State Estimation for Stochastic Nonlinear Systems with Applications to Viral Infections

State estimation of biological systems is a difficult task due to their complexity and stochasticity. In particular, bilinear and Michaelis-Menten terms are the base for many biological models such as in infectious diseases, cancer, diabetes, and many others. In this paper, mentioned non-linear terms are formulated into a polynomial form with state-dependent matrices driven by additive white Gaussian noises over linear observations. To show the effectiveness of the approach, two different models widely used for modeling viral infectious diseases are considered and compared with the extended Kalman filter (EKF) algorithm. Numerical results show the applicability of the polynomial approach.