Abstract
This chapter treats multistrain disease dynamics. It discusses the concept of competitive exclusion and illustrates it on a specific example. It lists possible mechanisms that cause coexistence in multistrain models. It introduces the invasion reproduction numbers as a tool to determine stability of equilibria in multistrain models and illustrates their use on an example. It extends the next-generation approach to the computation of invasion reproduction numbers and illustrates the application to a two-strain model with isolation.
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
B. Adams, E. Holmes, C. Zhang, M. Mammen, S. Nimmannitya, S. Kalayanarooj, and M. Boots, Cross-protective immunity can account for the alternating epidemic pattern of dengue virus serotypes circulating in Bangkok, PNAS, 103 (2006), pp. 14234–14239.
S. Bonhoeffer and M. NOWAK, Mutation and the evolution of parasite virulence, Proc. R. Soc. London, B, 258 (1994), pp. 133–140.
H.-J. Bremermann and H. R. Thieme, A competitive exclusion principle for pathogen virulence, J. Math. Biol., 27 (1989), pp. 179–190.
C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin, and W. M. Liu, Epidemiological models with age structure, proportionate mixing, and cross-immunity, J. Math. Biol., 27 (1989), pp. 233–258.
G. Gause, The struggle for existence, Williams & Wilkins, 1934.
X.-Z. Li, X.-C. Duan, M. Ghosh, and X.-Y. Ruan, Pathogen coexistence induced by saturating contact rates, Nonlinear Anal. Real World Appl., 10 (2009), pp. 3298–3311.
T. Lietman, T. Porco, and S. Blower, Leprosy and tuberculosis: the epidemiological consequences of cross-immunity, Am. J. Public Health, 87 (1997), pp. 1923–1927.
M. Martcheva, B. M. Bolker, and R. D. Holt, Vaccine-induced pathogen strain replacement: what are the mechanisms?, J. R. Soc. Interface, 5 (2008), pp. 3–13.
R. MAY and M. NOWAK, Coinfection and the evolution of parasite virulence, Proc. R. Soc. London, B, 261 (1995), pp. 209–215.
M. NOWAK and R. MAY, Superinfection and the evolution of parasite virulence, Proc. R. Soc. London, B, 255 (1994), pp. 81–89.
M. Nuño, Z. Feng, M. Martcheva, and C. Castillo-Chavez, Dynamics of two-strain influenza with isolation and partial cross-immunity, SIAM J. Appl. Math., 65 (2005), pp. 964–982 (electronic).
H. R. Thieme, Pathogen competition and coexistence and the evolution of virulence, in Mathematics for Life Sciences and Medicine (Y. Takeuchi and Y. Iwasa and K.Sato, eds.), Springer, Berlin, Heidelberg, 2007, pp. 123–153.
H. Wedemeyer, E. Mizukoshi, A. R. Davis, J. R. Bennink, and B. Rehermann, Cross-reactivity between hepatitis c virus and influenza a virus determinant-specific cytotoxic T cells, J. Virol., 75 (2001), p. 11392–11400.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Martcheva, M. (2015). Multistrain Disease Dynamics. In: An Introduction to Mathematical Epidemiology. Texts in Applied Mathematics, vol 61. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7612-3_8
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7612-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7611-6
Online ISBN: 978-1-4899-7612-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)