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Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages
Journal article   Peer reviewed

Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages

Robert J. Gallop, Charles J. Mode and Candace K. Sleeman
Mathematical biosciences, v 177(01-02), pp 287-315
2002
PMID: 11965260

Abstract

Embedded deterministic models Extra-marital sexual contacts Heterosexual HIV/AIDS Marital partnerships Monte Carlo simulation Stochastic models Threshold conditions
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.

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Collaboration types
Domestic collaboration
Web of Science research areas
Biology
Mathematical & Computational Biology
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