Impact of Climatic Factors and Intervention Strategies on the Dynamics of Malaria in Ethiopia: A Mathematical Model Analysis
AbstractIn this work we considered a nonlinear dynamical system to study the impact of temperature and rainfall on the transmission of malaria disease in Ethiopia. We found disease free and endemic equilibrium points and we proved their local and global stability. We calculate the effective reproduction number using real data collected from different health sectors in Ethiopia and we found that the malaria disease spreads in both high risk and low risk areas since the effective reproduction number is greater than unity. We perform sensitivity analysis to identify the most influential control parameter of the spread of malaria disease. And thus, the most temperature dependent influential control parameter is mosquito biting rate which can be controlled by insecticide treated net. The most rainfall dependent influential control parameter is larvae development rate which can be controlled by destruction of mosquitoes breeding sites and regular use of larvicides.
Abdelrazec A, Gumel AB. Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics. Journal of mathematical biology. 2017 May 1;74(6):1351-95.
Abiodun GJ, Witbooi P, Okosun KO. Modelling the impact of climatic variables on malaria transmission. Hacettepe journal of mathematics and statistics. 2018 Apr 1;47(2):219-35.
Alelign A, Dejene T. Current status of malaria in Ethiopia: evaluation of the burden, factors for transmission and prevention methods. Acta Parasitologica Globalis. 2016;7(1):01-6.
Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford university press; 1992 Aug 27.
Aron JL, May RM. The population dynamics of malaria. In The population dynamics of infectious diseases: theory and applications 1982 (pp. 139-179). Springer, Boston, MA.
Bakary T, Boureima S, Sado T. A mathematical model of malaria transmission in a periodic environment. Journal of biological dynamics. 2018 Jan 1;12(1):400-32.
Chitnis NR. Using mathematical models in controlling the spread of malaria.
Chiyaka C, Tchuenche JM, Garira W, Dube S. A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria. Applied Mathematics and Computation. 2008 Feb 1;195(2):641-62.
Deribew A, Dejene T, Kebede B, Tessema GA, Melaku YA, Misganaw A, et al. Incidence, prevalence and mortality rates of malaria in Ethiopia from 1990 to 2015: analysis of the global burden of diseases 2015. Malaria journal. 2017 Dec;16(1):271.
Diekmann O., Heesterbeek J. A and Metz J. A., On the definition and computation of R_0 in the model for infectious disease in heterogeneous population. Journal of mathematical Biology, 28 (1990), 365-382.
Girum T, Shumbej T, Shewangizaw M. Burden of malaria in Ethiopia, 2000-2016: findings from the Global Health Estimates 2016. Tropical Diseases, Travel Medicine and Vaccines. 2019 Dec 1;5(1):11.
Hilker FM, Westerhoff FH. Preventing extinction and outbreaks in chaotic populations. The American Naturalist. 2007 Aug;170(2):232-41.
J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1976.
Koella JC. On the use of mathematical models of malaria transmission. Acta tropica. 1991 Apr 1;49(1):1-25.
MacDonald G. The epidemiology and control of malaria. London: Oxford Univ. Pr.
Mandal S, Sarkar RR, Sinha S. Mathematical models of malaria-a review. Malaria journal. 2011 Dec;10(1):202.
Martens WJ, Niessen LW, Rotmans J, Jetten TH, McMichael AJ. Potential impact of global climate change on malaria risk. Environmental health perspectives. 1995 May;103(5):458-64.
Mohammed-Awel J, Agusto F, Mickens RE, Gumel AB. Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis. Infectious Disease Modelling. 2018 Jan 1;3:301-21.
Mukhtar AY. Mathematical modeling of the transmission dynamics of malaria in South Sudan.
Ngarakana-Gwasira ET, Bhunu CP, Mashonjowa E. Assessing the impact of temperature on malaria transmission dynamics. Afrika Matematika. 2014 Dec 1;25(4):1095-112.
Okosun KO, Makinde OD. Modelling the impact of drug resistance in malaria transmission and its optimal control analysis. International Journal of Physical Sciences. 2011 Nov 9;6(28):6479-87.
P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29–48, 2002.
Parham PE, Michael E. Modelling climate change and malaria transmission. In Modelling Parasite Transmission and Control 2010 (pp. 184-199). Springer, New York, NY.
Ross R. The prevention of malaria. John Murray; London; 1911.
Traoré B, Sangaré B, Traoré S. A mathematical model of malaria transmission with structured vector population and seasonality. Journal of Applied Mathematics. 2017 Jan 1;2017.
Turell MJ, Dohm DJ, Sardelis MR, O’guinn ML, Andreadis TG, Blow JA. An update on the potential of North American mosquitoes (Diptera: Culicidae) to transmit West Nile virus. Journal of medical entomology. 2005 Jan 1;42(1):57-62.
World Health Organization, 2018. World malaria report 2017. Geneva: World Health Organization.
World Health Organization. 2019. World malaria report 2018. Geneva: World Health Organization.
World Health Organization. 2020. World malaria report 2019. Geneva: World Health Organization.
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