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Keywords:

  • Difference equation;
  • Kalman filter;
  • missing data;
  • model selection;
  • Runge;
  • Kutta;
  • varying;
  • coefficient models

Mathematical models have been proposed and developed to model HIV dynamics over the past few decades, achieving remarkable gains. However, it remains a challenging problem to accurately and efficiently estimate all key parameters in these models from clinical data. In this article, we propose a state space approach to link these models with clinical data and estimate the corresponding parameters. Specifically, we approximate the target nonlinear differential equations by difference equations and add a stochastic perturbation in the dynamic of all cells and virions. The proposed model and methodology provide an alternative tool in HIV dynamic modeling and can be easily applied in other biomedical system characterized by dynamic systems. Simulation studies are conducted to compare the performance of the proposed model with some previous approaches and show superior performance. With moderate sample size, the approach is successful in estimating all HIV viral dynamic parameters without many constraints on the parameters. To illustrate the proposed method, we apply it on the clinical data of two individual HIV infected patients treated with antiretroviral therapies.