Stochastic SIR Household Epidemic Model with Misclassification

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.

How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks

In this paper,an extended heterogeneous SIR model is proposed,which generalizes the heterogeneous mean-field theory.Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree,our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates.Then,we analytically study the basic reproductive number and the final epidemic size.Combining with numerical simulations,it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent.If the mean of these two distributions is identical,increasing the variance of susceptibility may block the spread of epidemics,while the corresponding increase in the variance of disease course has little effect on the final epidemic size.It is also shown that positive correlations between individual susceptibility,course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence,whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence.