The use of generation stochastic models to study an epidemic disease

• Published in: Advances in difference equations Vol. 2013; no. 1; pp. 1 - 9
• Main Authors: Seddighi Chaharborj, S, Fudziah, I, Abu Bakar, MR, Seddighi Chaharborj, R, Majid, ZA, Ahmad, AGB
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2013; Springer Nature B.V
• Subjects: Analysis; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; deterministic model; probability function; epidemic diseases; stochastic model; susceptible-infective-susceptible
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2013-7

Stochastic models have an important role in modeling and analyzing epidemic diseases for small size population. In this article, we study the generation of stochastic models for epidemic disease susceptible-infective-susceptible model. Here, we use the separation variable method to solve partial differential equation and the new developed modified probability generating function (PGF) of a random process to include a random catastrophe to solve the ordinary differential equations generated from partial differential equation. The results show that the probability function is too sensitive to μ , β and γ parameters.