Examining the model of climate change by analyzing how changes in climate-related incidents spread within the environment, particularly in coastal areas, as a result of predictions, is the main goal of this study. Following some measurements of impact rates for various variables, a mathematical model is developed using the hypothesis of a healthy environment to investigate the rates of climate change affecting coastal communities. In addition to studying the model equilibrium points, the next generation method is used to determine the models reproductive number to climate incidents spread within the environment. To determine the most sensitive factors and look at how changes in the pace of change under various conditions affect coastal life, a sensitivity analysis was created. Both qualitative and quantitative analyses are performed on a proposed model, with particular focus on existence, boundedness, positivity, and unique solutions, which are key characteristics of the developed model. At endemic sites, the model's local stability is confirmed both theoretically and statistically. The Lyapunov derivative by endemic point of the model is used to investigate the worldwide stability of the model. Chaos control is also used to observe the chaotic behavior of the climate change. A two-step method, Lagrange polynomials, 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 climate change under coastal lives. The simulations show how different parameters affect the changes in climate incidents spread within the environment under coastal lives. Simulations have been developed to simulate the effects and behavior of climate change brought on by both natural and human activity, as well as to implement various environmental health initiatives. This type of research will be helpful in figuring out how climate change spreads and in developing future management plans for coastal lives, based on our verified results for various strategies.