Dynamics and control strategy for a delayed viral infection model

Abstract

In this paper, we derive a delayed epidemic model to describe the characterization of cytotoxic T lymphocyte (CTL)-mediated immune response against virus infection. The stability of equilibria and the existence of Hopf bifurcation are analysed. Theoretical results reveal that if the basic reproductive number is greater than 1, the positive equilibrium may lose its stability and the bifurcated periodic solution occurs when time delay is taken as the bifurcation parameter. Furthermore, we investigate an optimal control problem according to the delayed model based on the available therapy for hepatitis B infection. With the aim of minimizing the infected cells and viral load with consideration for the treatment costs, the optimal solution is discussed analytically. For the case when periodic solution occurs, numerical simulations are performed to suggest the optimal therapeutic strategy and compare the model-predicted consequences.

Keywords:

• Viral infection
• time delay
• Hopf bifurcation
• optimal control

Acknowledgments

This research was supported by National Natural Science Foundation of China under Grant 11801439 and Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2019JM338.

Data availability

The authors confirm that the data supporting the findings of this study are available in our manuscript and within the references.

Disclosure statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Funding

This research was supported by National Natural Science Foundation of China under Grant 11801439 and Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2019JM338.