Parameter identification for the Gumel-Mickens HIV transmission model under missing observable data

In this paper, based on the model proposed by Gumel, Moghadas and Mickens, which monitors the impact of live attenuated HIV vaccines, a new method for restoring the unknown data is proposed. Missing data in both epidemiological and ecological surveys and experiments can be due to a number of causes, like, unprovided domains of required data, complete refusal by respondents etc. Differential methods are used to linearize the non-linear equations for the model as the parameter space of the original models is increased. Least squares methods are employed to estimate the unknown model coefficients. Results show that the proposed method is able to restore the missing data with an acceptable accuracy. The efficiency of the proposed method is verified by comparing the restored and observed data using the absolute percentage error. The proposed method can be used in practical research and studies to provide a clue on which data to analytically restore in case of missing information.