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Home  >  Volume 27 (July 2014)

15. Effects of treatment rates in a stochastic Susceptible-Infectious –Removed (SIR) model by Emeka N. Onoyima and NafiuHussaini. Volume 27,(July 2014), pp119 – 128
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In this paper, we formulate a Continuous Time Markov Chain (CTMC) model with two types of treatment rates: (i) Constant treatment rate (ii) simple linear treatment rate. The model has been driven from the standard susceptible-infected-removed (SIR) epidemic model. Numerical simulations are used to assess the effect of variation in the treatment term relative to the constant recruitment rate A.  It is shown that with R_01 or R_02 less than unity, whether or not the recruitment rate is greater than or equal to the treatment term, the disease sample paths approach a disease free equilibrium, but for the basic reproduction number (R_01 or R_02 ) greater than unity, the sample paths approach an endemic equilibrium state. While the simple linear treatment rate predicts equal decay rate in all cases, the constant treatment rate shows the deterministic paths have higher disease prevalence at the peak of the outbreak and the stochastic realizations a faster decay rate. Our results further demonstrate the effects of treatment in predicting disease prevalence and decay rate.

Keywords: Basic reproduction number; deterministic; disease equilibrium; Markov chain; Continuous Time     Markov Chain.