Wuhan Ligong Daxue Xuebao (Jiaotong Kexue Yu Gongcheng Ban)/Journal of Wuhan University of Technology (Transportation Science and Engineering)

This paper discusses estimating parameters and optimal control for mathematical modelling of the Zika virus transmission. First, we consider an SEIR (susceptible-exposed-infected-recovered) model of the Zika virus dynamics, which consists of four ordinary differential equations. This SEIR model expresses the interaction among the four compartments. Assuming that the solution of the model is known and storing it for estimating the model parameters. To do so, a least squares optimization problem is introduced, and the Gauss-Newton recursion equation is derived to estimate the model parameters. In addition, an optimal control law is designed so that the model can reach the equilibrium early. The contributions of this paper are the use of the Gauss-Newton method for parameter estimation in a dynamical system and the linearized optimal control law for stabilizing the SEIR model. The simulation results showed the parameter estimates' accuracy and the controller's efficiency. Therefore, the study demonstrates the usefulness of parameter estimation and optimal control in the mathematical modelling of the Zika virus transmission, which will impact future studies on epidemic modelling.