Asian Research Journal of Mathematics

Recurrent infectious disease outbreaks continue to challenge public health systems despite advances in surveillance and vaccination. Motivated by recurrent Ebola virus disease outbreaks in the Democratic Republic of the Congo and the potential risk of importation into Kenya, this study develops a deterministic Susceptible–Exposed–Infectious–Vaccinated–Recovered–Waned Immunity (SEIVRW) model for preparedness and intervention assessment. The framework incorporates vaccination, temporary immunity, disease progression, recovery, disease-induced mortality, waning immunity, and reinfection. The model is formulated as a theoretical decision-support framework because Kenya has not reported confirmed local Ebola transmission and Kenya-specific outbreak data are therefore unavailable for calibration. Its mathematical properties are examined through analyses of positivity, boundedness, disease-free and endemic equilibria, the control reproduction number, and local and global stability. A forward bifurcation framework is also used to characterise the threshold behaviour of the system. The analysis indicates that vaccination and the persistence of acquired immunity are central determinants of the model’s transmission threshold. The disease-free equilibrium is stable when the control reproduction number remains below unity, whereas an endemic equilibrium may exist when the threshold exceeds unity. The model is not intended to provide numerical forecasts; rather, it establishes an analytical basis for future parameter estimation, outbreak assessment, and evaluation of surveillance, vaccination, isolation, contact tracing, and border-health measures when relevant epidemiological data become available.