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Recently, violence has been a very common and serious public health problem in the world. In this new mathematical modeling tactic study, we formulated and examined the firsthand violence mathematical model with five distinct classes of the human population (susceptible, violence-exposed, violence, negotiated, and reconciled). The model takes into account the diffusion of violence and infection. The violence-free and violence-dominance model equilibrium points are calculated, and their local and global stabilities are analyzed. The model threshold values are obtained. As a result of the model analysis, the violence diffusion is under control if the basic reproduction number is less than unity, and it diffuses through the community if this number exceeds unity. Besides, the sensitivity analysis of the parameter values of the basic reproduction number is demonstrated. We have applied the MATLAB ode45 solver to illustrate the numerical results of the model. Finally, from analytical and numerical solutions, we obtain jointly equivalent and consistent results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]