Parameter Estimation of Chikungunya in the Case of Incomplete Information about Its Model

Abstract

This paper presents solutions to the problem of parameter estimation of mathematical model of Chikungunya with incomplete information about the model parameters. The process involves finding a set of unknown parameters from the given model such that the behavior of the predicted system reflects the original behavior (measurement) using the same scientific assumptions. To achieve this, we solve the differential equations which describe the relation between unknown functions and their derivatives using the fundamental theorem of ordinary differential equation (ODE) (i.e., the theorem of existence) to obtain solutions for the initial value problems. The solutions to the ODE give unknown parameters which functionally depend on the original unknown parameters. And these parameters have two constraints between them. We further find solutions to the constraints minimization problem to obtain estimations of a-parameters. But, the method of constraint minimization problem stipulates the ill-conditioned problem and makes it impossible to accurately identify a-parameters. It is necessary therefore to formulate the goal function using the Least squares method to determine the unknown parameters. This method works reliably well and converges at a large interval of initial guess values of parameters.