Modeling and Analysis of SIRR Model (Ebola Transmission Dynamics Model) with Delay Differential Equation.

Background: Ebola virus disease (EVD) is a severe and often fatal illness with high transmission potential and recurring outbreaks. Traditional compartmental models often neglect biologically important delays, such as the latent period before an infected individual becomes infectious, limiting their ability to capture real-world epidemic patterns. Including such delays can provide a more accurate understanding of outbreak persistence and control strategies. Methods: In this study, we develop and analyze a novel deterministic SIRR model that captures the complex transmission dynamics of Ebola by explicitly combining nonlinear incidence rates with a delay differential equation framework. Unlike traditional models, this approach integrates a biologically motivated delay to represent the latent period before infectiousness, providing a more realistic depiction of disease spread. The basic reproduction number (R Results: The main novelty of this work lies in its detailed investigation of how delays influence outbreak persistence and can trigger oscillatory epidemics, patterns often observed in practice but rarely captured by classic models. For R Conclusions: Accounting for delayed recovery dynamics is crucial for accurately predicting outbreak patterns and designing effective interventions. This delay-based, nonlinear-incidence model offers a robust analytical and computational framework for guiding public health strategies, with direct implications for reducing transmission, shortening outbreak duration, and preventing epidemic resurgence.