Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T03:48:55.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Problems with continuous-time malaria models in describing gametocytogenesis

Published online by Cambridge University Press:  04 July 2008

L. CROOKS
L. CROOKS*
Affiliation:
Institutes of Evolution, Immunology and Infection Research, The University of Edinburgh, Ashworth Laboratories, The King's Buildings, West Mains Road, Edinburgh EH9 3JT, UK
*
*Corresponding author: Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Box 7023, SE-750 07 Uppsala, Sweden. Tel: +46 18 67 2034. Fax: +46 18 67 2848. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Most mathematical models of malaria infection represent parasites as replicating continuously at a constant rate whereas in reality, malaria parasites replicate at a fixed age. The behaviour of continuous-time models when gametocytogenesis is included, in comparison to a more realistic discrete-time model that incorporates a fixed replication age was evaluated. Both the infection dynamics under gametocytogenesis and implications for predicting the amount parasites should invest into gametocytes (level of investment favoured by natural selection) are considered. It is shown that the many malaria models with constant replication rates can be represented by just 3 basic types. For these 3 types, it is then shown that under gametocytogenesis (i) in 2 cases, parasite multiplication and gametocyte production is mostly much too low, (ii) in the third, parasite multiplication and gametocyte production is mostly much too high, (iii) the effect of gametocyte investment on parasite multiplication is mostly too high, (iv) the effect of gametocyte investment on gametocyte production is nearly always too low and (v) with a simple approximation of fitness, the predicted level of gametocyte investment is mostly much too low. However, a continuous model with 48 age-compartments compares well to the discrete model. These findings are a further argument for modelling malaria infections in discrete time.

Keywords

malariaPlasmodium falciparummathematical modelswithin-host dynamicsgametocytesoptimal gametocyte investment
Type
Original Articles
Information
Parasitology , Volume 135 , Issue 8 , July 2008 , pp. 881 - 896
Copyright
Copyright © 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, R. M. (1998). Complex dynamic behaviours in the interaction between parasite populations and the host's immune system. International Journal for Parasitology 28, 551–566.CrossRefGoogle ScholarPubMed
Anderson, R. M. and May, R. M. (1982). Coevolution of hosts and parasites. Parasitology 85, 411–426.CrossRefGoogle ScholarPubMed
Anderson, R. M., May, R. M. and Gupta, S. (1989). Non-linear phenomena in host-parasite interactions. Parasitology 99 (Suppl.), S59–S79.CrossRefGoogle ScholarPubMed
Austin, D. J., White, N. J. and Anderson, R. M. (1998). The dynamics of drug action on the within-host population growth of infectious agents: melding pharmacokinetics with pathogen population dynamics. Journal of Theoretical Biology 194, 313–339.CrossRefGoogle ScholarPubMed
Boyd, M. F. (1949). Malariology. Saunders, Philadelphia, USA.Google Scholar
Bruce, M. C., Alano, P., Duthie, S. and Carter, R. (1990). Commitment of the malaria parasite Plasmodium falciparum to sexual and asexual development. Parasitology 100, 191–200.CrossRefGoogle ScholarPubMed
Carter, R. and Miller, L. H. (1979). Evidence for environmental modulation of gametocytogenesis in Plasmodium falciparum in continuous culture. Bulletin of the World Health Organization 57 (Suppl. 1), 37–52.Google ScholarPubMed
