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

Abstract

Controlling the Marburg virus (MARV) remains challenging for humans due to its high mortality rate and rapid
transmission. We formulate a deterministic model incorporating limited hospital beds for MARV transmission.
We extend traditional integer-order approaches to a fractional-order perspective employing the Atangana-Baleanu
Caputo(ABC) derivative due to finding a derivative with a Mittag-Leffler kernel. We demonstrate the positivity
and boundedness of the solution, ensuring its biological relevance. We calculated the basic reproduction number
with the help of the next-generation matrix (NGM) approach for populations and performed a sensitivity analysis
to identify critical parameters influencing the spread of the virus. We explore Marburg-free equilibrium and obtain
its local and global stability. We prove that the solution exists and is unique to the proposed model. We also obtain
compactness and continuity of the solution.Furthermore, we explore the proposed model’s stability by applying the
Hyers-Ulam (HU) stability. We discuss the analysis of numerical solutions using a two-step Lagrange interpolation
approach. We conclude that increased hospital beds significantly reduce the Marburg virus infection. This study
provides valuable insights into how healthcare resource availability affects MARV transmission dynamics and
demonstrates the broader relevance of fractional calculus in epidemiological models.