In this manuscript, the dynamics of a fractional-order predator-prey model with age structure on predator and nonlinear harvesting on prey are studied. The Caputo fractional-order derivative is used as the operator of the model by considering its capability to explain the present state as the impact of all of the previous conditions. Three biological equilibrium points are successfully identified including their existing properties. The local dynamical behaviors around each equilibrium point are investigated by utilizing the Matignon condition along with the linearization process. The numerical simulations are demonstrated not only to show the local stability which confirms all of the previous analytical results but also to show the existence of periodic signal as the impact of the occurrence of Hopf bifurcation.

In this article, the SITR Model for the spread of Hepatitis A by Vaccination is discussed. This study aims to analyze the stability of the model for the spread of hepatitis A disease around the points, interpret the model that has been formed by performing numerical simulations, and determine the effect of vaccination and treatment on the human population infected with hepatitis A. indicated by (T1) is stable and the endemic fixed point indicated by (T2) is stable. Based on the simulation obtained from each class (S, I, T, R) for R0<1, it shows that the population dynamics is (0.13,0,0,0.87) of the total population. Meanwhile, for R0>1 with a basic reproduction number, it shows the population dynamics of each class (S, I, T, R) that is (0.12,0.0056,0.0053,0.85) of the total population.

This article investigates the dynamical properties of a discrete time SIS-Epidemic model incorporating logistic growth rate and Allee effect. The forward Euler discretization method is employed to obtain the discrete-time model. All possible fixed points are identified including their local dynamics. Some numerical simulations by varying the step size parameter are explored to show the analytical findings, the existence of Neimark-Sacker bifurcation, and the occurrence of period-10 and 20 orbits

In the era of sustainable development, education is a fundamental right for everyone. Education is a process of helping humans develop themselves so that they can face all problems with an open attitude. One way to help students clarify the concepts and understanding of mathematics that is being studied during the learning process is by using teaching aids. Teaching aids serve to facilitate the purpose of implementing learning in schools. However, the fact is that the use of mathematics teaching aids during learning at school is not yet entrenched, especially in areas far from urban areas, many of which do not have teaching aids. This directly impacts students' lack of understanding and learning experience, resulting in low student learning outcomes. This paper will introduce ALGATIKA, an application of lending mathematics teaching aids for elementary and junior high schools which can later solve these problems. The research methodology used is a qualitative descriptive method by deepening the material through literature studies. The result is that the lack of teaching aids in some schools can be overcome by the ALGATIKA application of lending mathematics teaching aids in elementary and junior high schools. Thus this application can help provide the teaching aids needed to build and improve educational facilities and provide an effective learning environment for all. It can develop students' teaching and learning processes and create higher quality education which leads to relevant and effective learning outcomes in accordance with the targets of the SDG's in education.

Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.