A nonlinear fractional epidemic model for the Marburg virus transmission with public health education

Abstract

In this study, a deterministic model for the dynamics of Marburg virus transmission that incorporates the impact of public health education is being formulated and analyzed. The Caputo fractional-order derivative is used to extend the traditional integer model to a fractional-based model. The model's positivity and boundedness are also under investigation. We obtain the basic reproduction number R0 and establish the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional-order derivative, we establish the existence-uniqueness theory using the Banach contraction mapping principle for the solution of the proposed model. We use functional techniques to demonstrate the proposed model's stability under the Ulam-Hyers condition. The numerical solutions are being determined through the Predictor-Corrector scheme. Awareness, as a form of education that lowers the risk of danger, is reducing susceptibility and the risk of infection. We employ numerical simulations to showcase the variety of realistic parameter values that support the argument that human awareness, as a form of education, considerably lowers susceptibility and the risk of infection.