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Introductory review. Some new thoughts about some old malaria models. (English) Zbl 0567.92020

92D25 Population dynamics (general)
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[1] Armitage, P., A note on the epidemiology of malaria, Trop. dis. bull., 50, 890-892, (1953)
[2] Aron, J.L., Population dynamics of immunity to malaria, ()
[3] Aron, J.L., Malaria epidemiology and detectability, Trans. roy. soc. trop. med. hyg., 76, 595-601, (1982)
[4] Aron, J.L.; May, R.M., The population dynamics of malaria, ()
[5] Bailey, N.T.J., The biomathematics of malaria, (1982), Charles Griffin London · Zbl 0494.92018
[6] Bates, M., Ecology of anopheline mosquitoes, (), 302-330
[7] Bekessy, A.; Molineaux, L.; Storey, J., Estimation of incidence and recovery rates of plasmodium falciparum parasitemia from longitudinal data, Bull. WHO, 54, 685-693, (1976)
[8] Boyd, M.F., Epidemiology: factors related to the definitive host, (), 608-697
[9] Bruce-Chwatt, L.J., Mathematical models in the epidemiology and control of malaria, Trop. geo. med., 28, 1-8, (1976)
[10] Busenberg, S.; Cooke, K.L., Periodic solutions of a periodic nonlinear delay differential equation, SIAM J. appl. math., 35, 704-721, (1978) · Zbl 0391.34022
[11] Cale, W.B.; O’Neill, R.V.; Shugart, H.H., Development and application of desirable ecological models, Ecological modeling, 18, 171-186, (1983)
[12] Carter, R.; Gwadz, R.W., Infectiousness and gamete immunization in man, (), 263-297
[13] Clements, A.N.; Paterson, G.D., The analysis of mortality and survival rates in wild populations of mosquitoes, J. appl. ecol., 18, 373-399, (1981)
[14] Cohen, J.E.; Singer, B., Malaria in nigeria: constrained continuous-time Markov models for discrete-time longitudinal data on human mixed-species infections, ()
[15] Cohen, S., Immunity to malaria, Proc. roy. soc. London ser. B, 203, 323-345, (1979)
[16] Cooke, K.L., Stability analysis for a vector disease model, Rocky mountain J. math., 9, 31-42, (1979) · Zbl 0423.92029
[17] Cornille-Brögger, R.; Mathews, H.M.; Storey, J.; Ashkar, T.S.; Brögger, S.; Molineaux, L., Changing patterns in the humoral immune response to malaria before, during, and after the application of control measures: A longitudinal study in the west african savanna, Bull. WHO, 56, 597-600, (1978)
[18] Cuellar, C.B., A theoretical model of the dynamics of an anopheles gambiae population under challenge with eggs giving rise to sterile males, Bull. WHO, 40, 205-212, (1969)
[19] Cushing, J., Stable positive periodic solutions of the time dependent logistic equation under possible hereditary influences, J. math. anal. appl., 60, 747-754, (1977) · Zbl 0367.34032
[20] Davidson, G.; Draper, C.C., Field study of some of the basic factors concerned in the transmission of malaria, Trans. roy. soc. trop. med. hyg., 47, 522-535, (1953)
[21] Dietz, K., Mathematical models for malaria, 7th international biometric conference, hannover, (16-21 Aug. 1970), presented at
[22] Dietz, K.; Molineaux, L.; Thomas, A., A malaria model tested in the african savannah, Bull. WHO, 50, 347-357, (1974)
[23] Draper, C.C., Observations on the infectiousness of gametocytes in hyperendemic malaria, Trans. roy. soc. trop. med. hyg., 47, 160-165, (1953)
[24] Dutertre, J., Etude d’un modèle epidemiologique appliqué au paludisme, Ann. soc. belge med. trop., 56, 127-141, (1976)
[25] Earle, W.C.; Perez, M.; del Rio, J.; Arzola, C., Observation on the course of naturally acquired malaria in puerto rico, Puerto rico J. pub. health and trop. med., 14, 391-406, (1939)
[26] Eisen, H.N., Immunology, (), 446
[27] Elderkin, R.H.; Berkowitz, D.P.; Farris, F.A.; Gunn, C.F.; Hickernell, F.J.; Kass, S.N.; Mansfield, F.I.; Taranto, R.G., On the steady state of an age dependent model for malaria, (), 491-512
[28] Fine, P.E.M., Superinfection: A problem in formulating a problem, Trop. dis. bull., 72, 475-488, (1975)
