In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Purthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.
In this paper, we consider the following chemotaxis model with ratio-dependent logistic reactionterm{δu/δt=D △↓（△↓ u-u△↓ω/ω＋u（a-bu/w）,（x,t）∈QT,δw/δt=βu-δw,（x,t）∈ QT u△↓ln（u/w）·^→n=0, x∈δΩ,0〈t〈T,u（x,0）=u0（x）〉0,x∈^-Ω,w（x,0）=w0（x）〉0, x∈^-Ω,w（x,0）=w0（x）〉0,x∈^-ΩIt is shown that the solution to the problem exists globally if b ＋β〉 0 and will blow up or quench if b -t- ]~ 〈： 0 by means of function transformation and comparison method. Various asymptotic behavior related to different coefficients and initial data is also discussed.
