Calibration and prediction for the inexact SIR model.

A Susceptible Infective Recovered (SIR) model is usually unable to mimic the actual epidemiological system exactly. The reasons for this inaccuracy include observation errors and model discrepancies due to assumptions and simplifications made by the SIR model. Hence, this work proposes calibration and prediction methods for the SIR model with a one-time reported number of infected cases. Given that the observation errors of the reported data are assumed to be heteroscedastic, we propose two predictors to predict the actual epidemiological system by modeling the model discrepancy through a Gaussian Process model. One is the calibrated SIR model, and the other one is the discrepancy-corrected predictor, which integrates the calibrated SIR model with the Gaussian Process predictor to solve the model discrepancy. A wild bootstrap method quantifies the two predictors' uncertainty, while two numerical studies assess the performance of the proposed method. The numerical results show that, the proposed predictors outperform the existing ones and the prediction accuracy of the discrepancy-corrected predictor is improved by at least 49.95%.

Global asymptotic stability for the SEIRS models with varying total population size.

In this paper, SEIRS epidemiological model with disease caused death and varying total population size is discussed. Based on the geometric approach developed by Li and Muldowney, a new criterion to determine the global asymptotic stability for nonlinear system is proposed. By applying this new criterion, global asymptotic stability of the endemic equilibrium when it is unique is proved. The above global result shows that the basic reproduction number is a sharp threshold for SEIRS model which removes restrictions of rate of loss of immunity and rate of disease caused death in Li and Muldowney's result.

Permanence for two-species Lotka-Volterra cooperative systems with delays.

In this paper, a two-species Lotka-Volterra cooperative delay system is considered, and the relationships between the delays and the permanence are obtained. Some sufficient conditions for the permanence under the assumption of smallness of the delays are obtained. Two examples are given to illustrate the theorems.