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A HYBRID MODEL FOR STUDYING SPATIAL ASPECTS OF INFECTIOUS DISEASES

Part of: Topological dynamics

Published online by Cambridge University Press:  07 February 2013

BENJAMIN J. BINDER ,
JOSHUA V. ROSS  and
MATTHEW J. SIMPSON
BENJAMIN J. BINDER*
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia 5005, Australia
JOSHUA V. ROSS*
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia 5005, Australia
MATTHEW J. SIMPSON*
Affiliation:
Mathematical Sciences School, Queensland University of Technology, Brisbane, Queensland 4001, Australia
*
✉[email protected]
✉[email protected]
✉[email protected]
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Abstract

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We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Keywords

agent-based modelcontinuum modelinfectious diseasesspatial heterogeneity

MSC classification

Secondary: 37B15: Cellular automata 92D30: Epidemiology
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 1-2 , October 2012 , pp. 37 - 49
Copyright
Copyright ©2013 Australian Mathematical Society 

References

Alarcón, T., Byrne, H. M. and Maini, P. K., “A cellular automaton model for tumour growth in inhomogeneous environment”, J. Theoret. Biol. 225 (2003) 257–274; doi:10.1016/S0022-5193(03)00244-3.CrossRefGoogle ScholarPubMed
Anderson, R. M. and May, R. M., Infectious diseases of humans (Oxford University Press, Oxford, 1991).CrossRefGoogle Scholar
Beauchemin, C., Samuel, J. and Tuszynski, J., “A simple cellular automaton model for influenza A viral infections”, J. Theor. Biol. 232 (2005) 223–234; doi:10.1016/j.jtbi.2004.08.001.CrossRefGoogle ScholarPubMed
Binder, B. J. and Landman, K. A., “Exclusion processes on a growing domain”, J. Theor. Biol. 259 (2009) 541–551; doi:10.1016/j.jtbi.2009.04.025.CrossRefGoogle ScholarPubMed
Binder, B. J. and Landman, K. A., “Quantifying evenly distributed states in exclusion and nonexclusion processes”, Phys. Rev. E. 83 (2011) 041914; doi:10.1103/PhysRevE.83.041914.CrossRefGoogle ScholarPubMed
Binder, B. J., Landman, K. A., Newgreen, D. F., Simkin, J. E., Takahashi, Y. and Zhang, D., “Spatial analysis of multi-species exclusion processes: application to neural crest cell migration in the embryonic gut”, Bull. Math. Biol. 74 (2012) 474–490; doi:10.1007/s11538-011-9703-z.CrossRefGoogle ScholarPubMed
Binder, B. J., Landman, K. A., Simpson, M. J., Mariani, M. and Newgreen, D. F., “Modeling proliferative tissue growth: a general approach and an avian case study”, Phys. Rev. E. 78 (2008) 031912; doi:10.1103/PhysRevE.78.031912.CrossRefGoogle Scholar
Bobashev, G. V., Goedecke, M. D., Yu, F. and Epstein, J. M., “A hybrid epidemic model: combining the advantages of agent-based and equation-based approaches”, in: Proceedings of the 2007 Winter Simulation Conference (ed. Henderson, S.), (IEEE, Washington DC, 2007), 1532–1537; doi:10.1109/WSC.2007.4419767.CrossRefGoogle Scholar
Chowdhury, D., Schadschneider, A. and Nishinari, K., “Physics of transport and traffic phenomena in biology: from molecular motors and cells to organisms”, Phys. Life Rev. 2 (2005) 318–352; doi:10.1016/j.plrev.2005.09.001.CrossRefGoogle Scholar
Chung, C. A., Lin, T.-H., Chen, S.-D. and Huang, H.-I., “Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs”, J. Theor. Biol. 262 (2010) 267–278; doi:10.1016/j.jtbi.2009.09.031.CrossRefGoogle ScholarPubMed
Dallon, J. C. and Othmer, H. G., “A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum”, Phil. Trans. R. Soc. Lond. B 352 (1997) 391–417; doi:10.1098/rstb.1997.0029.CrossRefGoogle ScholarPubMed
Dietz, K., “Epidemics and rumours: a survey”, J. R. Stat. Soc. A 130 (1967) 505–528; doi:10.2307/2982521.CrossRefGoogle Scholar
Diggle, P. J., Statistical analysis of spatial point patterns (Academic Press, London, 1983).Google Scholar
Erban, R. and Chapman, S. J., “Time scale of random sequential adsorption”, Phys. Rev. E 75 (2007) 041116; doi:10.1103/PhysRevE.75.041116.CrossRefGoogle ScholarPubMed
