Diffusion Approximation of Stochastic SIR Epidemic Model
D. Kiouach *
MSTI Laboratory, High School of Technology, Ibn Zohr University, Agadir, Morocco.
*Author to whom correspondence should be addressed.
Abstract
In this work we consider the general stochastic SIR (Susceptible - Infected - Removed) epidemic model with the transition intensity q(S,I),(S−1,I+1) = βg(S)I, where g(x) is a function density dependent. An approximation of the final size by a diffusion process is given. Finally, I introduce some numerical simulation graphics to illustrate the main result.
Keywords: Epidemic model, Final size, SIR, Stochastic model, Markov process, Density dependent, Diffusion approximation.