scholarly journals Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Chenquan Gan ◽  
Maobin Yang ◽  
Zufan Zhang ◽  
Wanping Liu
Keyword(s):  
Optimal Control ◽  
Infection Rate ◽  
Computer Virus ◽  
Infection Model ◽  
Global Dynamics ◽  
Viral Spread ◽  
Storage Media ◽  
Combined Impact ◽  
Viral Infection Model ◽  
Main Model

This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results.

scholarly journals A Viral Infection Model with a Nonlinear Infection Rate

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Yumei Yu ◽  
Juan J. Nieto ◽  
Angela Torres ◽  
Kaifa Wang
Keyword(s):  
Viral Infection ◽  
Infection Rate ◽  
Infection Model ◽  
Viral Infection Model

scholarly journals Global Dynamics Behaviors of Viral Infection Model for Pest Management

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Chunjin Wei ◽  
Lansun Chen
Keyword(s):  
Small Amplitude ◽  
Critical Value ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Virus Particles ◽  
All Solutions ◽  
Pest Eradication ◽  
Viral Infection Model

According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet's theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the amount of virus particles released is larger than some critical value. When the amount of virus particles released is less than some critical value, the system is shown to be permanent, which implies that the trivial pest-eradication solution loses its stability. Further, the mathematical results are also confirmed by means of numerical simulation.

scholarly journals Global dynamics for a class of infection-age model with nonlinear incidence

2018 ◽  
Vol 24 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Yuji Li ◽  
Rui Xu ◽  
Jiazhe Lin
Keyword(s):  
Viral Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Infection Age ◽  
Age Model ◽  
Viral Infection Model

In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations.

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