A Fractional Order Generalized SEIR Model: The Role of “COVID-19 Symptom Data” in Receding Horizon Vaccine Policies

Abstract

Novel Coronavirus (COVID-19) has spread worldwide, causing continued casualties and economic losses. To characterize the pandemic dynamics, we propose fractional order generalized SEIR epidemic models for COVID-19, considering real-world Facebook symptom data and state-level Google mobility. Fractional order models based on noninteger order calculus can better characterize inhomogeneity in human interactions and infection rates. Our models can describe psychological effect factors within the nonlinear incidence functions. Therefore, we can deliver better fitting and prediction performances. Comparative analysis of model predictions with different mitigation and intervention scenarios, which are affected by mobilities in California, are made. Now, vaccination is becoming a critical response so that the COVID-19 pandemic can become endemic in optimal possible ways.We propose the modified fractional order GSEIR model for near real-time COVID- 19 Receding Horizon vaccine policy study. The proposed Receding Horizon Control (RHC) optimal vaccine strategy can not only explicitly consider the constraints on vaccine availability, speed of replenishing, vaccine application rate, etc., but also can make the whole management in a closedloop manner with an optimization performance index. Additionally, our model can accommodate the age structure of the population, mobility level, community mitigation measures, the willingness to be vaccinated, etc. The closedloop vaccine system can achieve good tracking performance given a future desired and feasible trend. Specifically, our forecast trends of infections and death cases in different immunization scenarios can guide individual and policy decision-making processes in developing mitigation measures and monitoring community risk levels. Numerical simulations using Simulink Design Optimization (SLDO) are given to support our analysis.