A multi-route Caputo fractional-order model for Marburg virus disease: Stability analysis,sensitivity, and the role of environmental contamination and unsafe burial practices

Abstract

We propose a novel Caputo fractional-order compartmental model for Marburg virus disease (MVD) that integrates human-to-human transmission, zoonotic spillover from Egyptian rousette bats, environmental viral persistence, and unsafe burial practices. The model stratifies humans into seven compartments (including an education-based susceptible class) and bats into three compartments, with environmental viral concentration closing the loop. Existence, uniqueness, non-negativity, boundedness, and Ulam--Hyers stability are proved. The basic reproduction number \(\mathcal{R}_0^\kappa\) decomposes additively into four transmission pathways. At 2023 Kagera outbreak data, \(\mathcal{R}_0^\kappa = 1.6667 > 1\), with bat-only \(\mathcal{R}_{\text{bat}}=0.85<1\). Local and global asymptotic stability of the disease-free equilibrium are established. Sensitivity analysis identifies human contact rate (\(\Upsilon=+0.9055\)) and recovery rate (\(\Upsilon=-0.7252\)) as dominant. Fractional memory (\(\kappa<1\)) slows transients, delays peaks, and sustains endemicity above classical predictions.