Franz, B. and Erban, R., “Hybrid modelling of individual movement and collective behaviour”, in: Dispersal, individual movement and spatial ecology: a mathematical perspective (eds Lewis, M., Maini, P. K. and Petrovskii, S. V.), (Springer) in press.Google Scholar
Guo, Z., Sloot, P. M. A. and Tay, J. C., “A hybrid agent-based approach for modeling microbiological systems”, J. Theor. Biol. 255 (2008) 163–175; doi:10.1016/j.jtbi.2008.08.008.CrossRefGoogle ScholarPubMed
Heppenstall, A., Evans, A. and Birkin, M., “Using hybrid agent-based systems to model spatially-influenced retail markets”, J. Artificial Soc. Social Simulation 9 (2006) 2; http://jasss.soc.surrey.ac.uk/9/3/2.html.Google Scholar
Hickson, R. I., Mercer, G. N. and Lokuge, K. M., “A metapopulation model of tuberculosis transmission with a case study from high to low burden areas”, PLoS ONE 7 (2012) e34411; doi:10.1371/journal.pone.0034411.CrossRefGoogle ScholarPubMed
Jones, S. W., “The enhancement of mixing by chaotic advection”, Phys. Fluids A 3 (1991) 1081–1086; doi:10.1063/1.858089.CrossRefGoogle Scholar
Keeling, M. J. and Rohani, P., Modeling infectious diseases in humans and animals (Princeton University Press, Princeton, NJ, 2008).CrossRefGoogle Scholar
Keeling, M. J. and Ross, J. V., “On methods for studying stochastic disease dynamics”, J. R. Soc. Interface 5 (2008) 171–181; doi:10.1098/rsif.2007.1106.CrossRefGoogle ScholarPubMed
Kelly, H. A., Mercer, G. N., Fielding, J. E., Dowse, G. K., Glass, K., Carcione, D., Grant, K. A., Effler, P. V. and Lester, R. A., “Pandemic (H1N1) 2009 influenza community transmission was established in one Australian state when the virus was first identified in North America”, PLoS ONE 5 (2010) e11341; doi:10.1371/journal.pone.0011341.CrossRefGoogle ScholarPubMed
Phelps, J. H. and Tucker, C. L., “Lagrangian particle calculations of distributive mixing: limitations and applications”, Chem. Engrg. Sci. 61 (2006) 6826–6836; doi:10.1016/j.ces.2006.07.008.CrossRefGoogle Scholar
Roberts, M. G., Baker, M., Jennings, L. C., Sertsou, G. and Wilson, N., “A model for the spread and control of pandemic influenza in an isolated geographical region”, J. R. Soc. Interface 4 (2007) 325–330; doi:10.1098/rsif.2006.0176.CrossRefGoogle Scholar
Rousseau, G., Giorgini, B., Livi, R. and Chaté, H., “Dynamical phases in a cellular automaton model for epidemic propogation”, Physica D 103 (1997) 554–563; doi:10.1016/S0167-2789(96)00285-0.CrossRefGoogle Scholar
Sewall, J., Wilkie, D. and Lin, M. C., “Interactive hybrid simulation of large-scale traffic”, ACM Trans. Graphics 30 (2011) Article No. 35; doi:10.1145/2070781.2024169.CrossRefGoogle Scholar
Simpson, M. J., Landman, K. A. and Hughes, B. D., “Multi-species simple exclusion processes”, Physica A 388 (2009) 399–406; doi:10.1016/j.physa.2008.10.038.CrossRefGoogle Scholar
Simpson, M. J., Landman, K. A. and Hughes, B. D., “Cell invasion with proliferation mechanisms motivated by time-lapse data”, Physica A 389 (2010) 3779–3790; doi:10.1016/j.physa.2010.05.020.CrossRefGoogle Scholar
Simpson, M. J., Merrifield, A., Landman, K. A. and Hughes, B. D., “Simulating invasion with cellular automata: connecting cell-scale and population-scale properties”, Phys. Rev. E 76 (2007) 021918; doi:10.1103/PhysRevE.76.021918.CrossRefGoogle ScholarPubMed
Snow, J., On the mode of communication of cholera (John Churchill, London, 1854).Google Scholar
Venkatachalam, S. and Mikler, A. R., “An infectious disease outbreak simulator based on the cellular automata paradigm”, in: Innovative internet community systems, Volume 3473 of Lecture Notes in Computer Science (eds Böhme, T., Larios Rosillo, V. M., Unger, H. and Unger, H.), (Springer, Berlin, 2006), 198–211.CrossRefGoogle Scholar
Wang, Z. and Deisboeck, T. S., “Computational modeling of brain tumors: discrete, continuum or hybrid?”, Sci. Model. Simul. 15 (2008) 381–393; doi:10.1007/s10820-008-9094-0.CrossRefGoogle Scholar
White, S. H., del Rey, A. M. and Rodríguez Sánchez, G., “Modeling epidemics using cellular automata”, Appl. Math. Comput. 186 (2007) 193–202; doi:10.1016/j.amc.2006.06.126.Google ScholarPubMed