Demography and Diffusion in Epidemics: Malaria and Black Death Spread

Acta Biotheoretica

Volumn 58, Issue 2, 2010, Pages 277-305

  Gaudart, J ^a   Ghassani, M ^b   Mintsa, J ^b   Rachdi, M ^b   Waku, J ^b   Demongeot, J ^b  

^a AIX MARSEILLE UNIVERSITY   (France)

^b LABORATOIRE TIMC IMAG   (France)

Author keywords

Black Death; Contagious diseases; Demographic dynamics; Endemic state; Epidemics modelling; Reaction diffusion

Indexed keywords

DEMOGRAPHY; DIFFUSION; DISEASE SPREAD; DISEASE VECTOR; EPIDEMIC; FECUNDITY; INFECTIVITY; MALARIA; MIGRATION; MORTALITY; MUTATION;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; DISEASE CARRIER; DISEASE TRANSMISSION; EPIDEMIC; GENETIC DRIFT; HISTORY; HUMAN; MALARIA; MALI; PLAGUE; POPULATION DYNAMICS; STATISTICAL MODEL; STATISTICS; VIROLOGY; VIRUS INFECTION;

ANIMALS; DISEASE VECTORS; EPIDEMICS; GENETIC DRIFT; HISTORY, MEDIEVAL; HUMANS; MALARIA; MALI; MODELS, BIOLOGICAL; MODELS, STATISTICAL; PLAGUE; POPULATION DYNAMICS; VIRUS DISEASES;

MALI;

EID: 77955848699     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10441-010-9103-z     Document Type: Article

References (88)

