메뉴 건너뛰기




Volumn 12, Issue 4, 2009, Pages 827-864

A mathematical analysis of malaria and tuberculosis co-dynamics

Author keywords

Basic reproduction number; Co dynamics; Equilibrium; Malaria TB model; Sensitivity; Stability

Indexed keywords


EID: 73649090797     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.827     Document Type: Article
Times cited : (55)

References (40)
  • 3
    • 21444451814 scopus 로고    scopus 로고
    • A mathematical model for assessing control strategies against West Nile virus
    • C. Bowman, A. B. Gumel, P. van den Driessche, J. Wu and H. Zhu, A mathematical model for assessing control strategies against West Nile virus, Bull. Math. Biol., 67 (2005), 1107-1133.
    • (2005) Bull. Math. Biol , vol.67 , pp. 1107-1133
    • Bowman, C.1    Gumel, A.B.2    van den Driessche, P.3    Wu, J.4    Zhu, H.5
  • 5
    • 0003209221 scopus 로고    scopus 로고
    • Mathematical Models in Population Biology and Epidemiology
    • Springer-Verlag, New York
    • F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology", Text in Applied Mathematics Series, 40, Springer-Verlag, New York, 2001.
    • (2001) Text in Applied Mathematics Series , vol.40
    • Brauer, F.1    Castillo-Chavez, C.2
  • 6
    • 0034972445 scopus 로고    scopus 로고
    • The ears of the hippopotamus: Manifestations, determinants, and estimates of the malaria burden
    • J. Breman, The ears of the hippopotamus: Manifestations, determinants, and estimates of the malaria burden, Am. J. Trop. Med. Hyg., 64 (2001), 1-11.
    • (2001) Am. J. Trop. Med. Hyg , vol.64 , pp. 1-11
    • Breman, J.1
  • 8
    • 33748307685 scopus 로고    scopus 로고
    • Dynamical models of Tuberculosis and their applications
    • C. Castillo-Chavez and B. Song, Dynamical models of Tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.
    • (2004) Math. Biosci. Eng , vol.1 , pp. 361-404
    • Castillo-Chavez, C.1    Song, B.2
  • 9
    • 33847746157 scopus 로고    scopus 로고
    • Bifurcation analysis of a mathematical model for malaria transmission
    • N. Chitnis, J. M. Cushing and J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math., 67 (2006), 24-45.
    • (2006) SIAM J. Appl. Math , vol.67 , pp. 24-45
    • Chitnis, N.1    Cushing, J.M.2    Hyman, J.M.3
  • 10
    • 47349102730 scopus 로고    scopus 로고
    • Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model
    • N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272-1296.
    • (2008) Bull. Math. Biol , vol.70 , pp. 1272-1296
    • Chitnis, N.1    Hyman, J.M.2    Cushing, J.M.3
  • 11
    • 0031828818 scopus 로고    scopus 로고
    • Characterization of infectious aerosols in health care facilities: An aid to effective engineering controls and preventive strategies
    • E. Cole and C. Cook, Characterization of infectious aerosols in health care facilities: An aid to effective engineering controls and preventive strategies, Am. J. Infect. Control., 26 (1998), 453-464.
    • (1998) Am. J. Infect. Control , vol.26 , pp. 453-464
    • Cole, E.1    Cook, C.2
  • 13
    • 0031992574 scopus 로고    scopus 로고
    • Backwards bifurcations and catastrophe in simple models of fatal diseases
    • J. Dushoff, W. Huang and C. Castillo-Chavez, Backwards bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36 (1998), 227-248.
    • (1998) J. Math. Biol , vol.36 , pp. 227-248
    • Dushoff, J.1    Huang, W.2    Castillo-Chavez, C.3
  • 14
    • 33746597887 scopus 로고    scopus 로고
    • Theoretical assessment of public health impact of imperfect prophylactic HIV vaccines with therapeutic benefits
    • E. H. Elbasha and A. B. Gumel, Theoretical assessment of public health impact of imperfect prophylactic HIV vaccines with therapeutic benefits, Bull. Math. Biol., 68 (2006), 577-614.
    • (2006) Bull. Math. Biol , vol.68 , pp. 577-614
    • Elbasha, E.H.1    Gumel, A.B.2
  • 15
    • 73649121526 scopus 로고    scopus 로고
    • The Global Tuberculosis Epidemic, Geneva, Switzerland
    • "Global Fund Against AIDS, TB and Malaria", The Global Tuberculosis Epidemic, Geneva, Switzerland, 2004.
    • (2004) Global Fund Against AIDS, TB and Malaria
  • 18
    • 33750693054 scopus 로고    scopus 로고
    • Mathematical study of a staged-progression HIV model with imperfect vaccine
    • A. B. Gumel, C. C. McCluskey and P. van den Driessche, Mathematical study of a staged-progression HIV model with imperfect vaccine, Bull. Math. Biol., 68 (2006), 2105-2128.
    • (2006) Bull. Math. Biol , vol.68 , pp. 2105-2128
    • Gumel, A.B.1    McCluskey, C.C.2    van den Driessche, P.3
  • 19
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious disease
    • H. W. Hethcothe, The mathematics of infectious disease, SIAM Review, 42 (2000), 599-653.
    • (2000) SIAM Review , vol.42 , pp. 599-653
    • Hethcothe, H.W.1
  • 20
    • 0026616222 scopus 로고
    • Permanence and the dynamics of biological systems
    • V. Hutson and K. Schmitt, Permanence and the dynamics of biological systems, Math. Biosci., 111 (1992), 1-71.
