Modelling immune response and drug therapy in human malaria infection

References

• Anderson , R.M. , May , R.M. and Gupta , S. 1989 . Non-linear phenomena in host–parasite interactions . Parasitology , 99 : S59 – S79 .
   PubMed Web of Science ®Google Scholar
• Artvanis-tsakonas , K. , Tongren , J.E. and Riley , E.M. 2003 . The war between the malaria parasite and the immune system: Immunity, immunoregulation and immunopathology . Clin. Exp. Immunol. , 133 : 145 – 152 .
   Google Scholar
• Bailey , N.T.J. 1982 . “ The biomathematics of malaria ” . In Malaria , 1 – 93 . London : Charles Griffin & Co. Ltd .
   Google Scholar
• Bate , C.A. , Tarvene , J. and Playfair , J.H.L. 1988 . Malarial parasites induce TNF production by macrophages . Immunology , 64 : 227 – 231 .
   PubMed Web of Science ®Google Scholar
• Clark , I.A. , Virelizier , J.L. , Carswell , E.A. and Wood , P.R. 1981 . Possible importance of macrophage-derived mediators in acute malaria . Infect. Immun. , 32 : 1058 – 1066 .
   PubMed Web of Science ®Google Scholar
• De Leenheer , P. and Smith , H.L. 2003 . Virus dynamics: A global analysis . SIAM J. Appl. Math. , 63 : 1313 – 1327 .
   Web of Science ®Google Scholar
• Diebner , H.H. , Eincher , M. , Molineaux , L. , Collins , W.E. , Jeffert , G.M. and Dietz , K. 2000 . Modelling the transition of asexual blood stages of Plasmodium falciparum to gametocytes . J. Theor. Biol. , 202 : 113 – 127 .
   Google Scholar
• Diekmann , O. , Heesterbeek , J.A.P. and Metz , J.A.J. 1990 . On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous population . J. Math. Biol. , 28 : 365 – 382 .
   PubMed Web of Science ®Google Scholar
• Elloso , M.M. , van der Heyde , H.C. , vande Waa , J.A. , Manning , D.D. and Weidanz , W.P. 1994 . Inhibition of Plasmodium falciparum in vitro by human gamma delta T cells . J. Immunol. , 153 : 1187 – 1194 .
   Google Scholar
• Engwerda , C.R. and Good , M.F. 2005 . Interactions between malaria parasites and the host immune system . Curr. Opin. Immunol. , 17 : 381 – 387 .
   Google Scholar
• Fan , M. , Li , M.Y. and Wang , K. 2001 . Global stability of an SEIS epidemic model with recruitment and a varying total population size . Math. Biosci. , 170 : 199 – 208 .
   PubMed Web of Science ®Google Scholar
• Fritsche , G. , Larcher , C. , Schennach , H. and Weiss , G. 2001 . Regulatory interactions between iron and nitric oxide metabolism for immune defense against Plasmodium falciparum infection . J. Infect. Dis. , 183 : 1388 – 1394 .
   PubMed Web of Science ®Google Scholar
• Ganusov , V.V. , Bergstrom , C.T. and Antia , R. 2002 . Within-host dynamics and the evolution of microparasites in a heterogeneous host population . Evolution , 56 ( 2 ) : 213 – 223 .
   PubMedGoogle Scholar
• Good , M.F. , Xu , H. , Wykes , M. and Engwerda , C.R. 2005 . Development and regulation of cell-mediated immune responses to the blood stages of malaria: Implications for vaccine research . Annu. Rev. Immunol. , 23 : 69 – 99 .
   PubMed Web of Science ®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 .
   PubMed Web of Science ®Google 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 .
   Google Scholar
• 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 . J. Theor. Biol. , 217 : 137 – 148 .
   Google Scholar
• Gurarie , D. and McKenzie , F.E. 2006 . Dynamics of immune response and drug resistance in malaria infection . Malar. J. , 5 : 86
   Google Scholar
• Gurarie , 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 . J. Theor. Biol. , 240 : 185 – 199 .
   PubMed Web of Science ®Google 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 . Proc. R. Soc. Lond. , 270 : 289 – 298 .
   Google Scholar
• Hertzel , C. and Anderson , R.M. 1996 . The within-host dynamics of blood stage malaria: Theoretical and experimental studies . Parasitology , 113 : 25 – 38 .
   Google Scholar
• Hoshen , M.B. , Heinrich , R. , Stein , W.D. and Ginsburg , H. 2000 . Mathematical modelling of the within-host dynamics of Plasmodium falciparum . Parasitology , 121 : 227 – 235 .
   PubMed Web of Science ®Google Scholar
• 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 .
   PubMedGoogle Scholar
• Kirk , K. 2001 . Membrane transport in the malaria-infected erythrocyte . Physiol. Rev. , 81 : 495 – 537 .
   PubMed Web of Science ®Google Scholar
• Kosinski , R.J. 1980 . Antigenic variation in trypanosomes: A computer analysis of variant order . Parasitology , 80 : 343 – 357 .
