Intensifying heat waves, exacerbated by rise in carbon dioxide (CO \({_2}\) ) emissions, pose severe threats to global human health. Therefore, it becomes imperative to conduct analytical research on the control mechanisms that help mitigate the intensity of heat waves. This manuscript introduces a mathematical model to analyse the efficacy of mitigating heat wave intensity through optimal control of atmospheric CO \({_2}\) by spraying water droplets. The model integrates key variables including human population density, atmospheric CO \({_2}\) concentration, atmospheric temperature, and amount of water droplets. Using the suggested model, we also examine how heat waves affect the human population. According to the study of the model, when the atmospheric concentration of \(CO_2\) decreases due to the spraying of water droplets, heat wave intensity reduces, and human population density rises. The optimal control analysis is utilised to determine the dynamic spray rate of water droplets to control the atmospheric CO \({_2}\) , incurring the least associated cost. The numerical simulation of the model has been done to portray the analytical findings. Policies to optimally control the atmospheric CO \({_2}\) by spraying water droplets at strategic locations are found more suitable than constant heuristic control.
