Abstract
•We develop a mathematical model for culture hereditary transmission.•The fundamental properties of the model are established.•The reproduction number is evaluated.•The numerical results are presented in the form of graphs.
Cultural hereditary transmission is indeed very important for the recognition of human personalities and countries are seeking to integrate them into their school curriculum. A deterministic mathematical model for human behavior transmission is extracted and built into the present study. The fundamental characteristics of the model are well established and the reproduction number is evaluated. The stability analysis indicates that the model is undergoing a backward bifurcation phenomenon. Time dependent control is also introduced into the model and Pontryagin’s Maximum is employed to characterise the best strategy to spread cultural heredity. The numerical simulation findings are also provided and indicate that the best approach for improving cultural heritage in a society is to explore all three control methods at the same time.