Abstract
The aim of this paper is to provide an overview of existing models where multiple strains are coupled by cross-immunity. We discuss their differences and similarities, and propose a method to abstract some universal properties intrinsic to the coupling structure. More precisely, the coupling structure of a multiple-strain system can be organized as a matrix that is often invariant under many symmetry operations. Symmetries are known to constrain the behaviour of dynamical systems in many ways. Some symmetry effects are intuitive, but sometimes they can be rather subtle. Given that the assumptions and mechanisms of coupling strains are expected to have a major influence in determining the behaviour of the system, methods and techniques for abstracting their effects are valuable.
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References
R.M. Anderson and R.M. May (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
V. Andreasen, J. Lin, and S.A. Levin (1997). The dynamics of co-circulating influenza strains conferring partial cross-immunity. J. Math. Bio. 35, 825–842.
C. Castillo-Chavez, H.W. Hethcote, V. Andreasen, S.A. Levin, and W.M. Liu (1989). Epidemiological models with age structure, proportionate mixing, and cross-immunity. J. Math. Biol. 27, 233–258.
J. Cohen, and I. Stewart (1999). Polymorphism viewed as a phenotypic symmetry-breaking. University of Warwick preprint.
K. Dietz (1979). Epidemiologic interference of virus populations. J. Math. Biol. 8, 291–300.
N. Ferguson, R.M. Anderson, and S. Gupta (1999). The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. PNAS 96, 790–794.
N. Ferguson and V. Andreasen (1999). The influence of different forms of cross-protective immunity on the population dynamics of antigenically diverse pathogens. Submitted to this volume.
J. Gog and J. Swinton (2000). A status-based approach to multiple strain dynamics. Submitted to J. Math. Biol.
S. Gupta, N. Ferguson, and R.M. Anderson (1998). Chaos, persistence and evolution of strain structure in antigenically diverse infectious agents. Science 280, 912–915.
S. Gupta, M.C.J. Maiden, I.M. Feavers, S. Nee, R.M. May, and R.M. Anderson (1996). The maintenance of strain structure in populations of recombining infectious agentes. Nature Med. 2, 437–442.
M. Krupa (1997). Robust heteroclinic cycles. J. of Nonl. Sci. 7, 129–176.
J. Lin, V. Andreasen, and S.A. Levin (1999). Dynamics of influenza A drift: The linear three-strain model. Math. Biosci. 162, 33–51.
M. Lipsitch (1997). Vaccination against colonizing bacteria with multiple serotypes. Proc. Natl. Acad. Sci. 94, 6571–6576.
M. Lipsitch (1999). Bacterial vaccines and seropyte replacement: Lessons from Haemophilus influenzae and prospects for Streptococcus pneumoniae. Emerging Infectious Diseases 5, 336–345.
R.M. May and M.A. Nowak (1994). Superinfection, metapopulation dynamics, and the evolution of diversity. J. Theor. Biol. 170, 95–114.
R.M. May and M.A. Nowak (1995). Coinfection and the evolution of parasite virulence. Proc. R. Soc. Lond. B 261, 209–215.
A.R. McLean (1995). Vaccination, evolution and changes in the efficacy of vaccines: A theoretical framework. Proc. R. Soc. Lond. B 261, 389–393.
J. Moehlis and E. Knobloch (1998). Forced symmetry-breaking as a mechanism for bursting. Phys. Rev. Lett. 80, 5329–5332.
M.A. Nowak and R.M. May (1994). Superinfection and the evolution of parasite virulence. Proc. R. Soc. Lond. B 255, 81–89.
L.J. White, M.J. Cox, and G.F. Medley (1998). Cross immunity and vaccination against multiple microparasite strains. IMA J. Math. App. Med. Biol. 15, 211–233.
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Gomes, M.G.M., Medley, G.F. (2002). Dynamics of Multiple Strains of Infectious Agents Coupled by Cross-Immunity: A Comparison of Models. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., Yakubu, AA. (eds) Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. The IMA Volumes in Mathematics and its Applications, vol 126. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0065-6_10
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DOI: https://doi.org/10.1007/978-1-4613-0065-6_10
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