title: A state-time epidemiology model of tuberculosis: importance of re-infection.
abstract: An epidemiological model is presented that considers five possible states of a population: susceptible (S), exposed (W), infectious (Y), in treatment (Z) and recovered (R). In certain instances transition rates (from one state to another) depend on the time spent in the state; therefore the states W, Y and Z depend on time and length of stay in that state - similar to age-structured models. The model is particularly amenable to describe delays of exposed persons to become infectious and re-infection of exposed persons. Other transitions that depend on state time include the case finding and diagnosis, increased death rate and treatment interruption. The mathematical model comprises of a set of partial differential and ordinary differential equations. Non-steady state solutions are first presented, followed by a bifurcation study of the stationary states.
authors.affiliation: Department of Social Policy, London School of Economics, London WC2A 2AE, United Kingdom. hviljoen1@unl.edu
authors.forename: S
authors.initials: S
authors.lastname: Viljoen
authors.forename: E
authors.initials: E
authors.lastname: Pienaar
authors.forename: H J
authors.initials: HJ
authors.lastname: Viljoen
mesh_terms: D006801:Humans; D008954:Models, Biological; D013997:Time Factors; D014376:Tuberculosis / Q000453:epidemiology*