    • (1992) Math. Biosci , vol.111 , pp. 1-71
    • Hutson, V.1    Schmitt, K.2
  • 21
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • C. M. Kribs-Zaleta and J. X. Velasco-Hernandez, A simple vaccination model with multiple endemic states, Math. Biosci., 164 (2000), 183-201.
    • (2000) Math. Biosci , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernandez, J.X.2
  • 23
    • 4944233809 scopus 로고    scopus 로고
    • Modelling the effect of imperfect vaccines on disease epidemiology, Discrete Continuous Dynam
    • S. M. Moghadas, Modelling the effect of imperfect vaccines on disease epidemiology, Discrete Continuous Dynam. Systems-B, 4 (2004), 999-1012.
    • (2004) Systems-B , vol.4 , pp. 999-1012
    • Moghadas, S.M.1
  • 25
    • 28444486564 scopus 로고    scopus 로고
    • Mycobacterium induced potentiation of type 1 immune responses and Protection against malaria are host specific
    • K. R. Page, A. E. Jedlicka, B. Fakheri, G. S. Noland, A. K. Kesavan, A. L. Scott, N. Kumar and Y. C. Manabe, Mycobacterium induced potentiation of type 1 immune responses and Protection against malaria are host specific, Infect. Immun., 73 (2005), 8369-8380.
    • (2005) Infect. Immun , vol.73 , pp. 8369-8380
    • Page, K.R.1    Jedlicka, A.E.2    Fakheri, B.3    Noland, G.S.4    Kesavan, A.K.5    Scott, A.L.6    Kumar, N.7    Manabe, Y.C.8
  • 26
    • 33750085879 scopus 로고    scopus 로고
    • Co-infection of malaria with HIV: An immunological perspective
    • L. Rénia and S. M. Potter, Co-infection of malaria with HIV: an immunological perspective, Parasite Immunology, 28 (2006), 589-595.
    • (2006) Parasite Immunology , vol.28 , pp. 589-595
    • Rénia, L.1    Potter, S.M.2
  • 27
    • 0037033984 scopus 로고    scopus 로고
    • The economics and social burden of malaria
    • J. Sachs and P. Malaney, The economics and social burden of malaria, Nature, 415 (2002), 680-685.
    • (2002) Nature , vol.415 , pp. 680-685
    • Sachs, J.1    Malaney, P.2
  • 28
    • 37349018244 scopus 로고    scopus 로고
    • Curtailing smoking dynamics: A mathematical modeling approach
    • O. Sharomi and A. B. Gumel, Curtailing smoking dynamics: A mathematical modeling approach, Appl. Math. Comput., 195 (2007), 475-499.
    • (2007) Appl. Math. Comput , vol.195 , pp. 475-499
    • Sharomi, O.1    Gumel, A.B.2
  • 29
    • 36148968419 scopus 로고    scopus 로고
    • Role of incidence function in vaccine-induced backward bifurcation in some HIV models
    • O. Sharomi, C. N. Podder, A. B. Gumel, E. H. Elbasha and J. Watmough, Role of incidence function in vaccine-induced backward bifurcation in some HIV models, Math. Biosci., 210 (2007), 436-463.
    • (2007) Math. Biosci , vol.210 , pp. 436-463
    • Sharomi, O.1    Podder, C.N.2    Gumel, A.B.3    Elbasha, E.H.4    Watmough, J.5
  • 30
    • 45849102405 scopus 로고    scopus 로고
    • Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment
    • O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment, Math. Biosci. Engnr., 5 (2008), 145-174.
    • (2008) Math. Biosci. Engnr , vol.5 , pp. 145-174
    • Sharomi, O.1    Podder, C.N.2    Gumel, A.B.3    Song, B.4
  • 31
    • 1042300004 scopus 로고    scopus 로고
    • Modulation of Mycobacterium Tuberculosis infection by Plasmodium in the murine model
    • C. P. Scott, K. Nirbhay, R. W. Bishai and C. M. Yukari, Modulation of Mycobacterium Tuberculosis infection by Plasmodium in the murine model, Amer. Soc. Trop. Med. Hyg., 70 (2004), 144-148.
    • (2004) Amer. Soc. Trop. Med. Hyg , vol.70 , pp. 144-148
    • Scott, C.P.1    Nirbhay, K.2    Bishai, R.W.3    Yukari, C.M.4
  • 34
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
    • (2002) Math. Biosci , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 35
    • 33845390462 scopus 로고    scopus 로고
    • W. Viroj, Co-infection between tuberculosis and malaria, a consideration on interaction of molecule and pathogenesis, J. Vect. Borne Dis., 43 (2006), 195-197.
    • W. Viroj, Co-infection between tuberculosis and malaria, a consideration on interaction of molecule and pathogenesis, J. Vect. Borne Dis., 43 (2006), 195-197.
  • 36
    • 73649144786 scopus 로고    scopus 로고
    • World Health Organization (2006) Malaria/HIV, http://www.who.int/tb/hiv/ en/
    • (2006) Malaria/HIV
  • 38
    • 73649145044 scopus 로고    scopus 로고
    • WHO document WHO/HTM/MAL/2005, 1105 Annex 3, Geneva.
    • WHO document WHO/HTM/MAL/2005, 1105 Annex 3, Geneva.
  • 39
    • 73649087168 scopus 로고    scopus 로고
    • WHO-RBM Economic costs of malaria
    • WHO-RBM Economic costs of malaria, http://www.rbm.who.int/cmc-upload/0/ 000/015/363/RBMInfosheet-10.htm.
  • 40
    • 0012654992 scopus 로고
    • Comparison theorems on boundedness
    • S. N. Zhang, Comparison theorems on boundedness, Funkcial. Ekvac., 31 (1988), 179-196.
    • (1988) Funkcial. Ekvac , vol.31 , pp. 179-196
    • Zhang, S.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.