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Modelling Cultural Hereditary Transmission: Insight Through Optimal Control
Affiliation:1. Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi campus, Ghana;2. Department of Mathematics, Federal University of Technology, Akure, Nigeria;3. Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India;4. Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India;1. Department of Natural Resources, Isfahan University of Technology, 84156-83111 Isfahan, Iran;2. inter 3 GmbH - Institute for Resources Management, Berlin, Germany;1. Graduate Student, Department of Mathematics, University of Benin, Benin City, Nigeria;2. Department of Mathematics, University of Benin, Benin City, Nigeria;3. Department of Animal and Environmental Biology, University of Benin, Benin City, Nigeria;1. Institute for Groundwater Studies, University of the Free State, Bloemfontein 9301, South Africa;2. Department of Mathematics, University of Education Winneba (Kumasi campus), Ghana;3. Mathematics Department, College of Sciences and Humanities Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Saudi Arabia;4. Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt;1. Department of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana;2. Siirt University, Art and Science Faculty, Department of Mathematics, Siirt TR-56100, Turkey
Abstract: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.
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