A MATHEMATICAL MODEL OF MALARIA TRANSMISSION DYNAMICS IN GENETICALLY RESISTANT AND SUSCEPTIBLE POPULATION

AKINDELE A. ONIFADE, I. O. ADEMOLA

Abstract


The variation in host response to infection might have a genetic basis. Exposure to Plasmodium infection developed genetic mechanisms of protection against severe disease. Two genes affecting red cell confer relative host resistance to P. falciparum: the autosomal gene for haemoglobin S (Hb S) and the sex-linked gene for the glucose-6-phosphate dehydrogenase $(G6PD)$ variant. A mathematical model was developed to understand the transmission and spread of malaria parasites.  The existence of the region where the model is epidemiologically feasible and mathematically well-posed was established.  The reproduction number $R_0$ was obtained from next generation matrix and the stability analysis of disease-free equilibrium was conducted.  Numerical simulations of the model were presented by solving the system of differential equations to explore the behaviour of the model and confirm the analytical results.  The results of this study shows a reduction in the number of death of genetically resistant human population which leads to increase in the number of death cases of susceptible human and increase in the number of infected mosquitoes.  This study suggest that if genetically resistant person are encouraged to take prophylactic treatment the number of infected mosquitoes could reduce

Full Text:

PDF

References


S. J. Allen, A. O'Donnell , Alexander NDE,+-thalassaemia protects children against disease due to malaria and other infections, Proc. Natl. Acad. Sci. USA 94: 14736-14741, 1997.

J. Balla, H. S. Jacob, G. Balla, K. Nath, G. M. Vercellotti, Endothelial cell heme oxygenase and ferritin induction by heme proteins: a possible mechanism limiting shock damage, Transactions of the Association of American Physicians, vol. 105, pp. 1-6,1992.

K. Blayneh, Optimal control and vector - borne diseases treatment and prevention, Discrete and continuous Dynamical Sys. Series Bm 11, No. 3, 5887-611, doi:10.3934/dedsb.2009.11.587, 2009.

C. Chiyaka, Modelling immune response and drug therapy in human malaria in-fection, computational and mathematical methods in Medicine, 9 No. 2, 143-163, doi:10.1080/ 17486700701865661, 2008.

O. Diekmann, , On the denition and computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations, J. Math. Biol, 28, 365-382, doi:10.1007/BF00178324, 1990.

Hill A.V.S, Elvin. J., Willis. A. et al. Molecular analysis of the association of HLA-B53 and resistance to severe malaria. Nature 1992; 360: 434-439.

A. V. S. Hill, C. E. M Allsopp, D. Kwiatkowski, Common est African HLA anti-gens are associated with protection from severe malaria Nature, vol. 352, no. 6336, pp. 595-600, 1991.

D. Kirschner, G.F Webb, A model for treatment Strategy in the chemotherapy of AIDS, Bull Math Biol., pp367390, 1990.

J. C. Knight, J. Udalova, A. V. Hill, A polymorphism that aects OCT-1 binding to the TNF promoter region is associated with severe malari, Nat Genet 1999; 22: 145-150


Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Journal of the Nigerian Mathematical Society

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