Collins, W. E. and Jeffery, G. M. (1999). A retrospective examination of sporozoite- and trophozoite-induced infections with Plasmodium falciparum: development of parasitological and clinical immunity during primary infection. American Journal of Tropical Medicine and Hygiene 61, 4–19.CrossRefGoogle ScholarPubMed
Day, K. P., Hayward, R. E. and Dyer, M. (1998). The biology of Plasmodium falciparum transmission stages. Parasitology 116 (Suppl.), S95–S109.CrossRefGoogle ScholarPubMed
Dyer, M. and Day, K. P. (2000). Commitment to gametocytogenesis in Plasmodium falciparum. Parasitology Today 16, 102–107.CrossRefGoogle ScholarPubMed
Diebner, H. H., Eichner, M., Molineaux, L., Collins, W. E., Jeffery, G. M. and Dietz, K. (2000). Modelling the transition of asexual blood stages of Plasmodium falciparum to gametocytes. Journal of Theoretical Biology 202, 113–127.CrossRefGoogle ScholarPubMed
Eyles, D. E. (1951). Studies on Plasmodium gallinaceum: I. Characteristics of the infection in the mosquito, Aedes aegypti. American Journal of Hygiene 54, 101–112.Google Scholar
Garnham, P. C. C. (1966). Malaria Parasites and Other Haemosporidia. Blackwell Scientific Publications, Oxford.Google Scholar
Gatton, M. L. and Cheng, Q. (2004). Investigating antigenic variation and other parasite-host interactions in Plasmodium falciparum infections in naïve hosts. Parasitology 128, 367–376.Google Scholar
Gravenor, M. B. and Kwiatkowski, D. (1998). An analysis of the temperature effects of fever on the intra-host population dynamics of Plasmodium falciparum. Parasitology 117, 97–105.CrossRefGoogle ScholarPubMed
Gravenor, M. B. and Lloyd, A. L. (1998). Reply to: Models for the in-host dynamics of malaria revisited: errors in some basic models lead to large overestimates of growth rates. Parasitology 117, 409–410.CrossRefGoogle Scholar
Gravenor, M. B., Boele van Hensbroek, M. B. and Kwiatkowski, D. (1998). Estimating sequestered parasite population dynamics in cerebral malaria. Proceedings of the National Academy of Sciences, USA 95, 7620–7624.CrossRefGoogle ScholarPubMed
Gravenor, M. B., Lloyd, A. L., Kremsner, P. G., Missinou, M. A., English, M., Marsh, K. and Kwiatkowski, D. (2002). A model for estimating total parasite load in falciparum malaria patients. Journal of Theoretical Biology 217, 137–148. doi:10.1006/yjtbi.3030.CrossRefGoogle Scholar
Gravenor, M. B., McLean, A. R. and Kwiatkowski, D. (1995). The regulation of malaria parasitaemia: parameter estimates for a population model. Parasitology 110, 115–122.CrossRefGoogle ScholarPubMed
Guararie, D., Zimmerman, P. A. and King, C. H. (2006). Dynamic regulation of single- and mixed-species malaria infection: insights to specific and non-specific mechanisms of control. Journal of Theoretical Biology 240, 185–199. doi:10.1016/j.jtbi.2005.09.015.CrossRefGoogle Scholar
Haydon, D. T., Matthews, L., Timms, R. and Colegrave, N. (2003). Top-down or bottom-up regulation of intra-host blood-stage malaria: do malaria parasites most resemble the dynamics of prey or predator? Proceedings of the Royal Society of London, B 270, 289–298. doi:10.1098/rspb.2002.2203.CrossRefGoogle ScholarPubMed
Hellriegel, B. (1992). Modelling the immune response to malaria with ecological concepts: short-term behavior against long-term equilibrium. Proceedings of the Royal Society of London, B 250, 249–256.Google ScholarPubMed
Hetzel, C. and Anderson, R. M. (1996). The within-host cellular dynamics of bloodstage malaria: theoretical and experimental studies. Parasitology 113, 25–38.CrossRefGoogle ScholarPubMed
Hoshen, M. B., Heinrich, R., Stein, W. D. and Ginsburg, H. (2000 a). Mathematical modelling of the within-host dynamics of Plasmodium falciparum. Parasitology 121, 227–235.CrossRefGoogle ScholarPubMed
