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Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles
American Journal of Applied Mathematics
Volume 5, Issue 4, August 2017, Pages: 99-107
Received: Apr. 15, 2017; Accepted: May 2, 2017; Published: Jul. 6, 2017
Authors
Selam Nigusie Mitku, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya, School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
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Abstract
In this paper, a five compartmental model has been considered and investigated the transmission dynamics of measles disease in the human populations. The only one infected compartment in the standard model has been split into two: Infected catarrh, and infected eruption. Measles is a deadly disease that is very common and contagious in the world. However, if enough care is taken one can survive easily against Measles disease. The Measles disease has no specific treatment but vaccination is available. It has been shown that the model has a positive solution and is bounded. The basic reproduction number is derived using the next generation matrix method. The disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode 45 of MATLAB. The results and interpretations are elaborated and included in the text. Description of the model, Mathematical analysis, stability analysis, and simulation studies are conducted and the results are included. The standard model and the proposed models have been compared and the observations are presented in a tabular form.
Keywords
Measles, Modeling, Equilibrium Points, Stability Analysis, Reproduction Number, Simulation Study
Selam Nigusie Mitku, Purnachandra Rao Koya, Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles, American Journal of Applied Mathematics. Vol. 5, No. 4, 2017, pp. 99-107. doi: 10.11648/j.ajam.20170504.11
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