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The Impact of Infective Immigrants on the Spread of Dog Rabies
American Journal of Applied Mathematics
Volume 5, Issue 3, June 2017, Pages: 68-77
Received: Apr. 11, 2017; Accepted: May 2, 2017; Published: Jun. 23, 2017
Authors
Aberu Mengistu Tulu, 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, it is proposed and analyzed a new mathematical model and that is developed on the basis of some reasonable modification made to the standard epidemic model. The impact of immigration, treatment and the effect of vaccination are included in the model. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. Numerical simulation study is conducted using ode 45 of MATLAB. It has been shown that the solution is positive and bounded. Algebraic expression for the reproduction number is constructed. Equilibrium points are identified and their stability analysis is carried out. It is pointed out that the disease dies out if the immigration of the infected dogs is controlled and the vaccination and the treatments are improved. Otherwise, the disease spreads rapidly in the dog population and it becomes an epidemic. Further, it is also pointed out that the impact of infective immigrants on the spread of dog rabies is positive and additive. The details are presented and discussed in the text.
Keywords
Infective Immigrants, Rabies, Vaccination, Compartmental Model, Stability, Reproductive Number, Simulation
Aberu Mengistu Tulu, Purnachandra Rao Koya, The Impact of Infective Immigrants on the Spread of Dog Rabies, American Journal of Applied Mathematics. Vol. 5, No. 3, 2017, pp. 68-77. doi: 10.11648/j.ajam.20170503.12
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