The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission
American Journal of Applied Mathematics
Volume 6, Issue 3, June 2018, Pages: 117-127
Received: May 25, 2018;
Accepted: Jun. 26, 2018;
Published: Aug. 2, 2018
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Alemu Geleta Wedajo, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Boka Kumsa Bole, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
Malaria is one of infectious diseases and has become the most public health issue especially in developing countries. Mathematically, the spread of malaria can be modeled to predict the dynamics of the outbreak of the disease. The present research studies the impact of migration of susceptible population on the dynamics of malaria transmission. In this paper an improved mathematical model is constructed based on a set of reasonable assumptions. Validity of the model is proved by verifying positivity of the solution. Mathematical analysis is carried out including equilibrium point analysis. Basic reproduction number of the model is determined so as to study the effect of migration parameter on the malaria outbreak. It has been observed that the migration parameter is directly proportional to the malaria outbreak. Hence, it is suggested that in order to keep the malaria outbreak under control, the migration parameter is required to be minimized. That is, migration of populations is recommended to reduce so as to reduce the impact of malaria outbreak.
Alemu Geleta Wedajo,
Boka Kumsa Bole,
Purnachandra Rao Koya,
The Impact of Susceptible Human Immigrants on the Spread and Dynamics of Malaria Transmission, American Journal of Applied Mathematics.
Vol. 6, No. 3,
2018, pp. 117-127.
Abadi Abay Gebremeskel, Harald Elias Krogstad, “Mathematical Modelling of Endemic Malaria Transmission”, American Journal of Applied Mathematics, Vol. 3, No. 2, 2015, pp. 36-46. doi: 10.11648/j.ajam.20150302.12.
WHO, “Investing in health research for development”, Technical Report, World Health Organization, Geneva, 1996.
Tumwiine J., Mugisha J., Luboobi L., “A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity”, Journal of Applied Mathematics and Computation, vol. 189, pp. 1953-1965, 2005.
Bush A. O., Fernandez J. C., Esch G. W., Seed J. R., “Parasitism, the Diversity and Ecology of Animal Parasites”, First ed., Cambridge University Press, Cambridge, 2001.
Grimwade K., N. French, D. D. Mbatha, D. D. Zungu, M. Dedicoat, C. F. Gilks (2004). “HIV infection as a cofactor for severe falciparum malaria in adults living in a region of unstable malaria transmission in South Africa”, Journal, vol.18, pp. 547-554.
Plemmons W. R., “Mathematical study of malaria models of Ross and Ngwa”, Master Thesis, University of Florida, pp. 1-69, 2006.
Ross R., “The Prevention of Malaria”, John Murray, 1911.
Macdonald G., “The Epidemiology and Control of Malaria”, Oxford university press, 1957.
Bailey N.T.J., “The biomathematics of malaria”, Charles Gri, London, 1982.
Aron J. L., “Acquired immunity dependent upon exposure in an SIRS epidemic model”, Journal of Mathematical Biosciences, vol. 88, pp. 37-47, 1988.
Aron J. L., “Mathematical modelling of immunity to Malaria”, Journal of Mathematical Bio- sciences, vol. 90, pp. 385-396, 1988.
Tumwiine J., L.S. Luboobi, J.Y.T. Mugisha, “Modelling the effect of treatment and mosquitoes control on malaria transmission”, International Journal of Management and Systems, vol. 21, pp. 107-124, 2005.
Yang H. M., “Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)”, Revista de SaudePublica, vol. 34, pp. 223-231, 2000.
Ferreira M. U., H. M. Yang, “Assessing the effects of global warming and local social and economic conditions on the malaria transmission”, Revista de SaudePublica, vol. 34, pp. 214-222, 2000.
Koella J. C. and R. Antia, “Epidemiological models for the spread of anti-malarial resistance”, Malaria Journal, vol. 2, 2003.
Welch, J. Li, R. M., U. S. Nair, T. L. Sever, D. E. Irwin, C.Cordon-Rosales, N. Padilla, “Dynamic malaria models with environmental changes”, in Proceedings of the Thirty-fourth southeastern symposium on system theory, Huntsville, pp. 396-400, 2014.
Bacaer N. and C. Sokhna. “A reaction-diffusion system modeling the spread of resistance to an antimalarial drug”, Math. Biosci. Engrg, vol. 2, pp. 227-238, 2005.
Ngwa, G.A. and W.S. Shu, “A Mathematical model for endemic malaria with variable human and mosquito populations”, Mathematical and Computer Modeling Journal, vol. 32, pp. 747-763, 2000.
Ngwa G. A. “Modelling the dynamics of endemic malaria in growing populations”, Discrete Contin. Dyn. Syst. Ser. B, vol. 4, pp. 1173-1202, 2004.
Addo D. E., “Mathematical model for the control of Malaria”, Master Thesis, University of Cape Coast, 2009.
Yang H., Wei H., Li X., “Global stability of an epidemic model for vector borne disease”, J SystSci Complex Journal, vol. 23, pp. 279-292, 2010.
MiliyonTilahun. “Backward bifurcation in SIRS malaria model”, LsevierarXiv: 1707.00924v3, 2017.