Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female Anopheles mosquitoes. A mathematical model describes the dynamics of malaria and human population compartments in terms of mathematical equations and these equations represent the relations between relevant properties of the compartments. The aim of the study is to understand the important parameters in the transmission and spread of endemic malaria disease, and try to find appropriate solutions and strategies for its prevention and control by applying mathematical modelling. The malaria model is developed based on basic mathematical modelling techniques leading to a system of ordinary differential equations (ODEs). Qualitative analysis of the model applies dimensional analysis, scaling, and perturbation techniques in addition to stability theory for ODE systems. We also derive the equilibrium points of the model and investigate their stability. Our results show that if the reproduction number, R0, is less than 1, the disease-free equilibrium point is stable, so that the disease dies out. If R0 is larger than 1, then the disease-free equilibrium is unstable. In that case, the endemic state has a unique equilibrium, re-invasion is always possible, and the disease persists within the human population. Numerical simulations have been carried out applying the numerical software Matlab. These simulations show the behavior of the populations in time and the stability of disease-free and endemic equilibrium points.
| Published in | American Journal of Applied Mathematics (Volume 3, Issue 2) |
| DOI | 10.11648/j.ajam.20150302.12 |
| Page(s) | 36-46 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Malaria, Endemic Model, Reproduction Number, Equilibrium Points, Numerical Simulation
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APA Style
Abadi Abay Gebremeskel, Harald Elias Krogstad. (2015). Mathematical Modelling of Endemic Malaria Transmission. American Journal of Applied Mathematics, 3(2), 36-46. https://doi.org/10.11648/j.ajam.20150302.12
ACS Style
Abadi Abay Gebremeskel; Harald Elias Krogstad. Mathematical Modelling of Endemic Malaria Transmission. Am. J. Appl. Math. 2015, 3(2), 36-46. doi: 10.11648/j.ajam.20150302.12
AMA Style
Abadi Abay Gebremeskel, Harald Elias Krogstad. Mathematical Modelling of Endemic Malaria Transmission. Am J Appl Math. 2015;3(2):36-46. doi: 10.11648/j.ajam.20150302.12
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Download@article{10.11648/j.ajam.20150302.12,
author = {Abadi Abay Gebremeskel and Harald Elias Krogstad},
title = {Mathematical Modelling of Endemic Malaria Transmission},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {2},
pages = {36-46},
doi = {10.11648/j.ajam.20150302.12},
url = {https://doi.org/10.11648/j.ajam.20150302.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.12},
abstract = {Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female Anopheles mosquitoes. A mathematical model describes the dynamics of malaria and human population compartments in terms of mathematical equations and these equations represent the relations between relevant properties of the compartments. The aim of the study is to understand the important parameters in the transmission and spread of endemic malaria disease, and try to find appropriate solutions and strategies for its prevention and control by applying mathematical modelling. The malaria model is developed based on basic mathematical modelling techniques leading to a system of ordinary differential equations (ODEs). Qualitative analysis of the model applies dimensional analysis, scaling, and perturbation techniques in addition to stability theory for ODE systems. We also derive the equilibrium points of the model and investigate their stability. Our results show that if the reproduction number, R0, is less than 1, the disease-free equilibrium point is stable, so that the disease dies out. If R0 is larger than 1, then the disease-free equilibrium is unstable. In that case, the endemic state has a unique equilibrium, re-invasion is always possible, and the disease persists within the human population. Numerical simulations have been carried out applying the numerical software Matlab. These simulations show the behavior of the populations in time and the stability of disease-free and endemic equilibrium points.},
year = {2015}
}
TY - JOUR T1 - Mathematical Modelling of Endemic Malaria Transmission AU - Abadi Abay Gebremeskel AU - Harald Elias Krogstad Y1 - 2015/02/13 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150302.12 DO - 10.11648/j.ajam.20150302.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 36 EP - 46 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150302.12 AB - Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female Anopheles mosquitoes. A mathematical model describes the dynamics of malaria and human population compartments in terms of mathematical equations and these equations represent the relations between relevant properties of the compartments. The aim of the study is to understand the important parameters in the transmission and spread of endemic malaria disease, and try to find appropriate solutions and strategies for its prevention and control by applying mathematical modelling. The malaria model is developed based on basic mathematical modelling techniques leading to a system of ordinary differential equations (ODEs). Qualitative analysis of the model applies dimensional analysis, scaling, and perturbation techniques in addition to stability theory for ODE systems. We also derive the equilibrium points of the model and investigate their stability. Our results show that if the reproduction number, R0, is less than 1, the disease-free equilibrium point is stable, so that the disease dies out. If R0 is larger than 1, then the disease-free equilibrium is unstable. In that case, the endemic state has a unique equilibrium, re-invasion is always possible, and the disease persists within the human population. Numerical simulations have been carried out applying the numerical software Matlab. These simulations show the behavior of the populations in time and the stability of disease-free and endemic equilibrium points. VL - 3 IS - 2 ER -
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