Hoshen, M. B., Na-Bangchang, K., Stein, W. D. and Ginsburg, H. (2000 b). Mathematical modelling of the chemotherapy of Plasmodium falciparum malaria with artesunate: postulation of ‘dormancy’, a partial cytostatic effect of the drug, and its implication for treatment regimens. Parasitology 121, 237–246.CrossRefGoogle ScholarPubMed
Hoshen, M. B, Stein, W. D. and Ginsburg, H. (1998). Modelling the chloroquine chemotherapy of falciparum malaria: the value of spacing a split dose. Parasitology 116, 407–416.CrossRefGoogle ScholarPubMed
Hoshen, M. B., Stein, W. D. and Ginsburg, H. (2001). Pharmacokinetic-pharmacodynamic modelling of the antimalarial activity of mefloquine. Parasitology 123, 337–346. doi:10.1017/S003118200100854X.CrossRefGoogle ScholarPubMed
Hoshen, M. B., Stein, W. D. and Ginsburg, H. (2002). Mathematical modelling of malaria chemotherapy: combining artesunate and mefloquine. Parasitology 124, 9–15. doi:10.1017/S0031182001008952.CrossRefGoogle ScholarPubMed
Jakeman, G. N., Saul, A., Hogarth, W. L. and Collins, W. E. (1999). Anaemia of acute malaria infections in non-immune patients primarily results from destruction of uninfected erythrocytes. Parasitology 119, 127–133.Google Scholar
Janeway, C. A., Travers, P., Walport, M. and Shlomchik, M. J. (2001). Immunobiology: the Immune System in Health and Disease. 5th Edn. Garland Publishing, New York.Google Scholar
Koella, J. C. and Antia, R. (1995). Optimal pattern of replication and transmission for parasites with two stages in their life cycle. Theoretical Population Biology 47, 277–291.CrossRefGoogle Scholar
Kaushal, D. C., Carter, R., Miller, L. H. and Krishna, G. (1980). Gametocytogenesis by malaria parasites in continuous culture. Nature, London 286, 490–492.CrossRefGoogle ScholarPubMed
Kwiatkowski, D. and Nowak, M. (1991). Periodic and chaotic host-parasite interactions in human malaria. Proceedings of the National Academy of Sciences, USA 88, 5111–5113.Google Scholar
Marcus-Roberts, H. and Roberts, F. S. (1983). Malaria: models of the population dynamics of the malaria parasite. In Life Science Models (ed. Marcus-Roberts, H. and Thompson, M.), pp. 161–177. Springer-Verlag, New York.CrossRefGoogle Scholar
Mason, D. P. and McKenzie, F. E. (1999). Blood-stage dynamics and clinical implications of mixed Plasmodium vivax-Plasmodium falciparum infections. American Journal of Tropical Medicine and Hygiene 61, 367–374.Google Scholar
Mason, D. P., McKenzie, F. E. and Bossert, W. H. (1999). The blood-stage dynamics of mixed Plasmodium malariae-Plasmodium falciparum infections. Journal of Theoretical Biology 198, 549–566.Google Scholar
McKenzie, F. E. and Bossert, W. H. (1997). The dynamics of Plasmodium falciparum blood-stage infection. Journal of Theoretical Biology 188, 127–140.CrossRefGoogle ScholarPubMed
McKenzie, F. E. and Bossert, W. H. (1998). The optimal production of gametocytes by Plasmodium falciparum. Journal of Theoretical Biology 193, 419–428.Google Scholar
Molineaux, L. and Dietz, K. (1999). Review of intra-host models of malaria. Parassitologia 41, 221–231.Google ScholarPubMed
Molineaux, L., Diebner, H. H., Eichner, M., Collins, W. E., Jeffery, G. M. and Dietz, K. (2001). Plasmodium falciparum parasitaemia described by a new mathematical model. Parasitology 122, 379–391.Google Scholar
Mons, B. (1986). Intra-erythrocytic differentiation of Plasmodium berghei. Acta Leidensia 54, 1–124.Google ScholarPubMed
Paget-Nicol, S., Gatton, M., Hastings, I. and Saul, A. (2002). The Plasmodium falciparum var gene switching rate, switching mechanism and patterns of parasite recrudescence described by mathematical modelling. Parasitology 124, 225–235. doi:10.1017/S0031182001160.Google Scholar