   Google Scholar
• Kwiatkowski , D. 1995 . Malaria toxins and the regulation of parasite density . Parasitol. Today , 11 : 206 – 212 .
   PubMedGoogle Scholar
• LaSalle , J.P. 1976 . The Stability of Dynamical Systems , Philadelphia, PA : SIAM .
   Google Scholar
• Ma , W. , Takeuchi , Y. , Hara , T. and Beretta , E. 2002 . Permanence of an SIR epidemic model with distributed time delays . Tokohu Math. J. , 54 : 581 – 591 .
   Web of Science ®Google Scholar
• Mason , D.P. and McKenzie , F.E. 1999 . Blood-stage dynamics and clinical implications of mixed Plasmodium vivax–Plasmodium falciparum infections . Am. J. Trop. Med. Hyg. , 61 : 367 – 374 .
   PubMed Web of Science ®Google Scholar
• McKenzie , F.E. and Bossert , W.H. 1997 . The dynamics of Plasmodium falciparum blood stage infection . J. Theor. Biol. , 188 : 127 – 140 .
   PubMed Web of Science ®Google Scholar
• McQueen , P.G. and McKenzie , F.E. 2004 . Age-structured red blood cell susceptibility and the dynamics of malaria infections . Proc. Natl. Acad. Sci. USA , 101 : 9161 – 9166 .
   Google Scholar
• Molineaux , L. and Dietz , K. 1999 . Review of intra-host models of malaria . Parassitologia , 41 : 221 – 231 .
   PubMedGoogle Scholar
• Molineaux , L. , Diebner , H.H. , Eincher , 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
• Muldowney , J.S. 1990 . Compound matrices and ordinary differential equations . Rocky Mount. J. Math. , 20 : 857 – 872 .
   Web of Science ®Google Scholar
• Murase , A. , Sasaki , T. and Kagiwara , T. 2005 . Stability analysis of pathogen–immune interaction dynamics . J. Math. Biol. , 51 : 247 – 267 .
   PubMed Web of Science ®Google Scholar
• O'Donnell , R.A. , de Koning-Ward , T.F. , Burt , R.A. , Bockarie , M. , Reeder , J.C. , Cowman , A.F. and Crabb , B.S. 2001 . Antibodies against merozoite surface protein (MSP)-1(19) are a major component of the invasion-inhibitory response in individuals immune to malaria . J. Exp. Med. , 193 : 1403 – 1412 . (247–263)
   PubMed Web of Science ®Google Scholar
• Perlmann , P. and Troye-Blomberg , M. 2002 . Malaria and the immune system in humans . Malaria Immunol. , 80 : 229 – 242 .
   Google Scholar
• Piper , K.P. , Hayward , R.E. , Cox , M.J. and Day , K.P. 1999 . Malaria transmission and naturally acquired immunity to PfEMP-1 . Infect. Immun. , 67 : 6369 – 6374 .
   PubMedGoogle Scholar
• Rouzine , I.M. and McKenzie , F.E. 2003 . Link between immune response and parasite synchronization in malaria . Proc. Natl. Acad. Sci. USA , 100 : 3473 – 3478 .
   Google Scholar
• Saul , A. 1998 . Models for the in-host dynamics of malaria re-visited: Errors in some basic models lead to large overestimates of growth rate . Parasitology , 117 : 405 – 407 .
   Google Scholar
• Shiri , T. , Garira , W. and Musekwa , S.D. 2005 . A two strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters . J. Math. Biosci. Eng. , 2 : 811 – 832 .
   PubMed Web of Science ®Google Scholar
• Stevenson , M.M. and Riley , E.M. 2004 . Innate immunity to malaria . Nat. Rev. Immunol. , 4 : 169 – 180 .
   PubMed Web of Science ®Google Scholar
• Troye-Blomberg , M. , Worku , S. , Tangteerawatana , P. , Jamshaid , R. , Soderstrom , K. , Elghazali , G. , Moretta , L. , Hammarstrom , M. and Mincheva-Nilsson , L. 1999 . Human gamma delta T cells that inhibit the in vitro growth of the sexual blood stages of the Plasmodium falciparum parasite express cytolytic and proinflammatory molecules . Scand. J. Immunol. , 50 : 642 – 650 .
   Google Scholar
• van den Driessche , P. and Watmough , J. 2002 . Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission . Math. Biosci. , 180 : 29 – 48 .
   PubMed Web of Science ®Google Scholar
• White , N.J. 1998 . “ Malaria pathophysiology ” . In Malaria, Parasite Biology, Pathogenesis, and Protection , Edited by: Sherman , I.W. 371 – 385 . Washington, DC : ASM Press .
   Google Scholar
• Wickramasinghe , S.N. and Abdalla , S.H. 2000 . Blood and bone marrow changes in malaria . Bailliers Best Pract. Res. Clin. Haematol. , 13 : 277 – 299 .
   Google Scholar