1. Abbas L, Demongeot J, Glade N (2009) Synchrony in reaction-diffusion models of morphogenesis: applications to curvature-dependent proliferation and zero-diffusion front waves. Philos Trans R Soc A 367: 4829-4862.
2. Balenghien T, Fouque F, Sabatier P, Bicout DJ (2006) Horse-, bird-, and human-seeking behavior and seasonal abundance of mosquitoes in a West West Nile virus focus of southern France. J Med Entomol 43: 936-946.
3. Barry S, Gualde N (2006) The biggest epidemics of history. L'Histoire 310: 38-49.
4. Baum TP, Pasqual N, Thuderoz F, Hierle V, Chaume D, Lefranc MP, Jouvin-Marche E, Marche P, Demongeot J (2004) IMGT/GeneInfo: enhancing V(D)J recombination database accessibility. Nucleic Acids Res 32: 51-54.
5. Beaudoin D, Lakhal-Chaieb L (2008) Archimedean copula model selection under dependent truncation. Stat Med 27: 4440-4454.
6. Benedictow OJ (2004) The black death 1346-1353: the complete history. Boydell Press, Woodbridge.
7. Bernoulli D (1760) Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages del'inoculation pour la prévenir. Mém Acad Roy Sci, Paris.
8. Bicout DJ, Sabatier P (2004) Mapping rift valley fever vectors and prevalence using rainfall variations. Vector-Borne Zoonotic Dis 4: 33-42.
9. Bicout DJ, Chalvet-Monfray K, Sabatier P (2002) Infection persistence time of Aedes breeding habitats. Physica A Stat Mech Appl 305: 597-603.
10. Brandenburg A, Multamaki T (2004) How long can left and right handed life forms coexist? Int J Astrobiol 3: 209-219.
11. Brossollet J, Mollaret H (1994) Pourquoi la peste? Le rat, la puce et le bubon. Gallimard, Paris.
12. Brouhns N, Denuit M (2001) Risque de longévité et rente viagère. Institut de Statistique Université Catholique, Louvain, Discussion Paper 0137.
13. Cantor NF (2001) In the wake of the plague: the black death and the world it made. Free Press, New York.
14. Carpentier E (1993) Une ville devant la peste, Orvieto et la peste noire de 1348. De Boeck Université, Bruxelles.
15. Christakos G, Olea RA, Serre ML, Yu HL, Wang LL (2005) Interdisciplinary public health reasoning and epidemic modelling: the case of black death. Springer, Berlin.
16. Cohn SK Jr (2002) The black death: end of a paradigm. Am Hist Rev 107: 1-54.
17. Cooke RM, Morales-Napoles O (2006) Competing risk and the cox proportional hazard model. J Stat Plan Inference 136: 1621-1637.
18. D'Alembert J (1761) Opuscules Mathématiques. David, Paris.
19. de Magny GC, Paroissin C, Cazelles B, de Lara M, Delmas JF, Guégan JF (2005) Modeling environmental impacts of plankton reservoirs on cholera population dynamics. Esaim 14: 156-173.
20. Demetrius L (1979) Relations between demographic parameters. Demography 16: 329-338.
21. Demongeot J (1983) Thesis. Université J. Fourier, Grenoble.
22. Demongeot J (2009) Biological boundaries and biological age. Acta Biotheor 57: 397-419.
23. Demongeot J, Demetrius L (1989) La dérive démographique et la sélection naturelle: Etude empirique de la France (1850-1965). Population 2: 231-248.
24. Demongeot J, Fricot J (1986) Random fields and renewal potentials. NATO ASI Serie F 20: 71-84.
25. Demongeot J, Glade N, Forest L (2007a) Liénard systems and potential-Hamiltonian decomposition. I Methodology. Comptes Rendus Mathématique 344: 121-126.
26. Demongeot J, Glade N, Forest L (2007b) Liénard systems and potential-Hamiltonian decomposition. II Algorithm. Comptes Rendus Mathématique 344: 191-194.
27. Demongeot J, Glade N, Moreira A, Vial L (2009) RNA relics and origin of life. Int J Mol Sci 10: 3420-3441.
28. Depinay JMO, Mbogo CM, Killeen G, Knols B, Beier J, Carlson J, Dusho J, Billingsley P, Mwambi H, Githure J, Toure AM, McKenzie FE (2004) A simulation model of African Anopheles ecology and population dynamics for the analysis of malaria transmission. Malaria J 3: 29.
29. Dietz K, Heesterbeek JAP (2000) Bernoulli was ahead of modern epidemiology. Nature 408: 513.
30. Dietz K, Heesterbeek JAP (2002) Daniel Bernoulli's epidemiological model revisited. Math Biosci 180: 1-21.
31. Doliger C (2006) Démographie, fécondité et croissance économique en France. Thesis Université Louis Pasteur, Strasbourg.
32. Doumbo OK (2005) It takes a village: medical research and ethics in Mali. Science 307: 679-681.
33. Drancourt M, Aboudharam G, Signoli M, Dutour O, Raoult D (1998) Detection of 400-year-old Yersinia pestis DNA in human dental pulp: an approach to the diagnosis of ancient septicemia. Proc Natl Acad Sci USA 95: 2637-12640.
34. Dutertre J (1976) Étude d'un modèle épidémiologique appliqué au paludisme. Ann Soc Belge Méd Trop 56: 127-141.
35. Eckert EA (2000) The black death and the transformation of the West. Bull Hist Med 74: 356-357.
36. Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugenics 7: 353-369.
37. Forest L, Glade N, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition. Applications. C R Acad Sci Biol 330: 97-106.
38. Gani R, Leach S (2004) Epidemiologic determinants for modelling pneumonic plague outbreaks. Emerg Infect Dis 10: 608-614.
39. Gaudart J, Giorgi R, Poudiougou B, Ranque S, Doumbo OK, Demongeot J (2007) Spatial cluster detection: principle and application of different general methods. Rev Epidemiol Santé Publique 55: 297-306.
40. Gaudart J, Touré O, Dessay N, Dicko AL, Ranque S, Forest L, Demongeot J, Doumbo OK (2009) Modelling malaria incidence with environmental dependency in a locality of Sudanese savannah area, Mali. Malar J 8: 61.
41. Gaudart J, Ghassani M, Mintsa J, Waku J, Rachdi M, Doumbo OK, Demongeot J (2010) Demographic and spatial factors as causes of an epidemic spread, the copule approach. Application to the retro-prediction of the black death epidemy of 1346. In: IEEE AINA' 10 & BLSMC' 10. IEEE Press, Piscataway, pp 751-758.
42. Glade N, Forest L, Demongeot J (2007) Liénard systems and potential-Hamiltonian decomposition. III Applications in biology. Comptes Rendus Mathématique 344: 253-258.
