Investigation of climate change by mathematical modeling approach to observe the effects of the most sensitive parameters: Analysis and Control

Examining the model of climate change by observing how changing in climate events spread within the environment as a result of prediction is the main goal of this study. Following some measurements of impacts rates for various variables, a mathematical model is developed utilizing the hypothesis developed for a healthy environment in order to investigate the various rates of climate change. The model is then converted into a fractional ordered model with theoretical solutions for continuous monitoring using the Caputo operator. In addition to studying the model endemic points, the next generation method is used to determine the model’s reproductive number at endemic points. Sensitivity analysis was developed to identify the most sensitive parameters and investigate the effects of variations in the rate of change under different circumstances. A suggested model is analyzed both qualitatively and quantitatively, with special attention paid to boundedness, positivity, existence and unique solutions. Both theoretically and statistically, the local stability of the model is verified at endemic points. The Lyapunov derivative by endemic point of the model is used to investigate the global stability of the model. The endemic points are examined for stability by globally validating the Lyapunov function. A two-step Lagrange polynomial method is applied in numerical simulations to investigate the effect of the fractional operator on the generalized form of the power law kernel for ongoing surveillance of the climate change model. The simulations show how different parameters affect the changing in climate. Simulations have been built to mimic the behavior and impact of climate changed caused by the human and natural activities and to put different measures in place for a healthy environment with a hypersensitive reaction (HR). Based on our confirmed results for different strategies, this kind of research will be useful in determining how changing in climate spread and in creating management plans.