Lee, S., Rocha, L. E. C., Liljeros, F., and Holme, P. (2012). Exploiting temporal network structures of human interaction to effectively immunize populations.PLOS ONE, 7(5):1–10.
Mao, L. and Yang, Y. (2012). Coupling infectious diseases, human preventive behavior, and networks – a conceptual framework for epidemic modeling. Social Science & Medicine, 74(2):167 – 175.
Newman, M. (2010).Networks: An Introduction. Oxford University Press,Inc., USA.
Ogilvy, K. W., G., M. A., and Thomas, W. G. (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A, 115.
Robinson, S., Everett, M., and Christley, R. (2007). Recent network evolution increases the potential for large epidemics in the british cattle population. Journal of the Royal Society, Interface / the Royal Society, 4:669–74.
Ross, S. (2013). Chapter 7 - the discrete event simulation approach. In Simulation, pages 111 – 134. Academic Press.
Tavares, J. V. B. (2018). Simulação Escalável de Epidemias SIS Baseadas em Passeios Aleatórios com Caracterização de Transições de Fase. Master’s thesis,Federal University of Rio de Janeiro, Brazil.
Tchuenche, J., Dube, N., Bhunu, C., Smith, R., and Bauch, C.(2011). The impact of media coverage on the transmission dynamics of human influenza. BMC public health, 11 Suppl 1:S5.
Volz, E. and Meyers, L. (2007). Susceptible-infected-recovered epidemics in dynamic contact networks. Proceedings. Biological sciences / The RoyalSociety, 274:2925–33.
Wang, Z., Andrews, M. A., Wu, Z.-X., Wang, L., and Bauch, C. T.(2015). Coupled disease–behavior dynamics on complex networks: A review.Physicsof Life Reviews, 15:1 – 29.
Yang, H.-X., Tang, M., and Wang, Z. (2018). Suppressing epidemic spreading by risk-averse migration in dynamical networks. Physica A: Statistical Me-chanics and its Applications, 490:347 – 352.
Zhang, Z., Wang, H., Wang, C., and Fang, H. (2015). Modeling epidemics spreading on social contact networks. IEEE Transactions on Emerging Topicsin Computing, 3(3):410–419.
Zhou, J., Xiao, G., Cheong, S. A., Fu, X., Wong, L., Ma, S., and Cheng,T. H. (2012). Epidemic reemergence in adaptive complex networks.Phys. Rev. E,85:036107.
Publicado
30/06/2020
Como Citar
SOUZA, Ronald; FIGUEIREDO, Daniel.
Characterizing Protection Effects on Network Epidemics driven by Random Walks. In: WORKSHOP EM DESEMPENHO DE SISTEMAS COMPUTACIONAIS E DE COMUNICAÇÃO (WPERFORMANCE), 19. , 2020, Cuiabá.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2020
.
p. 97-108.
ISSN 2595-6167.
DOI: https://doi.org/10.5753/wperformance.2020.11109.
