Mathematical modeling analysis on the dynamics of university students animosity towards mathematics with optimal control theory

Abstract

Animosity towards mathematics is a very common worldwide problem and it is usually caused by wrong information, low participation, low challenge tolerance, falling further behind, being unemployed, and avoiding the advanced math classes needed for success in many careers. In this study, we have considered and formulated the new SEATS compartmental mathematical model with optimal control theory to analyze the dynamics of university students’ animosity towards mathematics. We applied the next-generation matrix, Ruth-Hurwitz criteria, Lyapunov function, and Volterra-Lyapunov stable matrices to show local and global stability of equilibrium points of the model respectively. The study demonstrated that the animosity-free equilibrium point is both locally and globally asymptotically stable whenever the model basic reproduction number is less than unity, whereas the animosity-dominance equilibrium point is both locally and globally asymptotically stable when the model basic reproduction number is greater than unity. Finally, we applied numerical ode45 solvers using the Runge–Kutta method and we have carried out numerical simulations and shown that applying both prevention and treatment controls is the best strategy to minimize and possibly eradicate the animosity-infection in the community under consideration.

Mathematical Model Analysis on the Diffusion of Violence

“…We are interested in finding the rate of change of R 0 due to each parameter value change. e rate of change of R 0 for a change in the value of parameters h can be estimated from a normalized sensitivity index, SI (h) defined as, SI (h) � h/R 0 zR 0 /zh [21,24].…”

“…Many researchers have applied the infectious disease dynamics model to analyze violence, corruption, and other social situations. Of those researchers, some applied mathematical modeling analysis on the dynamics of university student animosity towards mathematics with optimal control theory [24], some applied modeling for the dynamics of racism in cyberspace [25], and some applied modeling for violence [26][27][28], some applied modeling for the stability analysis of corruption [29], and others study universality of political corruption networks [30]. But, to the best of our knowledge, no one has developed and analyzed a mathematical model of the di usion of violence.…”

A Mathematical Modeling Analysis of Racism and Corruption Codynamics with Numerical Simulation as Infectious Diseases

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“…In the simulation part, they examined the optimal control under 11 control strategies and through the data analysis of incremental cost-effectiveness ratio and infection averted ratio of all control strategies and provide a flexible control strategy for the security management department. Teklu and Terefe [ 37 ] formulated and analyzed a mathematical model on the dynamics of university students' with animosity towards mathematics with optimal control theory. They have shown that the animosity-free equilibrium point is local and global stability when the basic reproduction number is less than unity, and the animosity-dominance equilibrium points local and global stability whenever the basic reproduction number is greater than unity.…”

A nonlinear system dynamics and simulation analysis of fractional order modelling on employees negative attitude towards their workplace with intervention strategies

“…Formulating and analyzing a mathematical and statistical model on realworld situations in natural sciences, social sciences, engineering, arts, and business and economics disciplines plays a fundamental role in providing worthwhile tools and techniques to predict and control their future dynamics [7][8][9][10][11]. Recently, it has attracted various researchers' attention [9,12].…”