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On the Dynamics of a Two-Strain Influenza Model with Isolation

Published online by Cambridge University Press:  06 June 2012

F. Chamchod  and
N.F. Britton
F. Chamchod*
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Miami, FL 33124-4250, USA Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
N.F. Britton
Affiliation:
Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling influenza. Furthermore, we investigate how effective isolation is by considering the host’s mean age at infection and the invasion rate of a novel strain. Our results suggest that isolation may help to extend the host’s mean age at infection and reduce the invasion rate of a new strain. When there is a delay in isolation, we show that it may lead to more serious outbreaks as compared to no delay.

Keywords

isolationinfluenzastrain dynamics
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 3: Epidemiology , 2012 , pp. 49 - 61
Copyright
© EDP Sciences, 2012

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References

Cattaneo, R., Schmid, A., Eschle, D., Baczko, K., Meulen, V. T., Billeter, M. A.. Biased hypermutation and other genetic changes in defective measles viruses in human brain infections. Cell 55 (1988), 255-265. CrossRefGoogle Scholar
Carman, W. F., Zannetti, A. R., Karayiannis, P., Waters, J., Manzillo, G., Tanzi, E., Zuckermann, A. J., Thomas, H. C.. Vaccine-induced escape mutant of hepatitis B virus. Lancet 336 (1990), 325-329. CrossRefGoogle Scholar
Sato, S., Suzuki, K., Akahane, Y., Akiyama, K., Yunomura, K., Tsuda, F., Tanaka, T., Okamoto, H., Miyakawa, Y., Mayumi, M.. Hepatitis B virus strains with mutations in the core promoter in patients with fulminant hepatitis. Ann. Internal Medicine 122 (1995), 241-248. CrossRefGoogle ScholarPubMed
Chen, W. N., Oon, C. J.. Hepatitis B virus surface antigen (HBsAg) mutants in Singapore adult and vaccinated children with high anti-hepatitis B virus antibody levels but negative for HBsAg. J. Clin. Microbiol. 38 (2000), 2793-2794. Google ScholarPubMed
Eron, J. J., Vernazza, P. L., Johnston, D. M., Seillier-Moiseiwitsch, F., Alcorn, T. M., Fiscus, S. A., Cohen, M. S.. Resistance of HIV-1 to antiretroviral agents in blood and seminal plasma : Implications for transmission. AIDS 15 (1998), 181-189. CrossRefGoogle Scholar
Ebel, G. D., Dupuis, A. P., Ngo, K., Nicholas, D., Kauffman, E., Jones, S. A., Young, D., Maffei, J., Shi, P. Y., Bernard, K., Kramer, L. D.. Partial genetic characterization of West Nile virus strains, New York State, 2000. Emerg. Infec. Dis. 7 (2000), 650-653. CrossRefGoogle Scholar
Cassiday, P. K., Sanden, G. N., Heuvelman, K., Mooi, F. R., Bisgard, K. M., Popovic, T.. Polymorphism in Bordetella pertussis pertactin and pertussis toxin virulence factors in the United States. J. Infect. Dis. 182 (2000), 1402-1408. CrossRefGoogle Scholar
Weber, C., Boursaux-Eude, C., Coralie, G., Caro, V., Guiso, N.. Polymorphism of Bordetella pertussis isolates circulating for the last 10 years in France, where a single effective whole-cell vaccine has been used for more than 30 years. J. Clin. Microbiol. 12 (2001), 4396-4403. CrossRefGoogle Scholar
Gupta, S., Trenholme, K., Anderson, R. M., Day, K. P.. Antigenic diversity and the transmission dynamics of Plasmodium falciparum. Science 263 (1994), 961-963. CrossRefGoogle Scholar
Palese, P., Young, J. F.. Variation of influenza A, B, and C viruses. Science 215 (1982), 1486-1474. CrossRefGoogle Scholar
Webster, R. G.. Influenza : An emerging disease. Emerg. Infec. Dis. 4 (1998), 436-441. CrossRefGoogle Scholar
J. Davies, E. Grilli, A. Smith. Influenza A : infection and reinfection. J. Hyg.(Cambridge) 92, 125-127.
H. Larson, D. Tyrrell, C. Bowker, C. Potter, G. Schild. Immunity to challenge in volunteers vaccinated with an inactivated current or earlier strain of influenza A(H3N2). J. Hyg. (Cambridge) 80, 243-248.
