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This study analyzes blood flow due to stenosis of blood vessels in the eye nerve in eye stroke. Eye stroke occurs due to the rupture of blood vessels in the retinal nerve of the eye caused by one of them stenosis of blood vessels, which results in loss of eye vision. Mathematical modeling as an applied mathematics science is one alternative to solve this problem. Mathematical modeling aims to obtain a formula that describes the state of blood flow according to actual conditions. The mathematical model is built using the finite volume method and will then be solved numerically using the SIMPLE algorithm. Based on the results of this simulation, we will know what level of narrowing (45-90% stenosed) of the renal vein is prone to causing renovascular hypertension in the kidney. The study results show that a 90% thickness can be dangerous because at this level of narrowing, the blood flow rate exceeds normal limits, and the pressure on the vein walls also increases. In contrast, the type of flow that appears becomes laminar. [ABSTRACT FROM AUTHOR]

The case of drug abuse is still a chronic problem for many countries, including Indonesia. One of the actions taken by the government in dealing with drug abuse cases is a rehabilitation program for addicts. Therefore, it is necessary to construct a mathematical model to observe the dynamics of the rehabilitation program for drug abuse cases. The mathematical model for the rehabilitation program for drug abuse cases is constructed based on the SIR epidemic model. Furthermore, through stability analysis, it was found that the model is asymptotically stable around the drug-free equilibrium point (E0) if R0 < 1 and is asymptotically stable around the drug-endemic equilibrium point (E1) if it meets the appropriate conditions obtained based on the Routh-Hurwitz criteria. The results of numerical simulations on the mathematical model of the rehabilitation program for drug abuse cases show that the more individuals who participate in the rehabilitation program, the faster the drug-free state will be obtained. [ABSTRACT FROM AUTHOR]

Nanofluids were a mixture of liquid fluids as base fluids with nanoparticles measuring 1-100 nanometers (nm). Magnetohydrodynamic (MHD) was the study of the movement of fluid flows that can conduct electricity (electrical conduction) which was influenced by a magnetic field. Equation builder containing continuity equation, momentum equation, and energy equation. Then the builder equation was transformed into the boundary layer approximation equation. The boundary layer equation obtained was transformed into a similarity equation. The similarity equation was solved numerically used the Keller-Box method. The results of the numerical solution analyzed the effect of magnetic (M) and radiation (R) parameters on the velocity (f') and temperature (s) profile of the nanofluids. The numerical simulation results obtained were that the effect of magnetic parameters on the velocity profile increases but the temperature profile decreases. The influence of the Prandtl number parameter did not have a significant effect, but the speed increases with increasing the value of η, and the temperature profile decreases with increasing Pr. If the radiation velocity profile did not change significantly with the variation of R, then the temperature profile will increase with the increase in the value of R. [ABSTRACT FROM AUTHOR]

Simulation studies and applications in mathematics continue to evolve as science and computer technology evolution. One of them is Magnetohydrodynamics (MHD) which is closely related to the field of engineering and industry. This study considers velocity and temperature analysis around the lower stagnation point on magnetohydrodynamics nano fluids through a vertical porous cylinder. Governing equations are derived from dimensional equations, which are mass or continuity equation, momentum equation, and energy equation. Further, the dimensional governing equations are converted to the non-dimensional governing equations. The non-dimensional governing equations are further transformed to similarity equations by introducing stream function. We obtain ordinary differential equation and boundary conditions, and we call mathematical model of the problem. We further solve the mathematical model numerically using finite difference method, i.e. Keller Box scheme or method. For running numerical simulation, we apply two nano fluids, i.e. nano particle Li2O and Fe2O3with water as basic fluid for the nano fluids. The numerical simulation results show that velocity of the nano-fluid increases when parameters of magnetic and porous increase. However, the velocity of the nano fluid increases when the volume fraction and Prandtl number decrease. Further, the temperature of nano fluid increases when the parameter of magnetic, porous, and Prandtl number decrease. However, the temperature of nano fluid increases when the volume fraction increases. [ABSTRACT FROM AUTHOR]

The chance of bankruptcy for the first time in an insurance company indicates the possibility of bankruptcy of an insurance company. This is indicated by the negative value of the surplus function or which means the company can no longer bear the burden of claims in the next period. The number of claims that occur in a certain period of time can be viewed as data with a random distribution of variables, which theoretically can be calculated using a statistical approach with the concept of ruin probability. In this study, the probability of loss function is calculated by analyzing the surplus function at a certain time. This concept can be used not only to calculate bankruptcy in its entirety, but also can be used to predict the loss of an insurance program at a certain time. The value of the probability function of bankruptcy risk is determined by using a mathematical model developed based on the concept of integro-differential equations, which is used as a reference to determine what the company will face in the future. In the simulation, the loss probability function of the Death Insurance Program at insurance companies against surplus value based on 2019 data, shows that the greater the surplus value, the smaller the loss probability function. [ABSTRACT FROM AUTHOR]