Skip to main content
Log in

Optimal Treatment Strategies for Malaria Infection

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

Abstract

We develop a numerical method for estimating optimal parameters in a mathematical model of the within-host dynamics of malaria infection. The model consists of a quasilinear system of partial differential equations. Convergence theory for the computed parameters is provided. Following this analysis, we present several numerical simulations that suggest that periodic treatments that are in synchronization with the periodic bursting rate of infected erythrocytes are the most productive strategies.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ackleh, A. S. (1999). Parameter identification in size-structured population models with nonlinear individual rates. Math. Comput. Model., 30(9–10), 81–92.

    Article  MathSciNet  MATH  Google Scholar 

  • Ackleh, A. S., & Thibodeaux, J. J. (2008). Parameter estimation in a structured erythropoiesis model. Math. Biosci. Eng., 5(4), 601–616.

    Article  MathSciNet  MATH  Google Scholar 

  • Ackleh, A. S., Banks, H. T., Deng, K., & Hu, S. (2005). Parameter estimation in a coupled system of nonlinear size-structured populations. Math. Biosci. Eng., 2(2), 289–315.

    Article  MathSciNet  MATH  Google Scholar 

  • Ackleh, A. S., Deng, K., Ito, K., & Thibodeaux, J. (2006). A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate. Math. Biosci., 204(1), 21–48.

    Article  MathSciNet  MATH  Google Scholar 

  • Banks, H. T. (1988). Computational techniques for inverse problems in size-structured population models. In Lecture notes in control and info. science: Vol. 114. Proc. IFIP conf. on optimal control of systems governed by PDE (pp. 3–10), Santiago de Compostela, July 1987. Berlin: Springer.

    Google Scholar 

  • Banks, H. T. (1994). Some remarks on estimation for size-structured population models. In S. Levin (Ed.), Lecture notes in biomathematics: Vol. 100. Frontiers of theoretical biology (pp. 609–623). Berlin: Springer.

    Google Scholar 

  • Banks, H. T., & Fitzpatrick, B. G. (1991). Estimation of growth rate distributions in size structured population models. Q. Appl. Math., 49, 215–235.

    MathSciNet  MATH  Google Scholar 

  • Banks, H. T., & Kunisch, K. (1989). Estimation techniques for distributed parameter systems. Boston: Birkhauser.

    Book  MATH  Google Scholar 

  • Banks, H. T., Botsford, L., Kappel, F., & Wang, C. (1988). Modeling and estimation in size structured population models. In Proc. math. ecology (pp. 521–541), Trieste, 1986.

    Google Scholar 

  • Banks, H. T., Botsford, L. W., Kappel, F., & Wang, C. (1991). Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis). J. Math. Biol., 30(2), 125–150.

    Article  MATH  Google Scholar 

  • Banks, H. T., Cole, C. E., Schlosser, P. M., & Tran, H. T. (2004). Modeling and optimal regulation of erythropoiesis subject to benzene intoxication. Math. Biosci. Eng., 1(1), 15–48.

    Article  MathSciNet  MATH  Google Scholar 

  • Bélair, J., & Mahaffy, J. M. (2001). Variable maturation velocity and parameter sensitivity in a model for hematopoiesis. IMA J. Math. Appl. Med. Biol., 18(2), 193–211.

    Article  MATH  Google Scholar 

  • Casals-Pascual, C., Kai, O., Cheung, J. O. P., Williams, S., Lowe, B., Nyanoti, M., Williams, T. N., Maitland, K., Molyneux, M., Newton, C. R. J. C., Peshu, N., Watt, S. M., & Roberts, D. J. (2006). Suppression of erythropoiesis in malarial anemia is associated with hemozoin in vitro and in vivo. Blood, 108(8), 2569–2577.

    Article  Google Scholar 

  • Chitnis, N., Cushing, J. M., & Hyman, J. M. (2006). Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math., 67(1), 24–45.

    Article  MathSciNet  MATH  Google Scholar 

  • Chiyaka, C., Garira, W., & Dube, S. (2007). Transmission model of endemic human malaria in a partially immune population. Math. Comput. Model., 46(5–6), 806–822.

    Article  MathSciNet  MATH  Google Scholar 

  • Cho, K., & Kwon, Y. (1999). Parameter estimation in nonlinear age-dependent population dynamics. IMA J. Appl. Math., 62(3), 227–244.

    Article  MathSciNet  MATH  Google Scholar 

  • De Leenheer, P., & Pilyugin, S. S. (2008). Immune response to a malaria infection: Properties of a mathematical model. J. Biol. Dyn., 2(2), 102–120.

    Article  MathSciNet  MATH  Google Scholar 

  • Gurarie, D., & McKenzie, F. E. (2006). Dynamics of immune response and drug resistance in malaria infection. Malar. J., 5, 86.

    Article  Google Scholar 

  • Mahaffy, J. M., Polk, S. W., & Roeder, R. K. W. (1999). An age-structured model for erythropoiesis following a phlebotomy (Technical Report). Centre Recherches Mathématiques, Université de Montréal, CRM-2598.

  • NIH (2007). Understanding Malaria (Publication No. 07-7139).

  • Rundell, W. (1989). Determining the birth function for an age-structured population. Math. Popul. Stud., 1(4), 377–395.

    Article  MathSciNet  MATH  Google Scholar 

  • Rundell, W. (1993). Determining the death rate for an age-structured population from census data. SIAM J. Appl. Math., 53(6), 1731–1746.

    Article  MathSciNet  MATH  Google Scholar 

  • Sawyer, S. T., Krantz, S. B., & Goldwasser, E. (1987). Binding and receptor-mediated endocytosis of erythropoietin in friend virus infected erythroid cells. J. Biol. Chem., 262, 5554–5562.

    Google Scholar 

  • Thibodeaux, J. J. (2010). Modeling erythropoiesis subject to malaria infection. Math. Biosci., 225(1), 59–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Tumwiine, J., Mugisha, J. Y. T., & Luboobi, L. S. (2008). On global stability of the intra-host dynamics of malaria and the immune system. J. Math. Anal. Appl., 341(2), 855–869.

    Article  MathSciNet  MATH  Google Scholar 

  • White, N. J. (2004). Antimalarial drug resistance. J. Clin. Invest., 113(8), 1084–1092.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeremy J. Thibodeaux.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thibodeaux, J.J., Schlittenhardt, T.P. Optimal Treatment Strategies for Malaria Infection. Bull Math Biol 73, 2791–2808 (2011). https://doi.org/10.1007/s11538-011-9650-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-011-9650-8

Keywords

Navigation