Acta Applicandae Mathematicae

, Volume 132, Issue 1, pp 127–138

Effects of Mosquitoes Host Choice on Optimal Intervention Strategies for Malaria Control



We consider a mathematical model for malaria transmission which takes into account of the increase of host’s attractiveness to mosquitoes when the host harbours the parasite’s gametocytes. We investigate how this behavioral manipulation by malaria parasite may impact the optimal interventions targeted to infectious humans like treatment and screening activities. In particular, our analysis suggests that it may produce an increase of total costs associated to the disease and its control.


Malaria Mathematical model Optimal control 


  1. 1.
    Anita, S., Arnautu, V., Capasso, V.: An Introduction to Optimal Control Problems in Life Sciences and Economics. Birkhäuser, Boston (2010) Google Scholar
  2. 2.
    Agusto, F.B., Tchuenche, J.M.: Control strategies for the spread of malaria in humans with variable attractiveness. Math. Popul. Stud. 20, 82–100 (2013) CrossRefMathSciNetGoogle Scholar
  3. 3.
    Agusto, F.B., Marcus, N., Okosun, K.O.: Application of optimal control to the epidemiology of malaria. Electron. J. Differ. Equ. 2012, 1–22 (2012) CrossRefMathSciNetGoogle Scholar
  4. 4.
    Buonomo, B.: A simple analysis of vaccination strategies for rubella. Math. Biosci. Eng. 8, 677–687 (2011) CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Buonomo, B.: On the optimal vaccination strategies for horizontally and vertically transmitted infectious diseases. J. Biol. Syst. 19, 263–279 (2011) CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Buonomo, B., Vargas-De-León, C.: Stability and bifurcation analysis of a vector-bias model of malaria transmission. Math. Biosci. 242, 59–67 (2013) CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Chamchod, F., Britton, N.F.: Analysis of a vector-bias model on malaria transmission. Bull. Math. Biol. 73, 639–657 (2011) CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Cornet, S., Nicot, A., Rivero, A., Gandon, S.: Both infected and uninfected mosquitoes are attracted toward malaria infected birds. Malar. J. 12, 179 (2013) CrossRefGoogle Scholar
  9. 9.
    Cornet, S., Nicot, A., Rivero, A., Gandon, S.: Malaria infection increases bird attractiveness to uninfected mosquitoes. Ecol. Lett. 16, 323–329 (2013) CrossRefGoogle Scholar
  10. 10.
    Drakeley, C., Sutherland, C., Bouserna, J.T., Sauerwein, R.W., Targett, G.A.T.: The epidemiology of plasmodium falciparum gametocytes: weapons of mass dispersion. Trends Parasitol. 22, 424–430 (2006) CrossRefGoogle Scholar
  11. 11.
    Felipe, J.A.N., Riley, E.M., Drakeley, C.J., Sutherland, C.J., Ghani, A.C.: Determination of the processes driving the aquisition of immunity to malaria using a mathematical transmission. PLoS Comput. Biol. 3, e255 (2007) CrossRefGoogle Scholar
  12. 12.
    Garba, S.M., Gumel, A.B., Abu Bakar, M.R.: Backward bifurcations in dengue transmission dynamics. Math. Biosci. 215, 11–25 (2008) CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Gupta, S., Swinton, J., Anderson, R.M.: Theoretical studies of the effects of heterogeneity in the parasite population on the transmission dynamics of malaria. Proc. R. Soc. Lond. B, Biol. Sci. 256, 231–238 (1994) CrossRefGoogle Scholar
  14. 14.
    Kingsolver, J.G.: Mosquito host choice and the epidemiology of malaria. Am. Nat. 130, 811–827 (1987) CrossRefGoogle Scholar
  15. 15.
    Kong, Q., Qiu, Z., Sang, Z., Zou, Y.: Optimal control of a vector–host epidemics model. Math. Control Relat. Fields 1, 493–508 (2011) CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Jung, E., Lenhart, S., Feng, Z.: Optimal control of treatments in a two–strain tuberculosis model. Discrete Contin. Dyn. Syst., Ser. B 2, 473–482 (2002) CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Lacroix, R., Mukabana, W.R., Gouagna, L.C., Koella, J.C.: Malaria infection increases attractiveness of humans to mosquitoes. PLoS Biol. 3, e298 (2005) CrossRefGoogle Scholar
  18. 18.
    Lenhart, S., Workman, J.T.: Optimal Control Applied to Biological Models. Chapman & Hall/CRC Mathematical and Computational Biology Series. Chapman & Hall, Boca Raton (2007) MATHGoogle Scholar
  19. 19.
    MATLAB. Matlab release 12. The mathworks Inc., Natich (2000) Google Scholar
  20. 20.
    Macdonald, G.: The Epidemiology and Control of Malaria. Oxford University Press, London (1957) Google Scholar
  21. 21.
    Murray, C.J.L., Rosenfeld, L.C., Lim, S.S., et al.: Global malaria mortality between 1980 and 2010: a systematic analysis. Lancet 379, 413–431 (2012) CrossRefGoogle Scholar
  22. 22.
    Olayemi, I.K., Ande, A.T.: Life table analysis of anopheles gambiae (diptera: culicidae) in relation to malaria transmission. J. Vector Borne Dis. 46, 295–298 (2009) Google Scholar
  23. 23.
    Okosun, K.O., Ouifki, R., Marcus, N.: Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. Biosystems 106, 136–145 (2011) CrossRefGoogle Scholar
  24. 24.
    Okosun, K.O., Makinde, O.D., Takaidza, I.: Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives. Appl. Math. Model. 37, 3802–3820 (2013) CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Ozair, M., Lashari, A.A., Jung, I.H., Okosun, K.O.: Stability analysis and optimal control of a vector–borne disease with nonlinear incidence. Discrete Dyn. Nat. Soc. 2012 (2012). Article ID 595487 Google Scholar
  26. 26.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Interscience, New York (1962) MATHGoogle Scholar
  27. 27.
    Prosper, O., Saucedo, O., Thompson, D., Torres–Garcia, G., Wang, X., Castillo–Chavez, C.: Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Math. Biosci. Eng. 8, 141–170 (2011) CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Sherman, I.W. (ed.): Malaria: Parasite Biology, Pathogenesis and Protection. ASM Press, Washington (1998) Google Scholar
  29. 29.
    Wan, H., Cui, J.: A model for the transmission of malaria. Discrete Contin. Dyn. Syst., Ser. B 11, 479–496 (2009) CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Vargas–De–León, C.: Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. Math. Biosci. Eng. 9, 165–174 (2012) CrossRefMATHMathSciNetGoogle Scholar
  31. 31.
    World, H.: Organization, Malaria, Fact sheet n.94, March 2013 (Accessed Jul 15, 2013). Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics and ApplicationsUniversity of Naples Federico IINaplesItaly
  2. 2.Unidad Académica de MatemáticasUniversidad Autónoma de GuerreroChilpancingoMéxico

Personalised recommendations