Abstract
In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-Infective-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities. The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
Highlights
Inference of the stochastic SIR household epidemic model without misclassification is well analyzed in [1]-[6]
We developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-Infective-Removed), household epidemic model, with false negative and false positive misclassification probabilities
We analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities
Summary
Inference of the stochastic SIR household epidemic model without misclassification is well analyzed in [1]-[6]. The work of [1] and [7] provided maximum likelihood based algorithm for its inferences. The final size epidemic data is subject to misclassification error. This occurs in categorical data when the actual and recorded categories for subject differs [8] [9]. The susceptibles may be wrongly be classified as infectives or an infectives wrongly classified as susceptibles. It becomes necessary to adjust our inferences to such errors in order to get the precise parameter estimates and model that adequately fits the final size epidemic data.
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