Respiratory Diseases Prediction from a Novel Chaotic System

Abstract

Pandemics can have a significant impact on international health systems. Researchers have found that there is a correlation between weather conditions and respiratory diseases. This paper focuses on the non-linear analysis of respiratory diseases and their relationship to weather conditions. Chaos events may appear random, but they may actually have underlying patterns. Edward Lorenz referred to this phenomenon in the context of weather conditions as the butterfly effect. This inspired us to define a chaotic system that could capture the properties of respiratory diseases. The chaotic analysis was performed and was related to the difference in the daily number of cases received from real data. Stability analysis was conducted to determine the stability of the system and it was found that the new chaotic system was unstable. Lyapunov exponent analysis was performed and found that the new chaotic system had Lyapunov exponents of (+, 0, -, -). A dynamic neural architecture for input-output modeling of nonlinear dynamic systems was developed to analyze the findings from the chaotic system and real data. A NARX network with inputs (maximum temperature, pressure, and humidity) and one output was used to to overcome any delay effects and analyze derived variables and real data (patients number). Upon solving the system equations, it was found that the correlation between the daily predicted number of patients and the solution of the new chaotic equation was 90.16%. In the future, this equation could be implemented in a real-time warning system for use by national health services.