Numerical solutions for norovirus epidemic spread: implications for public health control

Norovirus is a highly contagious virus and the leading cause of acute gastroenteritis worldwide. The World Health Organization (WHO) estimates that approximately 685 million cases of norovirus infection occur each year, with around 200 million affecting children under the age of five. The impact of this virus is substantial, contributing to roughly 200,000 deaths annually-about 50,000 of which are among young children-mostly in low-income countries. In addition to the human toll, norovirus imposes a significant economic burden, with global costs reaching approximately $60 billion each year due to healthcare expenses and lost productivity. In this paper, we present a fractional-order mathematical analysis of the norovirus epidemic model, focusing on its transmission dynamics, incorporating memory effects. The total population, denoted as N(t), is categorized into four compartments: susceptible, exposed, infected, and recovered. We analytically derive the equilibrium points and the basic reproduction number of the model. Furthermore, we discuss the properties of positivity, boundedness, uniqueness, and existence to ensure the model's validity. The non-linear model is linearized around its equilibrium points, and local stability is analyzed using the eigenvalues of the Jacobian matrix. In addition, global stability is examined using the Lyapunov function and LaSalle's invariance principle. To validate the theoretical findings, a numerical scheme based on the GL-Non-Standard Finite Difference (NSFD) method is developed, which serves to verify the theoretical analysis of the norovirus epidemic model.