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Constraints on the use of lifespan-shortening Wolbachia to control dengue fever. (English) Zbl 1336.92085

Summary: Dengue fever, a viral disease spread by the mosquito Aedes aegypti, affects 50-100 million people a year in many tropical countries. Because the virus must incubate within mosquito hosts for two weeks before being able to transmit the infection, shortening the lifespan of mosquitoes may curtail dengue transmission. We developed a continuous time reaction-diffusion model of the spatial spread of Wolbachia through a population of A. aegypti. This model incorporates the lifespan-shortening effects of Wolbachia on infected A. aegypti and the fitness advantage to infected females due to cytoplasmic incompatibility (CI). We found that local establishment of the Wolbachia infection can occur if the fitness advantage due to CI exceeds the fitness reduction due to lifespan-shortening effects, in accordance with earlier results concerning fecundity reduction. However, spatial spread is possible only if the fitness advantage due to CI is twice as great as the fitness reduction due to lifespan shortening effects. Moreover, lifespan-shortening and fecundity-reduction can have different effects on the speed of wave-retreat. Using data from the literature, we estimated all demographic parameters for infected and uninfected mosquitoes and computed the velocities of spread of infection. Our most optimistic estimates suggest that the spatial spread of lifespan-shortening Wolbachia may be so slow that efficient spatial spread would require a prohibitively large number of point releases. However, as these estimates of demographic parameters may not accurately reflect natural conditions, further research is necessary to corroborate these predictions.

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
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[1] Barton, N. H., The dynamics of hybrid zones, Heredity, 43, December, 341-359 (1979)
[2] Barton, N. H.; Turelli, M., Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects, Am. Nat., 178, E48-E75 (2011)
[3] Brownstein, J. S.; Hett, E.; O’Neill, S. L., The potential of virulent Wolbachia to modulate disease transmission by insects, J. Invertebr. Pathol., 84, September, 24-29 (2003)
[4] Caspari, E.; Watson, G. S., On the evolutionary importance of cytoplasmic sterility in mosquitoes, Evolution, 13, 568-570 (1959)
[5] Clyde, K.; Kyle, J. L.; Harris, E., Recent advances in deciphering viral and host determinants of dengue virus replication and pathogenesis, J. Virol., 80, 11418-11431 (2006)
[6] Curtis, C. F., Possible use of translocations to fix desirable genes in insect pest populations, Nature, 218, 1968 (1968)
[7] Diekmann, O.; Heesterbeek, J. A.P.; Metz, J. A.J., On the definition and the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28, 4, 365-382 (1990) · Zbl 0726.92018
[8] Fife, P. C., Mathematic Aspects of Reacting and Diffusing Systems (1979), Springer · Zbl 0403.92004
[9] Fine, P. E.M., On the dynamics of symbiote-dependent cytoplasmic incompatibility in culicine mosquitoes, J. Invertebr. Pathol., 30, 10-18 (1978)
[10] Fisher, R. A., The wave of advance of advantageous genes, Ann. Eugen., 7, 353-369 (1937) · JFM 63.1111.04
[11] Gubler, D. J., Dengue and dengue hemorrhagic fever, Clin. Microbiol. Rev., 11, July, 480-496 (1998)
[12] Harrington, L. C.; Buonaccorsi, J. P.; Edman, J. D.; Costero, A.; Kittayapong, P.; Clark, G. G.; Scott, T. W., Analysis of survival of young and old Aedes aegypti (Diptera: Culicidae), J. Med. Entomol., 38, 537-547 (2001)
[13] Hoffmann, A. A.; Turelli, M., Cytoplasmic incompatibility in insects, (O’Neill, S. L.; Hoffmann, A. A.; Werren, J. H., Influential Passengers: Inherited Microorganisms and Arthropod Reproduction (1997), Oxford University Press)
[14] Keener, J. P.; Sneyd, J., Mathematical Physiology, Cellular Physiology, vol. 1 (2009), Springer · Zbl 1273.92017
[15] Kolmogorov, A. N.; Petrovskii, I. G.; Piskunov, N. S., Study of a diffusion equation that is related to the growth of a quality of matter, and its application to a biological problem, Byull. Mosk. Gos. Univ. Ser. A. Mat. Mekh., 1, 1-26 (1937)
