Dynamics of a diffusive viral infection model with impulsive CTL immune response

Abstract

To explore the impacts of pulse vaccination on the dynamical behaviors of virus, the current paper investigates the persistence and global attractivity of a diffusive viral infection model incorporated with impulsive CTL immune response while the stronger logistic growth mechanism. Based on the comparison principle and the proper upper and lower solutions, we first discuss the existence of the infection-free steady state, and define the crucial CTL-activated viral infection reproduction number $R_0$. Then, the fundamental extinction and uniform persistence behaviors of virus are distinguished by various cases of the threshold parameter $R_0$. Finally, the existence and global attractivity of the positive steady state are still established by employing Brouwer's fixed point theorem and auxiliary functional. Our results indicate that high vaccination rates will stimulate the CTL response more effectively, and thus eventually can force the virus to eradicate.

Keywords:

• Diffusive viral infection model
• impulsive CTL immune response
• logistic growth mechanism
• persistence
• global attractivity

2010 AMS Subject Classifications:

• 35K57
• 92C60
• 35R12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jie Wang and Ruirui Yang are supported by National Natural Science Foundation of China [grant numbers 12161051, 11701243] and Science and Technology Plan Foundation of Gansu Province of China [grant number 21JR7RA209]; and Haifeng Huo is supported by National Natural Science Foundation of China [grant number 11861044] and Science and Technology Plan Foundation of Gansu Province of China [grant number 21JR7RA212]; and Ruirui Yang is still supported by the Excellent Postgraduate ‘Innovation Star’ of Department of Education of Gansu Province of China [grant number 2022CXZX-499].