Paper Info
Title
Analytic solution of the susceptible-infective epidemic model with state-dependent contact rates and different intervention policies
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.
Year
DOI
Venue
2013
10.1177/0075497147905
Simulation
Keywords
DocType
Volume
corresponding deterministic model,epidemiological model,Kermack-McKendrick model,continuous-time Markov chain,epidemic duration,contact rate,susceptible-infective epidemic model,state-dependent contact rate,SI model,different intervention policy,analytic solution,Markov chain,stochastic model,resultant model
Journal
89
Issue
ISSN
Citations 
6
0037-5497
2
PageRank 
References 
Authors
0.44
5
2
Name
Order
Citations
PageRank
Hamed Yarmand1162.73
Julie S. Ivy2339.12