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Frailty models are used in the survival analysis to account for the unobserved heterogeneityin individual risks to disease and death. To analyze the bivariate data on relatedsurvival times (e.g. matched pairs experiments, twin or family data), the shared frailtymodels were suggested. In this manuscript, we propose a new mixture shared inverse Gaussian frailty model based on modified Weibull as baseline distribution. The Bayesian approach of Markov Chain Monte Carlo technique is employed to estimate the parameters involved in the models. In addition, a simulation study is performed to compare the true values of the parameters with the estimated values. A comparison with the existing model was done by using Bayesian comparison techniques. A better model for infectious disease data related to kidney infection is suggested.