[29] Fine, P.E.M., Ross’s a priori pathometry—a perspective, Proc. roy. soc. med., 68, 547-551, (1975)
[30] Garrett-Jones, C., The human blood index of malaria vectors in relation to epidemiological asssessment, Bull. WHO, 30, 241-261, (1964)
[31] Garrett-Jones, C.; Boreham, P.F.L.; Post, C.P., Feeding habits of anophelines (diptera: culicidae) in 1971-78 with reference to the human blood index: A review, Bull. entomol. res., 70, 165-185, (1980)
[32] Garrett-Jones, C.; Shidrawi, G.R., Malaria vectorial capacity of a population of anopheles gambiae, Bull. WHO, 40, 531-545, (1969)
[33] Gillies, M.T., The recognition of age-groups within populations of anopheles gambiae by the pre-gravid rate and the sporozoite rate, Ann. trop. med. parasit., 48, 58-74, (1954)
[34] Gillies, M.T., Assessment of control: some problems in the measurement of anopheline populations, Misc. publ. entomol. soc. amer., 7, 156-167, (1970)
[35] Hethcote, H.W., Asymptotic behavior and stability in epidemic models, (), Lecture Notes in Biomathematics · Zbl 0212.52104
[36] Jeffrey, G.M.; Eyles, D.E., Infectivity to mosquitoes of plasmodium falciparum as related to gametocyte density and duration of infection, Amer. J. trop. med. hyg., 3, 219-224, (1954)
[37] Krafsur, E.S.; Armstrong, J.C., An integrated view of entomological and parasitological observations on falciparum malaria in gambela, western Ethiopian lowlands, Trans. roy. soc. trop. med. hyg., 72, 348-356, (1978)
[38] Kreier, J.P.; Green, T.J., The vertebrate Host’s immune response to plasmodia, (), 111-162
[39] Lotka, A.J., Contribution to the analysis of malaria epidemiology, Amer. J. hyg., 3, 1-121, (1923), (Suppl.)
[40] Macdonald, G., The analysis of infection rates in disease in which superinfection occurs, Trop. dis. bull., 47, 907-915, (1950)
[41] Macdonald, G., The analysis of the sporozoite rate, Trop. dis. bull., 49, 569-585, (1952)
[42] Macdonald, G., The epidemiology and control of malaria, (1957), Oxford U.P London
[43] Macdonald, G.; Göckel, G.W., The malaria parasite rate and interruption of transmission, Bull. WHO, 31, 365-377, (1964)
[44] Manson-Bahr, P.E.C.; Apsted, F.I.C., Manson’s tropical diseases, (1982), Bailliere Tindall London
[45] May, R.M.; Anderson, R.M., Population biology of infectious diseases,, Nature, 280, 455-461, (1979), Part II
[46] McGregor, I.A.; Williams, K.; Voller, A.; Billewicz, W.Z., Immunofluorescence and the measurement of immune response to hyperendemic malaria, Trans. roy. soc. trop. med. hyg., 59, 395-414, (1965)
[47] Miller, D.R.; Weidhass, D.E.; Hall, R.C., Parameter sensitivity in insect population modeling, J. theoret. biol., 42, 263-274, (1973)
[48] Miller, M.J., Observations on the natural history of malaria in the semiresistant west african, Trop. roy. soc. trop. med. hyg., 52, 152-168, (1958)
[49] Molineaux, L.; Gramiccia, G., The garki project: research on the epidemiology and control of malaria in the sudan savanna of west africa, (1980), WHO Geneva
[50] Muench, H., Catalytic models in epidemiology, (1959), Harvard U.P Cambridge
[51] Muirhead-Thomson, R.C., The malarial infectivity of an african village population to mosquitoes (anopheles gambiae): A random xenodiagnostic survey, Amer. J. trop. med. hyg., 6, 971-979, (1957)
[52] Muirhead-Thomson, R.C., Ecology of insect vector populations, (1968), Academic New York
[53] Najera, J.A., A critical review of the field application of a mathematical model of malaria eradication, Bull. WHO, 50, 449-457, (1974)
[54] Nardin, E.H.; Nussenzweig, R.S.; Bryan, J.H.; McGregor, I.A., Congenital transfer of antibodies against malarial sporozoites detected in Gambian infants, Amer. J. trop. med. hyg., 30, 1159-1163, (1981)
[55] I. Nåsell, A hybrid version of the Ross malaria model, Tech. Report 1980-2, Dept. of Math., Royal Institute of Technology, Stockholm.
