DYNAMICAL ANALYSIS AND OPTIMAL CONTROL FOR AN AGE-STRUCTURE HIV TRANSMISSION MODEL

In this paper, we investigate dynamical analysis and optimal con-trol for human immunodeficiency virus (HIV) transmission model with age-structure. Local asymptotic stability of disease-free equilibrium is proved by applying operator theory and spectral boundary principle. And the existence of endemic equilibrium is obtained by using fixed-point theorem and monotone iterative procedure. Optimal control of an age-structure HIV model is con-ducted by using prevention and control education and anti-HIV treatment as control strategies. Taking a suitable objective function is to prove existences of optimal control variables which are characterized by sensitivity system and adjoint system associated with optimal state system. Finally, numerical simu-lations with appropriate parameters are conducted to show that comprehensive publicity and education on prevention and control for susceptible individuals and prompt treatment of HIV-infected individuals can be better to reduce HIV impact.