title: A comparison of a deterministic and stochastic model for hepatitis C with an isolation stage.
abstract: We formulate a deterministic epidemic model for the spread of Hepatitis C containing an acute, chronic and isolation class and analyse the effects of the isolation class on the transmission dynamics of the disease. We calculate the basic reproduction number R(0) and show that for R(0)≤1, the disease-free equilibrium is globally asymptotically stable. In addition, it is shown that for a special case when R(0)>1, the endemic equilibrium is locally asymptotically stable. Furthermore, an analogous stochastic epidemic model for Hepatitis C is formulated using a continuous time Markov chain. Numerical simulations are used to estimate the mean, variance and probability distributions of the discrete random variables and these are compared to the steady-state solutions of the deterministic model. Finally, the expected time to disease extinction is estimated for the stochastic model and the impact of isolation on the time to extinction is explored.
authors.affiliation: a Department of Mathematics , Lahore University of Management Sciences , Lahore , Pakistan.
authors.forename: Mudassar
authors.initials: M
authors.lastname: Imran
authors.forename: Muhammad
authors.initials: M
authors.lastname: Hassan
authors.forename: Muhammad
authors.initials: M
authors.lastname: Dur-E-Ahmad
authors.forename: Adnan
authors.initials: A
authors.lastname: Khan
mesh_terms: D050936:Basic Reproduction Number; D019353:Endemic Diseases; D006526:Hepatitis C / Q000453:epidemiology*; D006801:Humans; D013269:Stochastic Processes