The Effects of Classical Trapping on the Control of Malaria Transmission
PDF

Keywords

 Trapping Probability, Ross-Macdonald Model, Gaussian Distribution, Mosquito Density, Malaria.

How to Cite

Zhenbu Zhang, Tor A. Kwembe, & Xing Yang. (2016). The Effects of Classical Trapping on the Control of Malaria Transmission. Journal of Basic & Applied Sciences, 12, 434–440. https://doi.org/10.6000/1927-5129.2016.12.67

Abstract

This paper investigates the effects of classical trapping on the control of malaria transmission. The Ross-Macdonald model is modified and a trapping probability function is introduced to construct a partial differential equation (PDE) system. The proof of existence and uniqueness of solution of density functions to the PDE system is given, numerical simulation results based on Gaussian distribution and exponential distribution are obtained for the solutions, and graphical representations of solutions are shown and interpreted.

https://doi.org/10.6000/1927-5129.2016.12.67
PDF

References

King AT, Mends-Brew E, Osei-Frimpong E, Ohene KR. Mathematical model for the control of malaria-Case study: Chorkor polyclinic, Accra, Ghana, Global. Adv Res J Med Med Sci 2012; 1: 108-18.

U.S. Global Health Policy, Fact Sheet, March 2011, The Henry J. Kaiser Family Foundation. [cited 2016 May 1

Chitnis N, Cushing JP, Hyman JM. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J Appl Math 2006; 67: 24-45. https://doi.org/10.1137/050638941

Al-Arydah M, Smith R. Controlling malaria with indoor residual spraying in spatially heterogeneous environments. Math Biosci Eng 2011; 8: 889-914. https://doi.org/10.3934/mbe.2011.8.889

Prosper O, Ruktanonchai N, Martcheva M. Assessing the role of spatial heterogeneity and human movement in malaria dynamics and control. J Theor Biol 2012; 303: 1-14. https://doi.org/10.1016/j.jtbi.2012.02.010

Koella JC. On the use of mathematical models of malaria transmission. Acta Tropic 1991; 49: 1-25. https://doi.org/10.1016/0001-706X(91)90026-G

Hoshen MC, Morse AP. A weather-driven model of malaria transmission. Malar J 2004; 3: 32. https://doi.org/10.1186/1475-2875-3-32

Makinde OD, Okosun KO. Impact of chemo-therapy on optimal control of malaria disease with infected immigrants. BioSyst 2011; 104: 32-41. https://doi.org/10.1016/j.biosystems.2010.12.010

Bacaër N, Sokhna C. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Math Bios Eng 2005; 2: 227-38. https://doi.org/10.3934/mbe.2005.2.227

Calderón CP, Kwembe TR. On the classical trapping problem. Math Bios 1990; 102: 183-90. https://doi.org/10.1016/0025-5564(90)90061-3

Carter R, Mendis KN, Roberts D. Spatial targeting of interventions against malaria. Bull WHO 2000; 78: 1401-11.

Mangel M. Information and area wide control in agriculture ecology: the classical trapping problem and its extensions. in levin AS, Hallam TG, Gross LJ, editors. Biomathematics texts.New York: Springer-Verlag 1989; pp. 81-112.

Haberman R. Applied differential equations with Fourier series and boundary value problems. 5th ed. New Jersey: Pearson Education 2012.

Ye QX, Li ZY. Introduction to reaction-diffusion equations. Beijing: Scientific Publisher of China 1994.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2016 Zhenbu Zhang, Tor A. Kwembe , Xing Yang