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 >

This study presents a mathematical framework to analyze the transmission dynamics of the Ebola Virus Disease (EVD) using an extended SEIRVH model. The model incorporates vaccinated and hospitalized compartments, addressing critical factors such as vaccination efficacy, healthcare interventions, and natural disease progression. Differential equations describe the transitions between six population compartments. The study evaluates model stability and bifurcation through well-posedness, positivity, and boundedness analyzes, ensuring realistic and biologically valid solutions. The basic reproduction number, R0, derived from the next generation matrix, serves as a threshold for outbreak control.... More >