Traditional non-heritage music art is gradually declining, driven by cultural heritage education, this paper studies the future inheritance trend of non-heritage music art. In this paper, the infectious disease dynamics model and complex network propagation theory are used to construct a mathematical model of the inheritance of non-heritage music art, an improved non-dominated sorting genetic algorithm is proposed, and the trend characteristics of the inheritance of non-heritage music art are simulated by solving the parameters of the model through the improved NSGA-Ⅱ algorithm which introduces the congestion calculation method and the crossover strategy. The improved NSGA- Ⅱ algorithm shows better convergence speed of optimization search and uniformity of solution distribution on single peak function and three ZDT functions. Its SP and IGD indexes are much better than the comparison algorithm, with values less than one-half of the comparison algorithm. Taking the heat of non-heritage music and art inheritance in Baidu index for several days as the simulation object, it is found that the simulation of the mathematical model of non-heritage music and art inheritance in this paper has a maximum heat value of 115,000 and the real maximum heat value of 117,241 are not much different from each other, which confirms that this paper’s non-heritage music and art inheritance mathematical model has a better fitting effect and reasonableness. The work of this paper has injected new vitality into the innovation of non-heritage music art inheritance.