A Novel Fractional-Order Framework for Modeling Marburg Virus Dynamics

Marburg virus (MVD) is a severe and often fatal hemorrhagic fever, with bats of the species Rousettus aegyptiacus serving as the primary reservoir. Understanding its transmission dynamics is critical for effective public health control. This paper proposes and rigorously analyzes a novel fractional-order compartmental model for MVD, capturing the complex interaction dynamics between human (SEIR) and bat (SIR) populations. The model is formulated using the Caputo fractional derivative to incorporate memory effects, offering a more realistic representation of transmission pathways. We employ the Laplace Transform Homotopy Perturbation Method (LTHPM) to derive a convergent semi-analytical series solution for the fractional system. The epidemiological threshold of the model, the basic reproduction number (Formula: see text), is derived using the next-generation matrix (NGM) method. A comprehensive sensitivity analysis is conducted to identify the most influential parameters on Formula: see text, revealing that the human-to-human transmission rate (Formula: see text) and the removal rate (Formula: see text) are the most critical factors for disease control. A key contribution of this work is the detailed analysis of the method’s convergence and the system’s fractional dynamics. We demonstrate the rapid convergence of the LTHPM solution by analyzing its higher-order approximations. Furthermore, extensive graphical analysis is presented to illustrate the impact of the fractional-order Formula: see text. These plots demonstrate that lower fractional orders (i.e., stronger memory effects) can significantly delay and suppress the epidemic peak, a finding with important implications for intervention planning. Finally, 3D surface plots are presented to visualize the simultaneous, non-linear impact of key parameters and time on the infected populations. To the best of our knowledge, this study presents one of the first fractional-order coupled human-bat models for Marburg virus dynamics integrating memory effects with a semi-analytical solution framework. The proposed approach not only extends classical epidemic modeling by incorporating hereditary characteristics but also provides new insights into outbreak control through the influence of fractional order, thereby offering a more realistic and flexible tool for understanding zoonotic disease transmission.