Modelling the Role of Prophylaxis in Malaria Prevention
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.
[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.
[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.
@article{"International Journal of Medical, Medicine and Health Sciences:57190", author = "Farai Nyabadza", title = "Modelling the Role of Prophylaxis in Malaria Prevention", 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.", volume = "2", number = "3", pages = "94-6", }
