Mathematical Modelling for COVID-19 Dynamics with Vaccination Class

• Main Authors: Lagura, Maria Czarina T, David, Roden Jason, De Lara-Tuprio, Elvira P
• Format: text
• Published: Archīum Ateneo 2022
• Subjects: COVID-19; Compartmental model; Vaccination; Stability analysis; Basic reproduction number; Next generation matrix; Applied Mathematics; Mathematics; Ordinary Differential Equations and Applied Dynamics; Physical Sciences and Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/228; https://link.springer.com/chapter/10.1007/978-3-031-04028-3_23#citeas
• Institution: Ateneo De Manila University

We develop a six-compartment differential equation model for the transmission of COVID-19 by dividing the human population into susceptible, vaccinated, exposed, infectious, confirmed, and recovered. We then use the basic reproduction number R0, derived using the next generation matrix, to determine when the disease will die out and when it will stay in the community. This is done by showing that when R0 < 1, then the disease-free equilibrium solution is globally asymptotically stable; and when R0 > 1, the endemic equilibrium is globally asymptotically stable. Finally, we use numerical solutions to confirm the results of our stability analysis.