Skip to main content

Advertisement

SpringerLink
Log in

Modelling Malaria Control by Introduction of Larvivorous Fish

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host–vector interaction and the predator–prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press.

    Google Scholar 

  • Aron, J. L., & May, R. M. (1982). The population dynamics of malaria. In R. M. Anderson (Ed.), The population dynamics of infectious diseases: theory and applications (pp. 139–179). London: Chapman and Hall.

    Google Scholar 

  • Auger, P., McHich, R., Chowdhury, T., Sallet, G., Tchuente, M., & Chattopadhyay, J. (2009). Effects of a disease affecting a predator on the dynamics of a predator–prey system. J. Theor. Biol., 258, 344–351.

    Article  Google Scholar 

  • Bowman, C., Gumel, A. B., van den Driessche, P., Wu, J., & Zhu, H. (2005). A mathematical model for assessing control strategies against West Nile virus. Bull. Math. Biol., 67, 1107–1133.

    Article  MathSciNet  Google Scholar 

  • Brito, I. (2001). Eradicating malaria: high hopes or a tangible goal? Health Policy Harvard, 2, 61–66.

    Google Scholar 

  • Chandra, G., Bhattacharjee, I., Chatterjee, S. N., & Ghosh, A. (2008). Mosquito control by larvivorous fish. Indian J. Med. Res., 127, 13–27.

    Google Scholar 

  • Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2009). The construction of next-generation matrices for compartmental epidemic models. J. R. Soc. Interface, 5, 1–13.

    Google Scholar 

  • Ghosh, S., & Dash, A. (2007). Larvivorous fish against malaria vectors: a new outlook. Trans. R. Soc. Trop. Med. Hyg., 101, 1063–1064.

    Article  Google Scholar 

  • Ghosh, S., Tiwari, S., Sathyanarayan, T., Sampath, T., Sharma, V., Nanda, N., Joshi, H., Adak, T., & Subbarao, S. (2005). Larvivorous fish in wells target the malaria vector sibling species of the complex in villages in Karnataka, India. Trans. R. Soc. Trop. Med. Hyg., 99, 101–105.

    Article  Google Scholar 

  • Gourley, S. A., Liu, R., & Wu, J. (2007). Eradicating vector-borne diseases via age-structured culling. J. Math. Biol., 54, 309–335.

    Article  MathSciNet  MATH  Google Scholar 

  • Greenwood, B. M., Bojang, K., Whitty, C. J., & Targett, G. A. (2005). Malaria. Lancet, 365, 1487–1498.

    Article  Google Scholar 

  • Greenwood, B. M., Fidock, D. A., Kyle, D. E., Kappe, S. H. I., Alonso, P. L., Collins, F. H., & Duffy, P. E. (2008). Malaria: progress, perils, and prospects for eradication. J. Clin. Invest., 118, 1266–1276.

    Article  Google Scholar 

  • Guo, H., & Li, M. Y. (2006). Global stability in a mathematical model of tuberculosis. Can. Appl. Math. Q., 14, 185–197.

    MathSciNet  MATH  Google Scholar 

  • Hancock, P. A., & Godfray, H. C. J. (2007). Application of the lumped age-class technique to studying the dynamics of malaria–mosquito–human interactions. Malar. J., 6, 98.

    Article  Google Scholar 

  • Hilker, F., & Schmitz, K. (2008). Disease-induced stabilization of predator–prey oscillations. J. Theor. Biol., 255, 299–306.

    Article  Google Scholar 

  • Hirsch, M. W., Smith, H. L., & Zhao, X.-Q. (2001). Chain transitivity, attractivity, and strong repellors for semidynamical systems. J. Dyn. Differ. Equ., 13, 107–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Howard, A. F., Zhou, G., & Omlin, F. X. (2007). Malaria mosquito control using edible fish in western Kenya: preliminary findings of a controlled study. BMC Public Health, 7, 199.

    Article  Google Scholar 

  • Jacob, S. S., Nair, N. B., & Balasubramanian, N. K. (1982). Toxicity of certain mosquito larvicides to the larvivorous fishes Aplocheilus lineatus (cuv. & val.) and Macropodus cupanus (cuv. & val.). Environ. Pollut. A, 28, 7–13.

    Article  Google Scholar 

  • Jenkins, D. W. (1964). Pathogens, parasites and predators of medically important arthropods. Annotated list and bibliography. Bull. World Health Organ., 30(Suppl), 1–150.

    Google Scholar 

  • Killeen, G. F., Fillinger, U., & Knols, B. G. (2002). Advantages of larval control for African malaria vectors: low mobility and behavioural responsiveness of immature mosquito stages allow high effective coverage. Malar. J., 1, 8.

