Nonlinear Dynamical Systems in Modeling and Control of Infectious Disease

This paper deals with nonlinear dynamical systems in the form of mathematical modeling to describe modeling of the dynamic behavior of biological and biomedical systems. Nonlinear ordinary differential equations have been studied to investigate the mysterious and complex mechanisms of the dynamics of infectious diseases in the human body. In particular, we study a nonlinear model of HIV immunology which describes the interactions between the human immune systems and the viruses. In this work, we propose a modification of the HIV model proposed by Joshi in Optim Control Appl Methods 23(4):199-213 (2002) by introducing state constraint to the dynamics. The aim is to obtain optimal immunotherapeutic strategy where the state constraint may play a crucial role. We treat our problem numerically and compare the results with existing literature to illustrate the significant effect of introducing state constraint to the dynamics of the model.