Abstract
We investigate the special role of the three-dimensional relationship between periodicity, persistence and synchronization on its ability of disease persistence in a meta-population. Persistence is dominated by synchronization effects, but synchronization is dominated by the coupling strength and the interaction between local population size and human movement. Here we focus on the quite important role of population size on the ability of disease persistence. We implement the simulations of stochastic dynamics in a susceptible-exposed-infectious-recovered (SEIR) metapopulation model in space. Applying the continuous-time Markov description of the model of deterministic equations, the direct method of Gillespie [10] in the class of Monte-Carlo simulation methods allows us to simulate exactly the transmission of diseases through the seasonally forced and spatially structured SEIR meta-population model. Our finding shows the ability of the disease persistence in the meta-population is formulated as an exponential survival model on data simulated by the stochastic model. Increasing the meta-population size leads to the clearly decrease of the extinction rates local as well as global. The curve of the coupling rate against the extinction rate which looks like a convex functions, gains the minimum value in the medium interval, and its curvature is directly proportional to the meta-population size.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Altizer, S., Dobson, A., Hosseini, P., Hudson, P., Pascual, M., Rohani, P.: Seasonality and the dynamics of infectious diseases. Ecol. Lett. 9(4), 467–484 (2006)
Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1992)
Bailey, N.T.J., et al.: The mathematical theory of epidemics (1957)
Bartlett, M.S.: The critical community size for measles in the united states. J. Roy. Stat. Soc. Ser. A (Gen.) 37–44 (1960)
Bjørnstad, O.N., Finkenstädt, B.F., Grenfell, B.T.: Dynamics of measles epidemics: estimating scaling of transmission rates using a time series sir model. Ecol. Monogr. 72(2), 169–184 (2002)
Black, F.L.: Measles endemicity in insular populations: critical community size and its evolutionary implication. J. Theor. Biol. 11(2), 207–211 (1966)
Conlan, A.J.K., Grenfell, B.T.: Seasonality and the persistence and invasion of measles. Proc. Biol. Sci. 274(1614), 1133–1141 (2007)
Conlan, A.J.K., Rohani, P., Lloyd, A.L., Keeling, M., Grenfell, B.T.: Resolving the impact of waiting time distributions on the persistence of measles. J. R. Soc. Interface (2010)
Ferrari, M.J., Grais, R.F., Bharti, N., Conlan, A.J.K., Bjørnstad, O.N., Wolfson, L.J., Guerin, P.J., Djibo, A., Grenfell, B.T.: The dynamics of measles in sub-Saharan Africa. Nature 451(7179), 679–684 (2008)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)
Grenfell, B., Harwood, J.: (Meta)population dynamics of infectious diseases. TREE 12, 395–399 (1997)
Grenfell, B.T., Bjørnstad, O.N., Kappey, J.: Travelling waves and spatial hierarchies in measles epidemics. Nature 414(6865), 716–723 (2001)
Grenfell, B.T., Bjørnstad, O.N., Finkenstädt, B.F.: Dynamics of measles epidemics: scaling noise, determinism, and predictability with the TSIR model. Ecol. Monogr. 72(2), 185–202 (2002)
Grenfell, B.T.: Cities and villages: infection hierarchies in a measles metapopulation. Ecol. Lett. 1, 68–70 (1998)
Grenfell, B.T., Bolker, B.M., Klegzkowski, A.: Seasonality and extinction in chaotic metapopulation. R. Soc. 259, 97–103 (1995)
Hamer, W.H.: The Milroy Lectures on Epidemic Disease in England: The Evidence of Variability and of Persistency of Type. Bedford Press, London (1906)
Holyoak, M., Lawler, S.P.: Persistence of an extinction-prone predator-prey interaction through metapopulation dynamics. Ecology 1867–1879 (1996)
Huffaker, C.B.: Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia 27, 343–383 (1958)
Keeling, M.J., Grenfell, B.T.: Understanding the persistence of measles: reconciling theory, simulation and observation. Proc. Biol. Sci. 269(1489), 335–343 (2002)
Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton (2008)
Kleinbaum, D.G.: Survival Analysis (2005)
Levins, R.: Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am. 15, 237–240 (1969)
Soper, H.E.: The interpretation of periodicity in disease prevalence. J. R. Stat. Soc. 92(1), 34–73 (1929)
Therneau, T.M.: A Package for Survival Analysis in S, 2014. R Package Version 2.37-7
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Tran-Thi, CG., Choisy, M., Zucker, J.D. (2017). Quantifying the Effect of Metapopulation Size on the Persistence of Infectious Diseases in a Metapopulation. In: Nguyen, N., Tojo, S., Nguyen, L., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2017. Lecture Notes in Computer Science(), vol 10192. Springer, Cham. https://doi.org/10.1007/978-3-319-54430-4_72
Download citation
DOI: https://doi.org/10.1007/978-3-319-54430-4_72
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54429-8
Online ISBN: 978-3-319-54430-4
eBook Packages: Computer ScienceComputer Science (R0)