Fractional-Order SEIHR(D) Model for Nipah Virus with Spillover: Well-Posedness, Ulam-Hyers Stability, and Global Sensitivity

In this research, we create a new fractional-order SEIHRD framework to examine how the Nipah virus moves from one species to another (zoonotic spillover) and how it later spreads throughout a community (via contact with one another) or in a hospital or isolation situation (via entering into a hospital or being placed under quarantine). We used the fractional-derivative formulation of the SEIHRD model to demonstrate memory-based effects related to the progression of an infection and also reflect time-distributed effects associated with surveillance and control measures placed on an infected patient. We first demonstrated that the basic epidemiologic properties of the model were consistent by showing that the solutions of the SEIHRD differential equations will always yield positive and bounded solutions within biologically relevant parameter ranges. We then established the well-posedness of this model by transforming the SEIHRD differential equations into an equivalent integral operator and applying various fixed-point arguments to demonstrate that there will always be unique solution(s) to the SEIHRD differential equations. To evaluate the threshold parameter for the transmission of Nipah virus within a given population we calculated the threshold level through the next generation method to determine the expected number of secondary infections from a new or chronically infected host. One of the main contributions of this work is to include an analysis of the robustness of a given solution to all potential perturbations (i.e., Ulam-Hyers and generalized Ulam-Hyers stability). In addition, we provide analytic results guaranteeing that small perturbations due to approximate modeling, numerical approximation (discretization), or the lack of data fidelity will produce controlled deviations in the solutions. To finish this project, we perform a global sensitivity analysis on uncertain coefficients to evaluate their contribution to the uncertainty of each coefficient and to find out the coefficients that most strongly influence major outcome metrics. This will allow us to develop a priority order for prioritizing spillover control (reduction of human contact and/or isolation), contact reduction, and expenditure of resources towards isolation-related interventions. The resulting framework converts fractional epidemic modeling from a descriptive simulation to a replicable method with robustly defined behavior and equal response prediction.