2026-06-08T12:05:31Zhttps://docta.ucm.es/rest/oai/request
oai:docta.ucm.es:20.500.14352/230012023-08-10T16:21:01Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense author Economou, A. author Gómez-Corral, Antonio author López-García, M. 2023-06-18T05:40:47Z 2023-06-18T05:40:47Z 2015-03-01 0378-4371 10.1016/j.physa.2014.10.054 https://hdl.handle.net/20.500.14352/23001 http://www.sciencedirect.com/science/article/pii/S0378437114008929 http://www.sciencedirect.com A stochastic model for the spread of an SIS epidemic among a population consisting of N individuals, each having heterogeneous infectiousness and/or susceptibility, is considered and its behavior is analyzed under the practically relevant situation when N is small. The model is formulated as a finite time-homogeneous continuous-time Markov chain X. Based on an appropriate labeling of states, we first construct its infinitesimal rate matrix by using an iterative argument, and we then present an algorithmic procedure for computing steady-state measures, such as the number of infected individuals, the length of an outbreak, the maximum number of infectives, and the number of infections suffered by a marked individual during an outbreak. The time till the epidemic extinction is characterized as a phase-type random variable when there is no external source of infection, and its Laplace-Stieltjes transform and moments are derived in terms of a forward elimination backward substitution solution. The inverse iteration method is applied to the quasi-stationary distribution of X, which provides a good approximation of the process X at a certain time, conditional on non-extinction, after a suitable waiting time. The basic reproduction number R-0 is defined here as a random variable, rather than an expected value. eng A stochastic SIS epidemic model with heterogeneous contacts journal article URL https://docta.ucm.es/bitstreams/2cf8055f-b3dd-4530-93e8-d064481d8af2/download File MD5 d28d69c3e6f389f71b5f7aaf442ac0ce 533570 application/pdf GCorral202elsevier.pdf URL https://docta.ucm.es/bitstreams/eb3a4573-02b6-49e4-9d96-42b5cda4b9c5/download File MD5 d3c67df71fd685e35dccea252fbd1f71 85273 text/plain GCorral202elsevier.pdf.txt