Final outcome probabilities for SIR epidemic model. Issue 8 (17th April 2016)

• Record Type: Journal Article
• Authors: El Maroufy, Hamid; Kiouach, Driss; Ziad, Taib
• Is Part Of: Communications in statistics. Volume 45:Issue 8(2016)
• Page Start: 2426
• Page End: 2437
• Publication Date: 2016-04-17
• Subjects: Stochastic epidemic model -- Markov chain -- Final size -- Diffusion process.; 92D30 -- 60J28 -- 68J20 -- 65C20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.881494
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: We consider an SIR stochastic epidemic model in which new infections occur at rate f ( x, y ), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation.