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

Area of Science:

• Mathematical modeling
• Computational biology
• Epidemiology

Background:

• Reaction-diffusion equations model systems with sources, applicable to disease and population spread.
• Identifying outbreak sources and environmental parameters (diffusion, proliferation) is crucial for understanding these processes.
• These identification tasks constitute inverse problems involving partial differential equations.

Purpose of the Study:

• To classify source locations and environmental parameters for reaction-diffusion models.
• To develop a computational approach for identifying disease outbreak origins and diffusion characteristics.
• To assess the accuracy of Support Vector Machines in solving these inverse problems.

Main Methods:

• Numerical solutions of reaction-diffusion problems were generated.
• Support Vector Machines (SVM) were trained using these numerical solutions.
• The SVM model was used to classify parameter values, including source location and environmental parameters.

Main Results:

• The SVM model achieved over 90% accuracy in classifying outbreak locations.
• The model demonstrated 77% accuracy in classifying both the outbreak location and environmental parameters.
• The approach is directly implementable using spatiotemporal population measurements.

Conclusions:

• Support Vector Machines provide an effective method for solving inverse problems in reaction-diffusion systems.
• Accurate identification of disease sources and environmental parameters is feasible with this computational approach.
• The methodology offers a practical tool for epidemiological and ecological studies involving diffusion processes.