[16] Kyle, J. L.; Harris, E., Global spread and persistence of dengue, Ann. Rev. Microbiol., 62, January, 71-92 (2008)
[17] Maciel-De-Freitas, R.; Codeço, T.; Lourenço-De-Olivera, Daily survival rates and dispersal of Aedes aegypti females in Rio de Janero, Brazil, Am. J. Trop. Med. Hygine, 76, 659-665 (2007)
[18] McMeniman, C. J.; Lane, R. V.; Cass, B. N.; Fong, A. W.C.; Sidhu, M.; Wang, Y. F.; O’Neill, S. L., Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegypti, Science, 323, 141-144 (2009)
[19] Medlock, J.; Luz, P. M.; Struchiner, C. J.; Galvani, A. P., The impact of transgenic mosquitoes on dengue virulence to humans and mosquitoes, Am. Nat., 174, 565-577 (2009)
[20] Min, K. T.; Benzer, S., Wolbachia, normally a symbiont of Drosophila, can be virulent, causing degeneration and early death, Proc. Natl. Acad. Sci., 94, 10792-10796 (1997)
[21] Moran, P. A.P., The Statistical Processes of Evolutionary Theory (1962), Clarendon Press · Zbl 0119.35901
[22] Moreira, L. A.; Iturbe-Ormaetxe, I.; Jeffery, J. A.; Lu, G.; Pyke, A. T.; Hedges, L. M.; Rocha, B. C.; Hall-Mendelin, S.; Day, A.; Riegler, M.; Hugo, L. E.; Johnson, K. N.; Kay, B. H.; McGraw, E. A.; vandenHurk, A. F.; Ryan, P. A.; O’Neill, S. L., A Wolbachia symbiont in Aedes aegypti limits infection with Dengue, Chikungunya, and Plasmodium, Cell, 139, 1268-1278 (2009)
[23] Muir, L. E.; Kay, B. H., Aedes aegypti survival and dispersal estimated by mark-release-recapture in northern Australia, Am. J. Trop. Med. Hygiene, 58, March, 277-282 (1998)
[24] Qi, R. F.; Zhang, L.; Chi, C. W., Biological characteristics of dengue virus and potential targets for drug design, Acta Biochim. Biophys. Sin., 40, 91-101 (2008)
[25] Rasgon, J. L.; Styer, L. M.; Scott, T. W., Wolbachia-induced mortality as a mechanism to modulate pathogen transmission by vector arthropods, J. Med. Entomol., 40, March, 125-132 (2003)
[26] Reiter, P.; Amador, M. A.; Anderson, R. A.; Clark, G. G., Short report: dispersal of Aedes aegypti in an urban area after blood feeding as demonstrated by rubidium-marked eggs, Am. J. Trop. Med. Hygiene, 52, 177 (1995)
[27] Rigau-Pérez, J. G., Severe dengue: the need for new case definitions, Lancet Infect. Dis., 6, 297-302 (2006)
[28] Schofield, P., Spatially explicit models of Turelli-Hoffmann Wolbachia invasive wave fronts, J. Theor. Biol., 215, 121-131 (2002)
[29] Sinkins, S. P.; O’Neill, S. L., Wolbachia as a vehicle to modify insect populations, (Handler, A. M.; James, A. A., Insect Transgenesis: Methods and Applications (2000), CRC Press)
[30] Styer, L. M.; Carey, J. R.; Wang, J. L.; Scott, T. W., Mosquitoes do senesce: departure from the paradigm of constant mortality, Am. J. Trop. Med. Hygiene, 76, 111-117 (2007)
[31] Turelli, M., Evolution of incompatibility-inducing microbes and their hosts, Evolution, 48, 1500-1513 (1994)
[32] Turelli, M., Cytoplasmic incompatibility in populations with overlapping generations, Evolution, 64, 232-241 (2010)
[33] Turelli, M.; Hoffmann, A. A., Rapid spread of an inherited incompatibility factor in California Drosophila, Nature, 353, 440-442 (1991)
[34] Turelli, M.; Hoffmann, A. A., Cytoplasmic incompatibility in Drosophila simulans: dynamics and parameter estimates from natural populations, Genetics, 140, 1319-1338 (1995)
[35] Wang, M. H.; Kot, M.; Neubert, M. G., Integrodifference equations, Allee effects and invasions, J. Math. Biol., 44, 150-168 (2002) · Zbl 0991.92032
[36] Weeks, A. R.; Turelli, M.; Harcombe, W. R.; Reynolds, K. T.; Hoffmann, A. A., From parasite to mutalist: rapid evolution of Wolbachia in natural populations of Drosophila, PLOS Biol., 5, 1 (2007)
[37] Weinberger, H. F., Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13, 353-396 (1982) · Zbl 0529.92010
[38] Werren, J. H., Biology of Wolbachia, Ann. Rev. Entomol., 42, January, 587-609 (1997)
[39] Whitehead, S. S.; Blaney, J. E.; Durbin, A. P.; Murphy, B. R., Prospects for a dengue virus vaccine, Nat. Rev. Microbiol., 5, July, 518-528 (2007)
[40] Whitten, M. J., Insect control by genetic manipulation of natural populations, Science, 171, 682-684 (1971)
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