Vaccinations in disease models with antibody-dependent enhancement. (English) Zbl 1131.92040
Summary: This paper examines the effects of single-strain vaccine campaigns on the dynamics of an epidemic multistrain model with antibody-dependent enhancement (ADE). ADE is a disease spreading process causing individuals with their secondary infection to be more infectious than during their first infection by a different strain. We follow the two-strain ADE model described by D. A. T. Cummings et al. [Dynamic effects of antibody dependent enhancement on the fitness of viruses. Proc Natl. Acad. Sci. USA 102, 15259ff (2005)] and I. B. Schwartz et al. [Chaotic desynchronization of multi-strain diseases. Phys. Rev. E 72, Art. No. 066201 (2005)]. After describing the model and its steady state solutions, we modify it to include vaccine campaigns and explore if there exists vaccination rates that can eradicate one or more strains of a virus with ADE.
MSC:
| 92C60 | Medical epidemiology |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
References:
| [1] | Billings, L.; Schwartz, I. B.; Shaw, L. B.; Burke, D. S.; Cummings, D. A.T., Instabilities in multiserotype disease models with antibody-dependent enhancement, J. Theor. Biol., 246, 18 (2007) · Zbl 1451.92090 |
| [2] | 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, 233 (1989) · Zbl 0715.92028 |
| [3] | D.A.T. Cummings, Doctoral Thesis, Johns Hopkins University, 2004.; D.A.T. Cummings, Doctoral Thesis, Johns Hopkins University, 2004. |
| [4] | Cummings, D. A.T.; Schwartz, I. B.; Billings, L.; Shaw, L. B.; Burke, D. S., Dynamic effects of antibody dependent enhancement on the fitness of viruses, Proc. Natl. Acad. Sci. USA, 102, 15259 (2005) |
| [5] | Esteva, L.; Vargas, C., Coexistence of different serotypes of dengue virus, J. Math. Biol., 46, 31 (2003) · Zbl 1015.92023 |
| [6] | Ferguson, N.; Anderson, R.; Gupta, S., The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens, Proc. Natl. Acad. Sci. USA, 96, 790 (1999) |
| [7] | Ferguson, N. M.; Donnelly, C. A.; Anderson, R. M., Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys, Phil. Trans. R. Soc. London Ser. B, 354, 757 (1999) |
| [8] | Center for Disease Control website, 2006. <http://www.cdc.gov/ncidod/dvbid/dengue/slideset/index.htm>; Center for Disease Control website, 2006. <http://www.cdc.gov/ncidod/dvbid/dengue/slideset/index.htm> |
| [9] | Center for Disease Control website, 2006. <http://www.cdc.gov/ncidod/dvbid/dengue/>; Center for Disease Control website, 2006. <http://www.cdc.gov/ncidod/dvbid/dengue/> |
| [10] | Gubler, D. J., Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century, Trends Microbiol., 10, 100 (2002) |
| [11] | Gubler, D. J.; Kuno, G.; Sather, G. E.; Waterman, S. H., A case of natural concurrent human infection with two dengue viruses, Am. J. Trop. Med. Hyg., 34, 170 (1985) |
| [12] | Halstead, S. B.; Deen, J., The future of dengue vaccines, The Lancet, 360, 1243 (2002) |
| [13] | Halstead, S. B.; Heinz, F. X.; Barrett, A. D.T.; Roehrig, J. T., Dengue virus: molecular basis of cell entry and pathogenesis, 25-27 june 2003, vienna, austria, Vaccine, 23, 849 (2005) |
| [14] | I.B. Schwartz, L.B. Shaw, D.A.T. Cummings, L. Billings, M. McCrary, D. Burke, Chaotic desynchronization of multi-strain diseases, Phys. Rev. E, 72:art. no. 066201, 2005.; I.B. Schwartz, L.B. Shaw, D.A.T. Cummings, L. Billings, M. McCrary, D. Burke, Chaotic desynchronization of multi-strain diseases, Phys. Rev. E, 72:art. no. 066201, 2005. |
| [15] | Shaw, L. B.; Billings, L.; Schwartz, I. B., Using dimension reduction to improve outbreak predictability of multistrain diseases, J. Math. Biol., 55, 1 (2007) · Zbl 1145.92022 |
| [16] | van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29 (2002) · Zbl 1015.92036 |
| [17] | Vaughn, D. W.; Green, S.; Kalayanarooj, S.; Innis, B. L.; Nimmannitya, S.; Suntayakorn, S.; Endy, T. P.; Raengsaakulrach, B.; Rothman, A. L.; Ennis, F. A.; Nisalak, A., Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity, J. Infect. Dis., 181, 2 (2000) |
| [18] | World Health Organization website, 2006, <http://www.who.int/mediacentre/factsheets/fs117/en/>; World Health Organization website, 2006, <http://www.who.int/mediacentre/factsheets/fs117/en/> |
| [19] | World Health Organization website, 2006, <http://w3.whosea.org/en/Section10/Section332/>; World Health Organization website, 2006, <http://w3.whosea.org/en/Section10/Section332/> |
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