Analyzing dynamics and stability of single delay differential equations for the dengue epidemic model

• Published in: Results in control and optimization 2024-06, Vol.15, p.100415, Article 100415
• Main Authors: Venkatesh, A., Prakash Raj, M., Baranidharan, B.
• Format: Article
• Language: English
• Subjects: Backward bifurcation; Global stability; Lyapunov function; Next-generation matrix; Stability; Time-delay
• ISSN: 2666-7207; 2666-7207
• DOI: 10.1016/j.rico.2024.100415

This paper introduces a mathematical model that simulates the transmission of the dengue virus in a population over time. The model takes into account aspects such as delays in transmission, the impact of inhibitory effects, the loss of immunity, and the presence of partial immunity. The model has been verified to ensure the positivity and boundedness. The basic reproduction number R0 of the model is derived using the advanced next-generation matrix approach. An analysis is conducted on the stability criteria of the model, and equilibrium points are investigated. Under appropriate circumstances, it was shown that there is local stability in both the virus-free equilibrium and the endemic equilibrium points when there is a delay. Analyzing the global asymptotic stability of equilibrium points is done by using the appropriate Lyapunov function. In addition, the model exhibits a backward bifurcation, in which the virus-free equilibrium coexists with a stable endemic equilibrium. By using a sensitivity analysis technique, it has been shown that some factors have a substantial influence on the behavior of the model. The research adeptly elucidates the ramifications of its results by effortlessly validating theoretical concepts with numerical examples and simulations. Furthermore, our research revealed that augmenting the rate of inhibition on infected vectors and people leads to a reduction in the equilibrium point, suggesting the presence of an endemic state. [Display omitted] •A time-delayed vector-host dengue epidemic model is presented in the study.•The model is validated by verifying that solutions are both positive and bounded.•The computed basic reproduction number is a significant epidemic indicator.•The equilibrium’s local and global stability are revealed using stability analysis.•A backward bifurcation explains complex epidemic characteristics in the model.