Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies
Pure and Applied Mathematics Journal
Volume 9, Issue 6, December 2020, Pages: 101-108
Received: Jan. 29, 2020;
Accepted: Mar. 9, 2020;
Published: Nov. 11, 2020
Views 140 Downloads 85
Fekadu Tadege Kobe, Department of Mathematics, College of Natural and Computational Science, Wachemo University, Hossana, Ethiopia
This paper proposes and analyses a basic deterministic mathematical model to investigate Simulation for controlling the spread of malaria Diseases Transmission dynamics. The model has seven non-linear differential equations which describe the control of malaria with two state variables for mosquito’s populations and five state variables for human’s population. To represent the classification of human population we have included protection and treatment compartments to the basic SIR epidemic model and extended it to SPITR model and to introduce the new SPITR modified model by adding vaccination for the transmission dynamics of malaria with four time dependent control measures in Ethiopia Insecticide treated bed nets (ITNS), Treatments, Indoor Residual Spray (IRs) and Intermittent preventive treatment of malaria in pregnancy (IPTP). The models are analyzed qualitatively to determine criteria for control of a malaria transmission dynamics and are used to calculate the basic reproduction R0. The equilibria of malaria models are determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the R0<1, the basic malaria model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The results also designing the effects of some model parameters, the infection rate and biting rate. The numerical analysis and numerical simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of malaria were suggest using insecticide treated bed nets, indoor residual spraying, prompt effective diagnosis and treatment of infected individuals with vaccination is more effective for children.
Fekadu Tadege Kobe,
Mathematical Model of Controlling the Spread of Malaria Disease Using Intervention Strategies, Pure and Applied Mathematics Journal.
Vol. 9, No. 6,
2020, pp. 101-108.
WHO (2009), "Global Malaria Program: Position Statement on ITNs".
Nita. H. Shah and Jyoti Gupta (2013),"SEIR Model and Simulation for Vector Borne Diseases", Applied Mathematics Vol. 4, Pp. 13–17.
Samwel Oseko Nyachae, Johana K. Sigey Jeconiah A. Okello, James M. Okwoyo and D. Theuri (2014),"A Study for the Spread of Malaria in Nyamira Town - Kenya, The SIJ Transactions on Computer Science Engineering and its Applications (CSEA), The Standard International Journals (The SIJ), Vol. 2, No. 3 (1), Pp. 53-60.
Rollback Malaria. What is malaria? http://www.rollbackmalaria.pdf. (2010-05-10).
WHO (2007) Insecticide treated mosquito nets: a WHO position statement. Technical report, World Health Organization.
Bayoh MN, Mathias DK, Odiere MR, Mutuku FM, Kamau L, et al.. (2010) Anopheles gambiae: historical population decline associated with regional distribution of insecticide-treated bed nets in western Nyanza province, Kenya. Malaria Journal 9.
WHO (2004) Global strategic framework for integrated vector management. Technical report, World Health Organization, Geneva.
WHO (2011) World Malaria Report. Technical report, World Health Organization, Geneva.
RBM (2013) Minutes of roll back malaria vector control working group 8th annual meeting. Technical report, Roll Back Malaria. Available: http://www.rollbackmalaria.org/mechanisms/vcwg.html.
P. M. M. Mwamtobe (2010), "Modeling the Effects of Multi Intervention Campaigns for the Malaria Epidemic in Malawi", M. Sc. (Mathematical Modeling) Dissertation, University of Dar es Salaam, Tanzania.
G. A. Ngwa, W. S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations. Mathematical and computer modeling, 32 (7), (2000), 747-763.
C. Chiyaka J. M. Tchuenche, W. Garira & S. Dube, A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria. Applied Mathematics and Computation, 195 (2), (2008), 641-662.
N. Chitnis J. M. Cushing & J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission. SIAM Journal on Applied Mathematics, 67 (1), (2006), 24-45.
A. M. Baba, A Mathematical Model for Assessing the Control of and Eradication strategies for Malaria in a Community, Science.pub.net 4 (2), (2012), 7-12.
Kermack WO, McKendrick AG (August 1, 1927). “A Contribution to the Mathematical Theory of Epidemics". Proceedings of the Royal Society A 115 (772): 700–721. doi: 10.1098/rspa.1927.0118.
Bartlett MS (1957). "Measles periodicity and community size". Journal of the Royal Statistical Society, Series A 120 (1): 48–70. Doi: 10.2307/2342553. JSTOR 2342553.
Dejen Ketema Mamo and Purnachandra Rao Koya. “Mathematical Modeling and Simulation Study of SEIR disease and Data Fitting of Ebola Epidemic spreading in West Africa” Journal of Multidisciplinary Engineering Science and Technology (JMEST) Vol. 2 Issue 1, January 2015, pp 106 – 14. http://www.jmest.org/wp-content/uploads/JMESTN42350340.pdf.
Purnachandra Rao Koya and Dejen Ketema Mamo, Ebola Epidemic Disease: Modelling, Stability Analysis, Spread Control Technique, Simulation Study and Data Fitting, Journal of Multidisciplinary Engineering Science and Technology (JMEST), Vol. 2, Issue 3, March 2015, pp 476 – 84. http://www.jmest.org/wp-content/uploads/JMESTN42350548.pdf.
O. J. Diekmann (1990), "Mathematical Biology" Vol. 28, Pp. 365–382.
Birkhoff G and Rota, G. C (1982), Ordinary Differential Equations, Ginn.
Namawejje H. (2011). Modelling the Effect of Stress on the Dynamics and Treatment of Tuberculosis. M. Sc. (Mathematical Modelling) Dissertation, University of Dares Salaam, Tanzania.
L. Perko, Differential Equations and Dynamics Systems in Applied Mathematics, vol. 7, Springer, Berlin, Germany, 2000.
WHO/World Malaria Report (2014) (www.who.int/malaria).
Chitnis N. (2005), "Using Mathematical Models in Controlling the Spread of Malaria", Ph. D. Thesis, Program in Applied Mathematics, University of Arizona, Tucson.
Niger A shrafi M and Gumel Abba B (2008,"Mathematical Analysis of the Role of Repeated Exposure on Malaria Transmission Dynamics", Differential Equations and Dynamical Systems, Volume 16, No. 3, pp 251-287.
Flores J. D. (2011). Math-735: Mathematical Modelling, 4.5 Routh-Hurwitz criteria. Department of Mathematical Sciences, The University of South Dakot.
Y. T. Tumwiine, Mugisha and L. S. Lubobi (2007), "Applied Mathematics and Computation", Vol. 189, Pp. 1953–1965.
Federal Democratic Republic of Ethiopia Ministry Of Health Ethiopia National Malaria Indicator Survey, Addis Ababa, 2008.