Application of Fractional SIQRV Model for SARS-CoV-2 and Stability Analysis

Abstract

Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that the appropriate precautions can be taken. The COVID-19 pandemic has highlighted the value of mathematical modeling of pandemics. The susceptible–infected–quarantined–recovered–vaccinated (SIQRV) epidemic model was used in this work. Symmetrical aspects of the proposed dynamic model, disease-free equilibrium, and stability were analyzed. The symmetry of the population size over time allows the model to find stable equilibrium points for any parameter value and initial conditions. The assumption of the strong symmetry of the initial conditions and parameter values plays a key role in the analysis of the fractional SIQRV model. In order to combat the pandemic nature of the disease, control the disease in the population, and increase the possibility of eradicating the disease, effective control measures include quarantine and immunization. Fractional derivatives are used in the Caputo sense. In the model, vaccination and quarantine are two important applications for managing the spread of the pandemic. Although some of the individuals who were vaccinated with the same type and equal dose of vaccine gained strong immunity thanks to the vaccine, the vaccine could not give sufficient immunity to the other part of the population. This is thought to be related the structural characteristics of individuals. Thus, although some of the individuals vaccinated with the same strategy are protected against the virus for a long time, others may become infected soon after vaccination. Appropriate parameters were used in the model to reflect this situation. In order to validate the model, the model was run by taking the COVID-19 data of Türkiye about a year ago, and the official data on the date of this study were successfully obtained. In addition to the stability analysis of the model, numerical solutions were obtained using the fractional Euler method.