43. Horie M, Honda T, Suzuki Y, Kobayashi Y, Daito T, Oshida T, Ikuta K, Jern P, Gojobori T, Coffin JM, Tomonaga K (2010) Endogenous non-retroviral RNA virus elements in mammalian genomes. Nature 463: 84-88.
44. Horrox R (1994) The black death. Manchester University Press, Manchester.
45. Huang J, Walker ED, Otienoburu PE, Amimo F, Vulule J, Miller JR (2006) Laboratory tests of oviposition by the african malaria mosquito, Anopheles gambiae, on dark soil as influenced by presence or absence of vegetation. Malaria J 5: 88.
46. Kelly J (2005) The great mortality: an intimate history of the black death, the most devastating plague of all time. Harper Collins, New York.
47. Kermack WO, McKendrick AG (1932) Contributions to the mathematical theory of epidemics. II. The problem of endemicity. Proc R Soc Lond A 138: 55-83.
48. Kermack WO, McKendrick AG (1933) Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity. Proc R Soc Lond A 141: 94-122.
49. Khan K, Arino J, Hu W, Raposo J, Sears J, Calderon F, Heidebrecht C, Macdonald M, Liauw J, Chan A, Gardam M (2009) Spread of a novel Influenza A (H1N1) virus via global airline transportation. N Engl J Med 361: 212-214.
50. L'Épine GJ (1764) Rapport de six des douze commissaires (contre l'inoculation). Quillau, Paris, pp 40-43.
51. La peste humaine en 1997 (1999) Relevé Epidémiologique Hebdomadaire OMS 74, 340-344.
52. Lambert JH (1772) "Beiträge zum Gebrauche der Mathematik und deren Anwendung". Dritter Theil, Berlin.
53. Leslie PH (1945) On the use of matrices in certain population mathematics. Biometrika 33: 183-212.
54. Mac Donald G (1957) The epidemiology and control of malaria. Oxford University Press, London.
55. Maupertuis PL Moreau de (1745, reed. 1965) Vénus physique, in Oeuvres. Georg Olms, Hildesheim.
56. May N (1770) Impartial remarks on the Suttonian method of inoculation. Tilley, Wheble & Brown, London.
57. May RM, Anderson RM (1984) Spatial heterogeneity and the design of immunization programs. Math Biosci 72: 83-111.
58. McKendrick AG (1925) Applications of mathematics to medical problems. Proc Edinburgh Math Soc 44: 1-34.
59. Mendez V, Fort J, Rotstein HG, Fedotov S (2003) Speed of reaction-diffusion fronts in spatially heterogeneous media. Phys Rev E 68: 041105.
60. Mischlewski A (1995) Un ordre hospitalier au Moyen Âge. Les chanoines réguliers de Saint-Antoine en Viennois. PUG, Grenoble.
61. Mocellin G, Experton I (1992) Saint Antoine et l'Ordre des Antonins aux XVIIème et XVIIIème siècles. Ed. Musée, St-Antoine l'Abbaye.
62. Mocellin-Spicuzza G (2002) Chroniques d'une abbaye au Moyen-Age. Guérir l'âme et le corps. Ed. Musée, Saint-Antoine l'Abbaye.
63. Murray JA (1763) Fata variolarum insitionis in Suecia. Doctoral dissertation University Göttingen, Göttingen.
64. Murray JD (2002) Mathematical biology I & II. Springer, Berlin.
65. Ndiaye PI, Bicout DJ, Mondet B, Sabatier P (2006) Rainfall triggered dynamics of Aedes mosquito aggressiveness. J Theor Biol 243: 222-229.
66. Neerinckx SB, Peterson AT, Gulinck H, Deckers J, Leirs H (2008) Geographic distribution and ecological niche of plague in sub-Saharan Africa. Int J Health Geogr 7: 54.
67. Orent W (2001) Will the black death return? Discover 22: 1-10.
68. Orent W (2004) Plague: the mysterious past and mystifying furture of the world's most dangerous disease. Free Press, New York.
69. Porphyre T, Bicout DJ, Sabatier P (2004) Modelling the abundance of mosquito vectors versus flooding dynamics. Ecol Modell 183: 173-181.
70. Porte M (1994) Passion des formes. A René Thom. ENS Editions, Paris.
71. Prentice MB, Rahalison L (2007) Plague. Lancet 369: 1196-1207.
72. Raoult D, Aboudharam G, Crubézy E, Larrouy G, Ludes B, Drancourt M (2000) Molecular identification of 'Suicide PCR' of Yersinia pestis as the agent of medieval black death. Proc Natl Acad Sci USA 97: 12800-12803.
73. Renouard Y (1948) Conséquences et intérêt démographiques de la Peste noire de 1348. Population 3: 459-466.
74. Ross R (1916) An application of the theory of probabilities to the study of a priori pathometry. Part I. Proc R Soc Lond A 92: 204-230.
75. Russell JC (1948) British medieval population. Univ. of New Mexico, Albuquerque.
76. Russell JC (1972) Population in Europe. In: Cipolla CM (ed) The Fontana economic history of Europe, vol. I, the middle ages. Collins/Fontana, Glasgow, pp 25-71.
77. Scott S, Duncan C (2004) Return of the black death: the world's greatest serial killer West Sussex. Wiley, New York.
78. Stenseth NC, Atshabar BB, Begon M, Belmain SR, Bertherat E, Carniel E, Gage KL, Leirs H, Rahalison L (2008) Plague: past, present, and future. PLOS Med 5: e3.
79. Thom R (1972) Stabilité structurelle et Morphogenèse. Benjamin, New York.
80. Thuderoz F, Simonet MA, Hansen O, Dariz A, Baum TP, Hierle V, Demongeot J, Marche PN, Jouvin-Marche E (2010) From the TCRAD rearrangement quantification to the computational simulation of the locus behavior. PloS Comp Biol 6: e1000682.
81. Trembley J (1796) Recherches sur la mortalité de la petite vérole. Mém Acad Roy Sci, Paris.
82. Usher MB (1969) A matrix model for forest management. Biometrics 25: 309-315.
83. Villani G (2001) Florence, 1336-38, the chronicle of Giovanni Villani. In: Medieval trade in the mediterranean world, Lopez, R. S. & I. W. Raymond Trads., Columbia Un. Press, New York.
84. Wheelis M (2002) Biological warfare at the 1346 Siege of Caffa. Emerg Infect Dis 8: 971-975.
85. WHO (1999) La peste humaine en 1997. Relevé Epidémiologique Hebdomadaire OMS 74: 340-344.
86. Wood JW (2003) The temporal dynamics of the fourteenth-century black death: new evidence from english ecclesiastical records. Hum Biol 75: 427-448.
87. Zeeman EC (1993) Controversy in science: on the ideas of Daniel Bernoulli and René Thom. Nieuw Arch Wisk 11: 257.
88. Zhang SY, Yu L, Daszak P (2008) EcoHealth and the black death in the year of the rat. Ecohealth 5: 99-100.