Analytic solution of the susceptible-infective epidemic model with state-dependent contact rates and different intervention policies. (June 2013)

• Record Type: Journal Article
• Authors: Yarmand, Hamed; Ivy, Julie S
• Is Part Of: Simulation. Volume 89:Number 6(2013)
• Page Start: 703
• Page End: 721
• Publication Date: 2013-06
• Subjects: susceptible-infective model -- epidemic duration -- state-dependent contact rates -- interventions; Computer simulation -- Periodicals; 003.3
• DOI: 10.1177/0037549713479052
• Languages: English
• ISSNs: 0037-5497

Abstract

We consider the susceptible-infective (SI) epidemiological model, a variant of the Kermack–McKendrick models, and let the contact rate be a function of the number of infectives, an indicator of disease spread during the course of the epidemic. We represent the resultant model as a continuous-time Markov chain. The result is a pure death (or birth) process with state-dependent rates, for which we find the probability distribution of the associated Markov chain by solving the Kolmogorov forward equations. This model is used to find the analytic solution of the SI model as well as the distribution of the epidemic duration. We use the maximum likelihood method to estimate contact rates based on observations of inter-infection time intervals. We compare the stochastic model to the corresponding deterministic models through a numerical experiment within a typical household. We also incorporate different intervention policies for vaccination, antiviral prophylaxis, isolation, and treatment considering both full and partial adherence to interventions among individuals.