[56] I. Nåsell, A hybrid model for malaria with superinfection, Tech. Report 1980-3, Dept. of Math., Royal Institute of Technology, Stockholm.
[57] I. Nåsell, On the Macdonald-Irwin treatment of superinfection in malaria, Tech. Report 1980-4, Dept. of Math., Royal Institute of Technology, Stockholm.
[58] Nedelman, J., Inoculation and recovery rates in the malaria model of dietz, molineaux, and Thomas, Math. biosci., 69, 209-233, (1984) · Zbl 0529.92019
[59] Nedelman, J., A negative binomial model for sampling mosquitoes in a malaria survey, Biometrics, 39, 1009-1020, (1983)
[60] J. Nedelman, Estimation and approximation for a model of multiple malaria infections, submitted for publication. · Zbl 0651.62103
[61] Payne, D.; Grab, B.; Fontaine, R.E.; Hempel, J.H.G., Impact of control measures on malaria transmission and general mortality, Bull. WHO, 54, 369-377, (1976)
[62] Pull, J.; Grab, B., A simple epidemiological model for evaluating the malaria inoculation rate and the risk of infection in infants, Bull. WHO, 51, 507-516, (1974)
[63] Ross, R., The prevention of malaria, (1911), John Murray London
[64] Service, M.W., A critical review of procedures for sampling populations of adult mosquitoes, Bull. entomol. res., 67, 343-382, (1977)
[65] Singer, B.; Cohen, J.E.; Singer, B.; Cohen, J.E., Estimating malaria incidence and recovery rates from panel surveys, Math. biosci., Math. biosci., 62, 151-152, (1982), Erratum · Zbl 0489.92022
[66] Smalley, M.E.; Brown, J.; Bassett, N.M., The rate of production of plasmodium falciparum gametocytes during natural infections, Trans. roy. soc. trop. med. hyg., 75, 318-319, (1981)
[67] Smalley, M.E.; Sinden, R.E., plasmodium flaciparum gametocytes: their longevity and infectivity, Parasitology, 74, 1-8, (1977)
[68] Targett, G.A.T., Immunology of malaria, (), 385-402
[69] Vanderberg, J.P.; Gwadz, R.W., The transmission by mosquitoes of plasmodia in the laboratory, (), 154-234
[70] Verma, B.L.; Ray, S.K.; Srivastava, R.N., Stochastic approach to the estimation of infective force and malaria parasite incidence rates in infants from longitudinal data, J. commun. dis., 12, 118-125, (1980)
[71] Verma, B.L.; Ray, S.K.; Srivastava, R.N., A stochastic model of malaria transition rates from longitudinal data considering the risk of “lost of followup”, J. epidem. comm. health, 37, 153-156, (1983)
[72] Voller, A.; Meuwissen, J.H.E.; Verhave, J.P., Methods for measuring the immunological response to plasmodia, (), 67-109
[73] Weiss, G.H.; Aron, J.L., Note on the formulation of a stochastic model of superinfection, Math. biosci., 67, 213-223, (1983) · Zbl 0528.92020
[74] Wernsdorfer, W.H., The importance of malaria in the world, ()
[75] Zavala, F.; Gwadz, R.W.; Collins, F.H.; Nussenzweig, R.S.; Nussenzweig, V., Monoclonal antibodies to circumsporozoite proteins identify the species of malaria parasite in infected mosquitoes, Nature, 299, 737-738, (1982)
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