Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T11:27:46.655Z Has data issue: false hasContentIssue false
  • English
  • Français

MODELLING THE INTRODUCTION OF WOLBACHIA INTO AEDES AEGYPTI MOSQUITOES TO REDUCE DENGUE TRANSMISSION

Published online by Cambridge University Press:  10 October 2012

MEKSIANIS Z. NDII ,
ROSLYN I. HICKSON  and
GEOFFRY N. MERCER
MEKSIANIS Z. NDII*
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia Department of Mathematics, The University of Nusa Cendana, East Nusa Tenggara, Indonesia (email: [email protected]) School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia (email: [email protected])
ROSLYN I. HICKSON
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia (email: [email protected]) National Centre for Epidemiology and Population Health, The Australian National University, Canberra, ACT 0200, Australia (email: [email protected])
GEOFFRY N. MERCER
Affiliation:
National Centre for Epidemiology and Population Health, The Australian National University, Canberra, ACT 0200, Australia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Infecting Aedes aegypti mosquitoes with the bacteria Wolbachia has been proposed as an innovative new strategy to reduce the transmission of dengue fever. Field trials are currently being undertaken in Queensland, Australia. However, few mathematical models have been developed to consider the persistence of Wolbachia-infected mosquitoes in the wild. This paper develops a mathematical model to determine the persistence of Wolbachia-infected mosquitoes by considering the competition between Wolbachia-infected and non-Wolbachia mosquitoes. The model has four steady states that are biologically feasible: all mosquitoes dying out, only non-Wolbachia mosquitoes surviving, and two steady states where non-Wolbachia and Wolbachia-infected mosquitoes coexist. The stability of the steady states is determined with respect to the key parameters in the mosquito life cycle. A global sensitivity analysis of the model is also conducted. The results show that the persistence of Wolbachia-infected mosquitoes is dominated by the reproductive rate, death rate, maturation rate and maternal transmission. For the parameter values where Wolbachia persists, it dominates the population, and hence the introduction of Wolbachia has great potential to reduce dengue transmission.

Keywords

WolbachiaAedes aegyptidenguemathematical modelsensitivity analysisstability

MSC classification

Secondary: 92D25: Population dynamics (general)
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 3 , January 2012 , pp. 213 - 227
Copyright
Copyright © Australian Mathematical Society 2012

References

[1]Burattini, M. N., Chen, M., Chow, A., Coutinho, F. A. B., Goh, K. T., Lopez, L. F., Ma, S. and Massad, E., “Modelling the control strategies against dengue in Singapore”, Epidemiol. Infect. 136 (2008) 309–319; doi:10.1017/S0950268807008667.CrossRefGoogle ScholarPubMed
[2]Hoffmann et al., A. A., “Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission”, Nature 476 (2011) 454–457; doi:10.1038/nature10356.CrossRefGoogle Scholar
[3]Iturbe-Ormaetxe, I., Walker, T. and O’Neill, S. L., “Wolbachia and the biological control of mosquito-borne disease”, EMBO Rep. 12 (2011) 508–518; doi:10.1038/embor.2011.84.CrossRefGoogle ScholarPubMed
[4]Kongnuy, R., Pongsumpun, P. and Tang, I.-M., “Mathematical model for dengue disease with maternal antibodies”, Int. J. Biol. Life Sci. 7 (2011) 74–83.Google Scholar
[5]Maidana, N. A. and Yang, H. M., “Describing the geographic spread of dengue disease by traveling waves”, Math. Biosci. 215 (2008) 64–67; doi:10.1016/j.mbs.2008.05.008.CrossRefGoogle ScholarPubMed
[6]Marino, S., Hogue, I. B., Ray, C. J. and Kirschner, D. E., “A methodology for performing global uncertainty and sensitivity analysis in system biology”, J. Theoret. Biol. 254 (2008) 178–196; doi:10.1016/j.jtbi.2008.04.011.CrossRefGoogle Scholar
[7]McMeniman, C. J., Lane, R. V., Cass, N. B., Fong, A. W. C., Sidhu, M., Wang, Y.-F. and O’Neill, S. L., “Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegpyti”, Science 323 (2009) 141–144; doi:10.1126/science.1165326.CrossRefGoogle Scholar
[8]Montella, I. R., Martins, A. J., Viana-Mendeiros, P. F., Lima, J. B. P., Braga, I. A. and Valle, D., “Insecticide resistance mechanisms of Brazilian Aedes aegypti populations from 2001 to 2004”, Am. J. Trop. Med. Hyg. 77 (2007) 467–477.CrossRefGoogle ScholarPubMed
[9]Ordóñez-Gonzalez, J. G., Mercado-Hernandez, R., Flores-Suarez, A. E. and Fernández-Salas, I., “The use of sticky ovitraps to estimate dispersal of Aedes aegypti in northeastern Mexico”, J. Am. Mosq. Control Assoc. 17 (2001) 93–97.Google ScholarPubMed
[10]Otero, M., Solero, H. G. and Schweigmann, N., “A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate”, Bull. Math. Biol. 68 (2006) 1945–1974; doi:10.1007/s11538-006-9067-y.CrossRefGoogle ScholarPubMed
[11]Read, A. F. and Thomas, M. B., “Mosquitoes cut short”, Science 323 (2009) 51–52; doi:10.1126/science.1168659.CrossRefGoogle ScholarPubMed
[12]Ruang-areerate, T. and Kittayapong, P., “Wolbachia transinfection in Aedes aegypti: a potential gene driver of dengue vectors”, Proc. Nat. Acad. Sci 103 (2006) 12,534–12,539; doi:10.1073/pnas.0508879103.CrossRefGoogle ScholarPubMed
[13]Sinkins, S. P., “Wolbachia and cytoplasmic incompatibility in mosquitoes”, Insect Biochem. Molec. Biol. 34 (2004) 723–729; doi:10.1016/j.ibmb.2004.03.025.CrossRefGoogle ScholarPubMed
[14]Swartzman, G. L. and Kaluzny, S. P., Ecological simulation primer (Macmillan, New York, 1987).Google Scholar
[15]Turley, A. P., Moreira, L. A., O’Neill, S. L. and McGraw, E. A., “Wolbachia infection reduces blood-feeding success in the dengue fever mosquito, Aedes aegypti”, PLoS Neglected Tropical Diseases 3 (2009) e516; doi:10.1371/journal.pntd.0000516.CrossRefGoogle ScholarPubMed
[16]Walker et al., T., “The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations”, Nature 476 (2011) 450–453; doi:10.1038/nature10355.CrossRefGoogle Scholar
[17] World Health Organization, Dengue and severe dengue, Fact Sheet No. 117 (2002), http://www.who.int/mediacentre/factsheets/fs117/en/index.html.Google Scholar
[18]Xi, Z., Khoo, C. C. H. and Dobson, S. L., “Wolbachia establishment and invasion in an Aedes aegpyti laboratory population”, Science 310 (2005) 326–328; doi:10.1126/science.1117607.CrossRefGoogle Scholar
[19]Yang, H. M., Macoris, M. L. G., Galvani, K. C., Andrighetti, M. T. M. and Wanderley, D. M. V., “Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue”, Epidemiol. Infect. 137 (2009) 1188–1202; doi:10.1017/S0950268809002040.CrossRefGoogle ScholarPubMed
[20]Yeap et al., H. L., “Dynamics of the ‘Popcorn’ Wolbachia infection in outbred Aedes aegypti informs prospects for mosquito vector control”, Genetics 187 (2011) 583–595; doi:10.1534/genetics.110.122390.CrossRefGoogle Scholar