Mathematical insights into the SEIQRD model with Allee and fear dynamics in the context of COVID-19

Abstract

In this study, we introduce and investigate the SEIQRD COVID-19 model incorporating Allee and fear effects. Employing the next-generation matrix method, we derive the basic reproduction number, a crucial epidemiological metric. Our model exhibits two significant equilibrium points: one representing the disease-free state and the other representing the endemic state. Utilizing the Routh–Hurwitz criteria, we demonstrate that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number (R0) is less than 1, while the endemic equilibrium attains local stability when R0 exceeds 1. Furthermore, we establish global stability for the endemic equilibrium through the application of Poincare–Bendixson properties and Dulac’s criteria. To complement our theoretical results, we conduct comprehensive simulation studies, validating the practical implications of our findings.

Keywords

• Mathematical model
• COVID-19
• Allee effect
• Local stability
• Global stability
• Numerical simulation