Abstract
This paper investigates the global dynamics and bifurcation structure of a viral infection logistic model with delayed nonlinear CTL response and periodic immune response. It is proved that the basic reproduction numbers, $R_{0}$ and $R_{1}$, determine the outcome of viral infection. Besides changes in the amplititude of lytic component, we show, via numerical simulations, that , the birth rate of susceptible host cells and the maximum proliferation of target cells are crucial to the outcome of a viral infection. Time delay can alter the period of oscillation for the larger level of periodic forcing. Period doubling bifurcations of the system are observed via simulations. Our results can provide a possible explanation of the oscillation behaviors of virus population,which were observed in chronic HBV or HCV carriers.
Highlights
The research on mathematical models has been very useful in order to understand the dynamics of immune responses
This paper investigates the global dynamics and bifurcation structure of a viral infection logistic model with delayed nonlinear cytotoxic T lymphocytes (CTLs) response and periodic immune response
Besides changes in the amplititude of lytic component, we show, via numerical simulations, that, the birth rate of susceptible host cells and the maximum proliferation of target cells are crucial to the outcome of a viral infection
Summary
The research on mathematical models has been very useful in order to understand the dynamics of immune responses. In (Liu,1997; Nowak & Bangham, 1996), the authors considered the dynamics of a virus population with lytic immune response, the infected cells become lysed by CTLs, z(t) at a rate pyz, where the parameter p expresses the strength of the lytic component and it is a positive constant. Different sufficient conditions are obtained for E1, corresponding to the survival of free virus and the extinction of CTL response, it is called as immune-exhausted equilibrium; stability and numerical simulations are provided to illustrate our results for cases R1 < R0 < 1, R1 < 1 < R0, where R0 and R1 are called the basic reproduction number and the immune response reproductive number, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
