Global Stability Analysis of Dengue Model with Awareness, Vector Control and Time Delays

• Main Authors: Macalalag, Jay Michael R, Teng, Timothy Robin Y, De Lara-Tuprio, Elvira P
• Format: text
• Published: Archīum Ateneo 2021
• Subjects: Dengue fever; Delay differential equations; Global stability; Lyapunov functional; Hopf bifurcation; Applied Mathematics; Public Health
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/174; https://link.springer.com/chapter/10.1007/978-3-030-79606-8_14
• Institution: Ateneo De Manila University

In this paper; a mathematical model for a single-strain dengue virus transmission; incorporating vector control; disease awareness among susceptible humans; and both the latent delays for human and mosquitoes; is proposed and studied. The global stability properties of disease-free equilibrium and endemic equilibrium are completely established through Lyapunov functionals and LaSalle's invariance principle. The global dynamics of the equilibrium points are characterized by the value of basic reproductive number R0 . The disease-free equilibrium is globally asymptotically stable if R0 < 1 ; and is unstable if R0 > 1 . Furthermore; the endemic equilibrium is globally asymptotically stable if R0>1 . Numerical simulations are presented to illustrate the theoretical results.