Dynamics of a fractional-order model for Marburg virus: Impact of quarantine, pathogen persistence and awareness interventions

Abstract

This study introduces a fractional-order model to examine Marburg virus disease ($\m$) transmission, considering public health education, quarantine, and environmental pathogens. Using the Caputo fractional derivative ($\c-\d$), the model provides a more realistic, memory-dependent representation of disease spread. The research establishes the model's epidemiological relevance by proving the positivity and boundedness of solutions, derives the basic reproduction number ($R_0$), and confirms the existence and uniqueness of solutions using the Picard-Lindelof method and Leray-Schauder's fixed point theorem. Ulam-Hyers stability is also established using functional analysis. The model, solved numerically with a Predictor-Corrector scheme, uniquely incorporates quarantined exposed and infected individuals, as well as the environmental pathogen reservoir. Simulations highlight that increased public awareness and quarantine effectively reduce susceptibility and infection rates, emphasizing the importance of these strategies in controlling Marburg virus outbreaks.