Frank, A. L., Taber, L. H., Wells, J. M.. Individuals infected with two subtypes of influenza A virus in the same season. J. Infect. Dis. 147 (1983), 120-124. CrossRefGoogle ScholarPubMed
Sonoguchi, T., Naito, H., Hara, M., Takeuchi, Y., Fukumi, H.. Cross-subtype protection in humans during sequential, overlapping and/or concurrent epidemics caused by H3N2 and H1N1 influenza viruses. J. Infect. Dis. 151 (1985), 81-88. CrossRefGoogle Scholar
Castillo-Chavez, C., Hethcote, H. W., Andreasen, V., Levin, S. A., Liu, W. M.. Epidemiological models with age structure, proportionate mixing, and cross-immunity. J. Math. Biol. 27 (1989), 233-258. CrossRefGoogle ScholarPubMed
Gupta, S., Maiden, M. C. J., Feavers, I. M., Nee, S., May, R. M., Anderson, R. M.. The maintenance of strain structure in populations of recombining infectious agents. Nat. Med. 2 (1996), 437-442. CrossRefGoogle ScholarPubMed
Andreasen, V., Lin, J., Levin, S. A.. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J. Math. Biol. 35 (1997), 825-842. CrossRefGoogle ScholarPubMed
Gupta, S., Ferguson, N., Anderson, R. M.. Chaos, persistence, and evolution of strain structure in antigenically diverse infectious agents. Science 280 (1998), 912-915. CrossRefGoogle ScholarPubMed
Lin, J., Andreason, V., Levin, S. A.. Dynamics of influenza A drift :the linear three-strain model. Math. Biosci. 162 (1999), 33-51. CrossRefGoogle ScholarPubMed
Gog, J. R., Swinton, J.. A Status-based Approach to Multiple Strain Dynamics. J. Math. Biol. 44 (2002), 169-184. CrossRefGoogle ScholarPubMed
Gog, J. R., Grenfell, B. T.. Dynamics and selection of many-strain pathogens. Proc. Natl. Acad. Sci. USA 99 (2002), 17209-17214. CrossRefGoogle ScholarPubMed
Kamo, M., Sasaki, A.. The Effect of Cross-immunity and Seasonal Forcing in a multi-strain epidemic model. Physica D 165 (2002), 228-241. CrossRefGoogle Scholar
Lin, J., Andreasen, V., Casagrandi, R., Levin, S. A.. Travelling waves in a model of influenza A drift. J. Theor. Biol. 222 (2003), 437-445. CrossRefGoogle Scholar
Andreasen, V., Lin, J., Levin, S. A.. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J. Math. Biol. 35 (1997), 825-842. CrossRefGoogle ScholarPubMed
Boni, M. F., Gog, J. R., Andreasen, V., Christiansen, F. B.. Influenza drift and epidemic size : the race between generating and escaping immunity. Theor. Popul. Biol. 65 (2004), 179-191. CrossRefGoogle Scholar
Restif, O., Grenfell, B. T.. Integrating life history and cross-immunity into the evolutionary dynamics of pathogens. Proc. R. Soc. B 273 (2006), 409-416. CrossRefGoogle ScholarPubMed
Adams, B., Sasaki, A.. Cross-immunity, invasion and coexistence of pathogen strains in epidemiological models with one-dimensional antigenic space. Math. Biosci. 210 (2007), 680-699. CrossRefGoogle ScholarPubMed
Minayev, P., Ferguson, N.. Improving the realism of deterministic multi-strain models : implications for modelling influenza A. J. R. Soc. Interface. 6 (2009), 509-518. CrossRefGoogle ScholarPubMed
Pease, C.. An evolutionary epidemiological mechanism, with applications to type A influenza. Theor. Popul. Biol. 31 (1987), 422-452. CrossRefGoogle ScholarPubMed
Casagrandi, R., Bolzoni, L., Levin, S. A., Andreasen, V.. The SIRC model and influenza A. Math. Biosci. 200 (2006), 152-169. CrossRefGoogle ScholarPubMed
Nuno, M., Feng, Z., Martcheva, M., Castillo-Chavez, C.. Dynamics of two-strain influenza with isolation and partial cross-immunity. SIAM J. Appl. Math. 65 (2005), 964-982. CrossRefGoogle Scholar
Nuno, M., Chowell, G., Wang, X., Castillo-Chavez, C.. On the role of cross-immunity and vaccines on the survival of less fit flu-strains. Theor. Popul. Biol. 71 (2007), 20-29. CrossRefGoogle ScholarPubMed
M. J. Keeling, P. Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, New Jersey, 2008.
L. Edelstein-Keshet. Mathematical Models in Biology. Random House, New York, 1986