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 >

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 >