Parker, G. A. and Maynard Smith, J. (1990). Optimality theory in evolutionary biology. Nature, London 348, 27–33.CrossRefGoogle Scholar
Recker, M., Al-Bader, R. and Gupta, S. (2005). A mathematical model for a new mechanism of phenotypic variation in malaria. Parasitology 131, 151–159. doi:10.1017/S0031182005007481.CrossRefGoogle ScholarPubMed
Robert, V., Read, A. F., Essong, J., Tchuinkam, T., Mulder, B., Verhave, J. P. and Carnevale, P. (1996). Effect of gametocyte sex ratio on infectivity of Plasmodium falciparum to Anopheles gambiae. Transactions of the Royal Society of Tropical Medicine and Hygiene 90, 621–624.CrossRefGoogle ScholarPubMed
Ross, R. (1911). The Prevention of Malaria. John Murray, London.Google Scholar
Rouzine, I. M. and McKenzie, F. E. (2003). Link between immune response and parasite synchronization in malaria. Proceedings of the National Academy of Sciences, USA 100, 3473–3478. doi:10.1073/pnas.262796299.CrossRefGoogle ScholarPubMed
Saul, A. (1998). Models for the in-host dynamics of malaria revisited: errors in some basic models lead to large over-estimates of growth rates. Parasitology 117, 405–407.CrossRefGoogle ScholarPubMed
Simpson, J. A., Aarons, L., Collins, W. E., Jeffery, G. M. and White, N. J. (2002). Population dynamics of untreated Plasmodium falciparum malaria within the adult human host during the expansion phase of the infection. Parasitology 124, 247–263. doi:10.1017/S0031182001001202.CrossRefGoogle ScholarPubMed
Smalley, M. E. and Brown, J. (1981). Plasmodium falciparum gametocytogenesis stimulated by lymphocytes and serum from infected Gambian children. Transactions of the Royal Society of Tropical Medicine and Hygiene 75, 316–317.Google Scholar
Smalley, M. E., Brown, J. and Bassett, N. M. (1981). The rate of production of Plasmodium falciparum gametocytes during natural infections. Transactions of the Royal Society of Tropical Medicine and Hygiene 75, 318–319.CrossRefGoogle ScholarPubMed
Smith, T., Dietz, K., Vounatsou, P., Müller, I., English, M. and Marsh, K. (2004). Bayesian age-stage modelling of Plasmodium falciparum sequestered parasite loads in severe malaria patients. Parasitology 129, 289–299. doi:10.1017/S003118200400575X.CrossRefGoogle ScholarPubMed
Swinton, J. (1996). The dynamics of blood stage malaria: modelling strain specific and strain transcending immunity. In Models for Infectious Human Diseases: Their Structure and Relationship to Data (ed. Isham, V. and Medley, G.), pp. 210–212. Cambridge University Press, Cambridge.Google Scholar
Taylor, L. H. and Read, A. F. (1997). Why so few transmission stages? Reproductive restraint by malaria parasites. Parasitology Today 13, 135–140.CrossRefGoogle ScholarPubMed
Tchuinkam, T., Mulder, B., Dechering, K., Stoffels, H., Verhave, J. P., Cot, M., Carnevale, P., Meuwissen, J. and Robert, V. (1993). Experimental infections of Anopheles gambiae with Plasmodium falciparum of naturally infected gametocyte carriers in Cameroon: factors influencing the infectivity to mosquitoes. Tropical Medicine and Parasitology 44, 271–276.Google ScholarPubMed
White, N. J., Chapman, D. and Watt, G. (1992). The effects of multiplication and synchronicity on the vascular distribution of parasites in falciparum malaria. Transactions of the Royal Society of Tropical Medicine and Hygiene 86, 590–597.CrossRefGoogle ScholarPubMed
Williams, J. L. (1999). Stimulation of Plasmodium falciparum gametocytogenesis by conditioned medium from parasite cultures. American Journal of Tropical Medicine and Hygiene 60, 7–13.CrossRefGoogle ScholarPubMed