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• W2032084937 abstract "When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm." @default.
• W2032084937 created "2016-06-24" @default.
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• W2032084937 date "2002-05-01" @default.
• W2032084937 modified "2023-09-27" @default.
• W2032084937 title "Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages" @default.
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• W2032084937 doi "https://doi.org/10.1016/s0025-5564(01)00093-1" @default.
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• W2032084937 hasPublicationYear "2002" @default.
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