The paper considers a mathematical model that describes the interactions between the economic system and the ecological system through waste emissions, resource consumption, and the restoration of restorable resources. It is assumed that the state levies a tax on waste emissions, thereby controlling emissions and the consumption of resources by the economy. The model also describes the impact of economic and environmental factors on demographics. The state should strive for economic growth and avoid environmental disasters, and the model can be useful for achieving these goals. Besides, a software implementation of the model was constructed. Some technical details of the software implementation were also considered. Numerical experiment with one of the possible sets of parameters’ values was carried out, which displayed one of the possible situations of stable development.