Phase control of resonant systems: Interference, chaos and high periodicity

Journal of Theoretical Biology

Volumn 278, Issue 1, 2011, Pages 74-86

  Greenman, J V ^a   Pasour, V B ^b  

^a UNIVERSITY OF STIRLING   (United Kingdom)

^b U S ARMY RESEARCH OFFICE   (United States)

Author keywords

Dengue fever; Eco epidemiological models; Epidemic suppression; Noise excitation; Subharmonics

Indexed keywords

CHAOTIC DYNAMICS; EPIDEMIOLOGY; NOISE; PERIODICITY; REINFORCEMENT;

ARTICLE; CHAOS THEORY; CONTROLLED STUDY; DYNAMICS; EXCITATION; MATHEMATICAL ANALYSIS; NOISE; NONLINEAR SYSTEM; PERIODICITY; PRIORITY JOURNAL; SIMULATION;

COMMUNICABLE DISEASES; HUMANS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; PERIODICITY; REPRODUCIBILITY OF RESULTS;

EID: 79952987784     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2011.03.002     Document Type: Article

References (37)

1. Adams B., Holmes E.C., Zhang C., Mammen M.P., Nimmannitya S., Kalayanarooj S., Boots M. Cross-protective immunity can account for the alternating epidemic pattern of dengue virus serotypes circulating in Bangkok. Proc. Nat. Acad. Sci. USA 2006, 103:14234-14239.
2. Altizer S., Dobson A., Hosseini P., Hudson P., Pascual M., Rohani P. Seasonality and the dynamics of infectious diseases. Ecol. Lett. 2006, 9:467-484.
3. Anderson R.M., Jackson H.C., May R.M., Smith A.M. Population dynamics of fox rabies in Europe. Nature 1981, 289:765-771.
4. Bacaer N., Abdurahman X. Resonance of the epidemic threshold in a periodic environment. J. Math. Biol. 2008, 57:649-673.
5. Bacaer N. Periodic matrix population models: growth rate, basic reproductive number and entropy. Bull. Math. Biol. 2009, 71:1781-1792.
6. Berryman A.A. The theory and classification of outbreaks. Insect Outbreaks 1987, Academic Press, San Diego. P. Barbosa, J.C. Schultz (Eds.).
7. Bjornstad O.N., Fromentin J.M., Stenseth N.C., et al. Cycles and trends in cod populations. Proc. Nat. Acad. Sci. USA 1999, 96:5066-5071.
8. Bowers R.G., White A., Boots M., Geritz S.A.H., Kisdi E. Evolutionary branching/speciation: contrasting results with explicit or emergent carrying capacities. Evol. Ecol. Res. 2003, 5:883-891.
9. Cai G.Q., Lin Y.K. Stochastic analysis of the Lotka-Volterra model for ecosystems. Phys. Rev. E 2004, 70:041910-1-041910-7.
10. Chesson P.L. The stabilising effect of a random environment. J. Math. Biol. 1982, 15:1-36.
11. Choisy M., Rohani P. Harvesting can increase severity of wildlife disease epidemics. Proc. R. Soc. B 2006, 273:2025-2034.
12. Dietz K. Overall population patterns in the transmission cycle of infectious disease agents. Population Biology of Infectious Diseases 1982, 87-102. Springer-Verlag, New York. R.M. Anderson, R.M. May (Eds.).
13. Dwyer G., Dushoff J., Yee S.H. The combined effects of pathogens and predators on insect outbreaks. Nature 2004, 430:341-345.
14. Gard T.C. Introduction to Stochastic Differential Equations 1988, Marcel Dekker, Inc., New York.
15. Greenman, J.V., Kamo, M., Boots, M., 2004. External forcing of ecological and epidemiological systems: a resonance approach. Physica D 190, 136-151.
16. Greenman J.V., Benton T.G. The frequency spectrum of structured discrete time population models: its properties and their ecological implications. OIKOS 2005, 110:369-389.
17. Greenman J.V., Benton T.G. The impact of environmental fluctuations on structured discrete time population models: resonance, synchrony and threshold behaviour. Theor. Popul. Biol. 2005, 68:217-235.
18. Greenman J.V., Norman R.A. Environmental forcing, invasion and control of ecological and epidemiological systems. J. Theor. Biol. 2007, 247:492-506.
19. Greenman J.V., Hoyle A.S. Pathogen exclusion from eco-epidemiological systems. Am. Nat. 2010, 176:149-158.
20. Hastings A. Transient dynamics and persistence of ecological systems. Ecol. Lett. 2001, 4:215-220.
21. Hosseini P.R., Dhondt A.A., Dobson A. Seasonality and wildlife disease: how seasonal birth, aggregation and variation in immunity affect dynamics of Mycoplasma gallisepticum in house finches. Proc. R. Soc. B 2004, 271:2569-2577.
22. Ireland J.M., Norman R.A., Greenman J.V. The effect of seasonal host birth rates on population dynamics: the importance of resonance. J. Theor. Biol. 2004, 231:229-238.
23. Ives A.R., Jansen V.A.A. Complex dynamics in stochastic tritrophic models. Ecology 1998, 79:1039-1052.
24. Jenkins G.M., Watts D.G. Spectral Analysis and its Applications 1969, Holden-Day, San Francisco.
25. Jordan D.W., Smith P. Nonlinear Ordinary Differential Equations 1977, Oxford University Press, Oxford, UK.
26. Kamo M., Sasaki A. The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model. Physica D 2002, 165:228-241.
27. Keeling M.J., Rohani P., Grenfell B.T. Seasonally forced disease dynamics explored as switching between attractors. Physica D 2001, 148:317-335.
28. Koelle K., Pascual M. Disentangling extrinsic from intrinsic factors in disease dynamics: a nonlinear time series approach with an application to cholera. Am. Nat. 2004, 163:901-913.
29. MacDonald, J.I., 2007. A Computational Investigation of Seasonally Forced Disease Dynamics. Ph.D. Thesis, Mathematics Institute, University of Warwick, UK.
30. Nagashima H., Baba Y. Introduction to Chaos 1999, Institute of Physics, Bristol, UK.
31. Recker M., Blyuss K.B., Simmons C.P., Hien T.T., Wills B., Farrar J., Gupta S. Immunological serotype interactions and their effect on the epidemiological pattern of dengue. Proc. R. Soc. B 2009, 276:2541-2548.
32. Reinsel G.C. Elements of Multivariate Time Series Analysis 1997, Springer, New York.
33. Seydel R. Practical Bifurcation and Stability Analysis 1994, Springer-Verlag, New York.
34. Strogatz S.H. Nonlinear Dynamics and Chaos 2000, Westview Press, Cambridge, MA.
35. Swinton J., Harwood J., Grenfell B.T., Gilligan C.A. Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations. J. Anim. Ecol. 1998, 67:54-68.
36. Takens F. Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics, vol. 898 1981, Springer-Verlag, New York.
37. Wichmann M.C., Johst K., Moloney K.A., Wissel C., Jeltsch F. Extinction risk in periodically fluctuating environments. Ecol. Model. 2003, 167:221-231.