Seok-Kyoon Kim, Choon-Nyeon Kim, and Tae-Woong Yoon
HIV model with mutants, parameter estimation, ultimate boundedness
The human immunodeficiency virus (HIV) causes acquired immune deficiency syndrome (AIDS). The process of infection and mutation by HIV can be described by 3rd order ordinary differential equations [1-2]. For this model of HIV that includes the dynamics of the mutant virus, we present an output feedback parameter estimation algorithm by using two state variables out of the three. We first consider a standard parameter estimator [6] for the case where all states are available. We then substitute the estimated variable for the unavailable state in this state feedback estimator, leading to the proposed output feedback estimation algorithm. The resulting estimator is shown to be ultimately bounded under some conditions, and the effectiveness of the parameter estimator is demonstrated by computer simulations. In addition, the estimated parameters are used to analyze the equilibrium points of the HIV model, and the results are shown to be consistent with those obtained previously [7].
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