Modelling and simulation of a schistosomiasis infection with biological control

Acta Tropica

Volumn 87, Issue 2, 2003, Pages 251-267

  Allen, E J ^a   Victory Jr , H D ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

Computational simulation; Mathematical model; Numerical method; Schistosomiasis; Stochastic differential equation

Indexed keywords

BIOLOGICAL CONTROL; NUMERICAL MODEL; PARASITIC DISEASE; SCHISTOSOMIASIS; SNAIL;

ARTICLE; BIOLOGICAL PEST CONTROL; DEMOGRAPHY; DISEASE SIMULATION; HOST; INFECTION SENSITIVITY; MAMMAL; MATHEMATICAL MODEL; PARAMETER; POPULATION MODEL; RANDOMIZATION; SCHISTOSOMIASIS; SNAIL; STOCHASTIC MODEL; SYSTEM ANALYSIS;

GASTROPODA; MAMMALIA;

EID: 0038095207     PISSN: 0001706X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0001-706X(03)00065-2     Document Type: Article

References (42)

1. Allen, E.J., 1999. Stochastic differential equations and persistence time of two interacting populations. Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 5, pp. 271-281.
2. Allen L.J.S. An Introduction to Stochastic Processes with Applications to Biology. 2003;Prentice-Hall, Englewood Cliffs, NJ.
3. Allen, L.J.S., Allen, E.J., submitted for publication. Persistence time estimation for stochastic population models. Theoret. Population Biol.
4. Allen, E.J., Baglama, J., Boyd, S.K., 2000. Numerical approximation of the product of the square root of a matrix with a vector. Linear Algebra and Its Applications, Vol. 310, pp. 167-181.
5. Anderson R.M., May R.M. Helminth infections of humans: mathematical models, population dynamics, and control. Baker J.R., Muller R. Advances in Parasitology. 24:1985;1-101.
6. Anderson R.M., May R.M. Infectious Diseases of Humans: Dynamics and Control. 1992;Oxford University Press, Oxford.
7. Behrman J.N. Tropical Diseases: Responses of Pharmaceutical Companies. 1980;American Enterprise Institute for Public Policy Research, Washington.
8. Chitsulo L., Engels D., Montresor A., Savioli L. The global status of schistosomiasis and its control. Acta Trop. 77:2000;41-51.
9. Dasmann R.F. Wildlife Biology. 1964;Wiley, New York.
10. Dillon R.T. The Ecology of Freshwater Molluscs. 2000;Cambridge University Press, Cambridge.
11. Emmel T.C. Population Biology. 1976;Harper & Row, New York.
12. Feng Z., Curtis J., Minchella D.J. The influence of drug treatment on the maintenance of schistosome genetic diversity. J. Math. Biol. 43:2001;52-68.
13. Gard T.C. Introduction to Stochastic Differential Equations. 1987;Marcel Dekker, New York.
14. Garrett L. The Coming Plague: Newly Emerging Diseases in a World Out of Balance. 1994;Penguin Books, New York.
15. Ghiboda M., Engels D., Berquist N.R. Post-transmission schistosomiasis: a new agenda (Editorial: Schistosomiasis in the post-transmission phase). Acta Trop. 77:2000;3-7.
16. Heesterbeek J.A.P., Roberts M.G. Threshold quantities for helminth infections. J. Math. Biol. 33:1995;415-434.
17. Herbert J., Isham V. Stochastic host-parasite interaction models. J. Math. Biol. 40:2000;343-371.
18. Hirsch M.W. Systems of differential equations which are competitive or cooperative. I. limit sets. SIAM J. Math. Anal. 13:1982;167-179.
19. Hirsch W.M., Hanisch H., Gabriel J.-P. Differential equation models of some parasitic infections: methods for the study of asymptotic behavior. Commun. Pure Appl. Math. XXXVIII:1985;733-753.
20. Kimbir, A.R., 1997-1998. A mathematical model of the transmission dynamics of schistosomiasis. J. Nigerian Math. Soc. 16/17, 39-63.
21. Kirstensen T.K., Malone J.B., McCarroll J.C. Use of satellite remote sensing and geographic information systems to model the distribution and abundance of snail intermediate hosts in Africa: a preliminary model for Biomphalaria pheifferi in Ethiopia. Acta Trop. 79:2001;73-78.
22. Kloeden P.E., Platen E. Numerical Solution of Stochastic Differential Equations. 1992;Springer, New York.
23. Kurtz T.G. Solutions of ordinary differential equations as limits of pure jump processes. J. Appl. Probab. 7:1970;49-58.
24. Kurtz T.G. Approximation of Population Processes. 1981;Society for Industrial and Applied Mathematics, Philadelphia, PA.
25. Li Y., Sleigh A.C., Williams G.M., Ross A.G.P., Li Y., Forsyth S.J., Tanner M., McManus D.P. Measuring exposure to Schistosoma japonicum in China. III. Activity diaries, snail and human infection, transmission ecology and options for control. Acta Trop. 75:2000;279-289.
26. Luchsinger C.J. Approximating the long-term behavior of a model for parasitic infection. J. Math. Biol. 42:2001;555-581.
27. Luchsinger C.J. Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios. J. Math. Biol. 42:2001;532-554.
28. McNeill W.H. Plagues and Peoples. 1977;Doubleday, New York.
29. Millar J.S. Reproduction and development. Kirkland G.L. Jr., Layne J.N. Advances in the Study of Peromyscus (Rodentia). 1989;169-232 Texas Tech University Press, Lubbock.
30. Murray B.G. Population Dynamics: Alternate Models. 1979;Academic Press, New York.
31. Murray J.D. Mathematical Biology. 2nd ed:1993;Springer, New York.
32. Nasell I. On eradication of schistosomiasis. Theoret. Popul. Biol. 10:1976;133-144.
33. Nasell I., Hirsch W.M. The transmission dynamics of schistosomiasis. Commun. Pure Appl. Math. XXVI:1973;395-453.
34. Pellegrinelli A., Gabriel J.-P. Eradication of helminthic infections. Math. Biosci. 117:1993;179-195.
35. Pointier J.P., Jourdane J. Biological control of the snail hosts of schistosomiasis in areas of low transmission: the example of the Caribbean area. Acta Trop. 77:2000;53-60.
36. Stauffer J.R., Arnegard M.E., Cetron M., Sullivan J.J., Chitsulo L.A., Turner G.F., Chiotha S., McKaye K.R. Controlling vectors and hosts of parasitic diseases using fishes. BioScience. 47:1997;41-49.
37. Talay D., Tubaro L. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8:1990;483-509.
38. Woolhouse M.E.J. On the application of mathematical models of schistosome transmission dynamics. I. Natural transmission. Acta Trop. 49:1991;1241-1270.
39. Woolhouse M.E.J. On the application of mathematical models of schistosome transmission dynamics. II. Control. Acta Trop. 50:1992;189-204.
40. World Health Organization, 1993. The control of schistosomiasis. Second Report of the WHO Expert Committee. WHO Technical Report Series No. 830.
41. Wu J., Feng Z. Mathematical models for schistosomiasis with delays and multiple definite hosts. Castillo-Chavez C., Blower S., van der Driessche P., Kirchner D., Yakubu A.-A. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. 2002;215-229 Springer, New York.
42. Zhou X.N., Malone J.B., Kirstensen T.K., Bergquist N.R. Application of geographic information systems and remote sensing to schistosomiasis control in China. Acta Trop. 79:2001;97-106.