Computational algebraic geometry of epidemic models

Martín Rodríguez Vega

doi:10.1117/12.2049255

Abstract

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R₀) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R₀, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

Citation Download Citation

Martín Rodríguez Vega, Martín Rodríguez Vega, "Computational algebraic geometry of epidemic models", Proc. SPIE 9112, Sensing Technologies for Global Health, Military Medicine, and Environmental Monitoring IV, 91121J (5 June 2014); doi: 10.1117/12.2049255; https://doi.org/10.1117/12.2049255

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