Modeling marburg virus control with limited hospital beds: a fractional approach

Abstract The Marburg virus is a serious global health threat due to its high mortality rate and rapid transmission. Effective control measures, such as hospital beds, are vital but often limited by inadequate healthcare resources. This study aims to address this challenge by developing a fractional-order epidemic model for Marburg virus, which considers the effects of limited hospital beds on transmission dynamics. We present a model to provide a more accurate understanding of Marburg virus transmission patterns and prevalence incorporating the memory effect through a fractional-order approach. The study explores the impact of constrained healthcare resources on virus progression and calculates the basic reproduction number using the next-generation matrix technique. Further analysis of the model’s global dynamics is conducted using reproduction numbers, the Lyapunov functional approach, and the Routh-Hurwitz criterion, shedding light on how hospital bed availability influences disease progression.We also apply Hyers-Ulam stability criterion to find the stability of the model and obtain numerical solutions through a fractional Lagrange two-step interpolation method. The fractional-order Marburg virus model, by accounting for memory effects, offers a more nuanced understanding of the disease dynamics compared to classical models. Our results demonstrate that increasing hospital bed availability significantly reduces Marburg virus infection rates. This approach highlights the value of fractional calculus in epidemiological modeling, offering significant insights into optimal control measures and strategies to improve public health outcomes during Marburg virus outbreaks.