Location of sources in reaction-diffusion equations using support vector machines

• Published in: PloS one 2019-12, Vol.14 (12), p.e0225593-e0225593
• Main Authors: Chávez-Medina, Venecia, González, José A, Guzmán, Francisco S
• Format: Article
• Language: English
• Subjects: Animals; Biology and Life Sciences; Chemical reactions; Classification; Climate change; Communicable Diseases - epidemiology; Computer and Information Sciences; Diffusion; Diffusion coefficient; Diffusion equations; Diffusion processes; Disease Outbreaks; Disease Vectors; Environmental parameters; Evolution; Growth models; Inverse problems; Medicine and Health Sciences; Models, Biological; Neural networks; Organic chemistry; Outbreaks; Parameter estimation; Partial differential equations; Physical Sciences; Population; Population studies; Process parameters; Propagation; Reaction-diffusion equations; Research and Analysis Methods; Reynolds number; Support Vector Machine; Support vector machines; Viruses; West Nile virus
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0225593

The reaction-diffusion equation serves to model systems in the diffusion regime with sources. Specific applications include diffusion processes in chemical reactions, as well as the propagation of species, diseases, and populations in general. In some of these applications the location of an outbreak, for instance, the source point of a disease or the nest of a vector spreading a virus is important. Also important are the environmental parameters of the domain where the process diffuses, namely the space-dependent diffusion coefficient and the proliferation parameter of the process. Determining both, the location of a source and the environmental parameters, define an inverse problem that in turn, involves a partial differential equation. In this paper we classify the values of these parameters using Support Vector Machines (SVM) trained with numerical solutions of the reaction-diffusion problem. Our set up has accuracy of classifying the outbreak location above 90% and 77% of classifying both, the location and the environmental parameters. The approach presented in our analysis can be directly implemented by measuring the population under study at specific locations in the spatial domain as function of time.