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Mathematical Analysis of the Global Dynamics of an SVEIR Epidemic Model with Herd Immunity

Journal Name:

  • International Journal of Science and Engineering Investigations

Publication Year:

  • 2017

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
The SVEIR epidemiological model was presented to gain insight into the mathematical epidemiological model with herd immunity in the population. Positivity of solution was shown for the mathematical and epidemiological well posed of the model. The stability of the model was analyzed for the existence of disease free and endemic equilibrium points. The threshold quantity “Basic Reproduction Number” ( 0 R ) with and without vaccine was derived using next generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally asymptotically stable whenever the basic reproduction number is less than unity i.e. ( R0 1 ), otherwise endemic whenever it exceeds unity ( 0 R 1). Global stability of endemic equilibrium was analyzed using Lyapunov method and numerical simulation of the model was carried out using Runge-Kutta method of order four (4) with MAPLE 18. Results showed that herd immunity can only be attained whenever everyone in the population is vaccinated against the infection, since ( Vaccine 0 R R ).
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