Modelling the Role of Prophylaxis in Malaria Prevention
Authors: Farai Nyabadza
Abstract:
Malaria is by far the world-s most persistent tropical parasitic disease and is endemic to tropical areas where the climatic and weather conditions allow continuous breeding of the mosquitoes that spread malaria. A mathematical model for the transmission of malaria with prophylaxis prevention is analyzed. The stability analysis of the equilibria is presented with the aim of finding threshold conditions under which malaria clears or persists in the human population. Our results suggest that eradication of mosquitoes and prophylaxis prevention can significantly reduce the malaria burden on the human population.
Keywords: Prophylaxis prevention, basic reproductive number, stability.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070279
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1454References:
[1] S. Busenberg and K. Cooke, Vertically transmitted diseases - models and dynamics, Springer-Verlag, 1993.
[2] N. T. J. Bailey, The Biomathematics of Malaria, A Charles Griffin Book, 1981.
[3] B. Chilundo, J. Sundby and M. Aanestad, 2004. Analyzing the quality of routine malaria data in Mozambique, Malaria Journal 3(3), 1-11.
[4] J. Small, S. J. Goetz and S. I. Hay, 2003. Climatic suitability for malaria transmission in Africa, 1911-1995, Applied Biological Science, 100(26), 15341-15345.
[5] The Burden of Malaria in Southern Africa, Retreaved from http://www.malaria.org.zw/malaria burden.html on 10 July 2006.
[6] K. Dietz K, 1988. Mathematical models for transmission and control of malaria. In Malaria - Principles and Practice of Malariology 2 (Churchill Livingstone), W. H. Wernsdorfer and Sir I. McGregor.
[7] A. N. Hill and I. M. Longini Jr., 2003. The critical vaccination fraction for heterogeneous epidemic models, Mathematical Biosciences, 181, 85- 106.
[8] C. M. Kribs-Zaleta and J. X. Velasco-Hernandez, 2000. A simple vaccination model with multiple endemic states, Mathematical Biosciences, 164, 183-201.
[9] S. Blower, K. Koelle and J. Mills, 2002. Health policy modeling: epidemic control, HIV vaccines and risky behavior. Quantitative Evaluation of HIV Prevention Programs (Yale University Press, 2002), 260-289, Kaplan and Brookmeyer.
[10] K. P. Hadeler and C. Castillo-Chavez, 1995. A Core Group Model for Disease Transmission, Mathematical Biosciences, 128, 41-55.
[11] L. Esteva and C. Vargas, 1999. A model for dengue disease with variable human population, Journal of Mathematical Biology, 38, 220-240.
[12] L. Esteva and M. Matias, 2001. A model for vector transmitted diseases with saturation incidence, Journal of Biological Systems, 9, 235-245.
[13] L. Esteva and C. Vargas, 2003. Coexistence of different serotypes of dengue virus, Journal of Mathematical Biology, 46, 31-47.
[14] G. A. Ngwa and W. S. Shu, 2000. A mathematical model for endemic malaria with variable human and mosquito populations, Mathematical and Computer Modelling, 32, 747-763.
[15] P. van den Driessche and J. Watmough, 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48.
[16] O. Diekmann, J. Heesterbeek and J. Metz, 1990. On the definition and the computation of the basic reproductive ratio r0 in models of infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28, 356-382.
[17] Press Release WHO, 4 June 2000, WHO Issues New Healthy Life Expectancy Rankings Japan Number One in New Healthy Life System, World Health Organisation.
[18] Anopheles Mosquito, retreaved from http://www.anopheles.com, on 10 July 2006.
[19] W. O-Meara, D. L.Smith and F. E. Mckenzie, 2006. Potential impact of intermittent preventive treatment on spread of drug-resistant ralaria, PLoS Medicine, 3(5), 63-642.
[20] A. Derouich and A. Boutayeb, 2006. Dengue fever; mathematical modelling and computer simulation, Applied Mathematics and Computation, 177, 528-544.
[21] J. C. Koella and R. Antia, 2003. Epidemiological models for the spread of anti-malaria resistance, Malaria Journal, 2(3), 1-11.
[22] F. E. McKenzie and E. M. Samba, 2004. The role of mathematical modelling in evidence-based malarica control, Ammerican Journal of Tropical Medicine and Hygiene, 71(2) 94-96.