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 >

The initial mathematical model for rabies consists of six compartments representing the human and dog populations: $S_h, I_h, V_h, S_d, I_d, V_d$. To obtain a more realistic description of rabies transmission dynamics, we extend the model by introducing two additional human compartments: Exposed ($E_h$) and Recovered ($R_h$) individuals. The extended system therefore comprises eight compartments: $S_h, E_h, I_h, V_h, R_h, S_d, I_d, V_d$. This extension captures important differences in disease progression, treatment response, and transmission pathways. Within this framework, we examine the positivity and boundedness of solutions, derive the basic reproduction number ($R_0$), analyse the sens... More >