Integral estimation of ecological model parameters with missing information

Abstract

We introduce an integral method for state variables and coefficient estimation and apply it to a simplified compartmental ecological model, proposed by Lubuma and Gumel, which monitors the transmission dynamics of Bovine tuberculosis in a buffalo-only population. The method uses integral approaches to linearize the system of equations. The ordinary least-squares method is subsequently used to compute the system coefficients under given appropriate constraints on the designed objective function. Results of the objective function (model coefficients) are then used to estimate and restore the system's state variables (assumed missing) by using appropriate algebraic formulations. Both the estimated and observed data have similar trends, indicating that the introduced method restores the missing information from the ecological system quite well. Performance of the integral method is measured by carrying out an error analysis using the absolute percentage error. We conclude that the developed approach works well and capable of estimating and restoring missing information in an ecological system to enable both qualitative and quantitative predictions to be made about the population under study.