Picture of smart phone in human hand

World leading smartphone and mobile technology research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by Strathclyde researchers from the Department of Computer & Information Sciences involved in researching exciting new applications for mobile and smartphone technology. But the transformative application of mobile technologies is also the focus of research within disciplines as diverse as Electronic & Electrical Engineering, Marketing, Human Resource Management and Biomedical Enginering, among others.

Explore Strathclyde's Open Access research on smartphone technology now...

The SIS epidemic model with Markovian switching

Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng (2012) The SIS epidemic model with Markovian switching. Journal of Mathematical Analysis and Applications, 394 (2). pp. 496-516. ISSN 0022-247X

[img] PDF
SIS_MS_final.pdf - Preprint

Download (2MB)

Abstract

Population systems are often subject to environmental noise. Motivated by Takeuchi et al. (2006), we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing computer simulations. We also establish the conditions for extinction and persistence for the stochastic SIS epidemic model and compare these with the corresponding conditions for the deterministic SIS epidemic model. We first prove these results for a two-state Markov chain and then generalise them to a finite state space Markov chain. Computer simulations based on the explicit solution and the Euler--Maruyama scheme are performed to illustrate our theory. We include a more realistic example using appropriate parameter values for the spread of Streptococcus pneumoniae in children.