This study formulates a mathematical and computational model of tumor-cell-density regression in pancreatic cancer treated with carbon-ion hadron therapy. A reaction-diffusion equation with logistic proliferation and a local radiation-induced loss term is derived term by term, discretized with a two-dimensional finite-difference scheme and forward Euler time stepping, and implemented in Python. The treatment input follows a published carbon-ion schedule of 48~Gy(RBE) in 12 fractions of 4~Gy(RBE). The simulation produces sequential two- and three-dimensional maps of the modeled tumor-cell density as a function of accumulated dose; in the three-dimensional reconstruction the relative tumor vo... More >

Corporate carbon abatement is commonly modeled as a direct and continuous response to environmental regulation or green innovation. Such representations cannot fully explain persistent differences among firms facing similar policy conditions or distinguish the pressure required to initiate a low-carbon transition from that needed to sustain it. This study develops a three-state continuous-time model linking corporate carbon abatement, accumulated green innovation, and effective regulatory pressure, with green market preference treated as an external demand-pull parameter. Green innovation lowers the marginal cost of abatement, abatement generates learning and commercial returns to innovation... More >

In this study, a compartmental mathematical model is developed to study the rabies transmission process from dog to human. The model consists of eight compartments: susceptible, exposed, infected, recovered groups for dogs and humans $(S_D, E_D, I_D, R_D, S_H, E_H, I_H, R_H)$. The basic reproduction number $R_0$ is derived, and sensitivity analysis is performed to identify the most influential epidemiological parameters. Disease-free equilibrium stability analysis is also carried out to identify the conditions for rabies eradication. One of the main goals of this work is to compare the disease dynamics in vaccinated and unvaccinated cases, which is carried out with the support of numerical s... More >