    Article  Google Scholar 

  • Korobeinikov, A., & Maini, K. P. (2004). A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Math. Biosci. Eng., 1, 57–60.

    Article  MathSciNet  MATH  Google Scholar 

  • LaSalle, J. P. (1976). The stability of dynamical systems. In Regional conference series in applied mathematics. Philadelphia: SIAM.

    Google Scholar 

  • Li, J. (2009). Simple stage-structured models for wild and transgenic mosquito populations. J. Differ. Equ. Appl., 15, 327–347.

    Article  MATH  Google Scholar 

  • Lou, Y., & Zhao, X.-Q. (2010). Periodic Ross–Macdonald model with diffusion and advection. Appl. Anal., 89, 1067–1089.

    Article  MathSciNet  MATH  Google Scholar 

  • Ma, Z., Liu, J., & Li, J. (2003). Stability analysis for differential infectivity epidemic models. Nonlinear Anal., Real World Appl., 4, 841–856.

    Article  MathSciNet  MATH  Google Scholar 

  • Mohamed, A. A. (2003). Study of larvivorous fish for malaria vector control in Somalia, 2002. East. Mediterr. Health J., 9, 618–626.

    Google Scholar 

  • Moore, S. M., Borer, E. T., & Hosseini, P. R. (2010). Predators indirectly control vector-borne disease: linking predator–prey and host–pathogen models. J. R. Soc. Interface, 42, 161–176.

    Article  Google Scholar 

  • Oliveira, N. M., & Hilker, F. M. (2010). Modelling disease introduction as biological control of invasive predators to preserve endangered prey. Bull. Math. Biol., 72, 444–468.

    Article  MathSciNet  MATH  Google Scholar 

  • Reiskind, M. H., & Lounibos, L. P. (2009). Effects of intraspecific larval competition on adult longevity in the mosquitoes Aedes aegypti and Aedes albopictus. Med. Vet. Entomol., 23, 62–68.

    Article  Google Scholar 

  • Singh, N., Shukla, M. M., Mishra, A. K., Singh, M. P., Paliwal, J. C., & Dash, A. P. (2006). Malaria control using indoor residual spraying and larvivorous fish: a case study in Betul, central India. Trop. Med. Int. Health, 11, 1512–1520.

    Article  Google Scholar 

  • Smith, H. L. (1995). Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Amer. Math. Soc. Math. Surveys and Monographs.

  • Smith, H. L., & Waltman, P. (1995). The theory of the chemostat. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Snow, R. W., Guerra, C. A., Noor, A. M., Myint, H. Y., & Hay, S. I. (2005). The global distribution of clinical episodes of Plasmodium falciparum malaria. Nature, 434, 214–217.

    Article  Google Scholar 

  • Thieme, H. (1993). Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal., 24, 407–435.

    Article  MathSciNet  MATH  Google Scholar 

  • van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180, 29–48.

    Article  MathSciNet  MATH  Google Scholar 

  • Walker, K., & Lynch, M. (2007). Contributions of Anopheles larval control to malaria suppression in tropical Africa: review of achievements and potential. Med. Vet. Entomol., 21, 2–21.

    Article  Google Scholar 

  • Wonham, M. J., de Camino-Beck, T., & Lewis, M. A. (2004). An epidemiological model for West Nile Virus: Invasion analysis and control applications. Proc. R. Soc. Lond. B, Biol. Sci., 271, 501–507.

    Article  Google Scholar 

  • Wonham, M. J., Lewis, M. A., Renclawowicz, J., & van den Driessche, P. (2006). Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus. Ecol. Lett., 9, 706–725.

    Article  Google Scholar 

  • World Health Organization (2000). The world health report 1999, WHO.

  • World Health Organization (2010). The world health report 2009, WHO.

  • Zhang, X., Chen, L., & Neumann, A. U. (2000). The stage-structured predator–prey model and optimal harvesting policy. Math. Biosci., 168, 201–210.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao, X.-Q. (2003). Dynamical systems in population biology. New York: Springer.

    MATH  Google Scholar 

  • Zhao, X.-Q., & Jing, Z. (1996). Global asymptotic behavior in some cooperative systems of functional-differential equations. Can. Appl. Math. Q., 4, 421–444.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Yijun Lou

    Present address: MITACS Centre for Disease Modelling, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada

Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada

    Yijun Lou & Xiao-Qiang Zhao

Authors
  1. Yijun Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Qiang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yijun Lou.

Additional information

Supported in part by the NSERC of Canada and the MITACS of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lou, Y., Zhao, XQ. Modelling Malaria Control by Introduction of Larvivorous Fish. Bull Math Biol 73, 2384–2407 (2011). https://doi.org/10.1007/s11538-011-9628-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-011-9628-6

Keywords

Search

Navigation