The computational viral extension direct and inverse problems are problems of long-standing interest in mathematics, epidemic and natural disaster studies. We designed and developed a set of algorithms for the construction of the closure of the arbitrary chaotic set that can efficiently be used in evaluations of the propagations autooscillatory waves. The algorithms presented in this paper are readily applicable to applications in the management of epidemics, disaster handling, political propaganda issues, and the study of marketing (and others). The first author of this paper has successfully applied these algorithms to Chomobyl Zone, forest fire in Siberia, cholera epidemic in Odessa (Ukraine) and Astrakhan (Russia), and anthrax in Altai (Russia).
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