Understanding Dynamics of Pandemic Models to Support Predictions of COVID-19 Transmission: Parameter Sensitivity Analysis of SIR-Type Models

Abstract

Despite efforts made to model and predict COVID-19 transmission, large predictive uncertainty remains. Failure to understand the dynamics of the nonlinear pandemic prediction model is an important reason. To this end, local and multiple global sensitivity analysis approaches are synthetically applied to analyze the sensitivities of parameters and initial state variables and community size (N) in susceptible-infected-recovered (SIR) and its variant susceptible-exposed-infected-recovered (SEIR) models and basic reproduction number (R0), aiming to provide prior information for parameter estimation and suggestions for COVID-19 prevention and control measures. We found that N influences both the maximum number of actively infected cases and the date on which the maximum number of actively infected cases is reached. The high effect of N on maximum actively infected cases and peak date suggests the necessity of isolating the infected cases in a small community. The protection rate and average quarantined time are most sensitive to the infected populations, with a summation of their first-order sensitivity indices greater than 0.585, and their interactions are also substantial, being 0.389 and 0.334, respectively. The high sensitivities and interaction between the protection rate and average quarantined time suggest that protection and isolation measures should always be implemented in conjunction and started as early as possible. These findings provide insights into the predictability of the pandemic models by estimating influential parameters and suggest how to effectively prevent and control epidemic transmission.

Fig. 1.

Variation in the infected population (simulated by SIR) with the variation in the initial actively infected cases (I₀, Fig. 1a), the total number of the population (N, Fig. 1b), infectious rate (β, Fig. 1c), and cure rate (λ, Fig. 1d). The initial state variables, parameters, and outputs of the model vary by the same interorders of magnitude.

Fig. 2.

Variation in the infected population (simulated by SIR) with the variation in the initial infected cases (I₀, Fig. 2a), the total number of the population (N, Fig. 2b), infectious rate (β, Fig. 2c), and cure rate (λ, Fig. 2d). The initial state variables, parameters, and outputs of the model vary over orders of magnitude.

Fig. 3.

Variation in the actively infected (dashed line) and cumulative (solid line) populations (simulated by SEIR) with variation in α, β, γ, and δ.

Fig. 4.

Parameter SIs from Sobol's and FAST methods on infected and cumulative populations and basic reproduction number (R0). The main sensitivity index, total sensitivity index, and interactive effects are represented by the MSI (blue bar), TSI (blue plus orange bar), and TSI-MSI (orange bar), respectively.

Fig. 5.

Dynamic variation in the parameter SIs measured by Sobol's method under the full ranges of the parameters. With the evolution of time, the parameters’ main SIs (a), total SIs (b), and differences between the total and main SIs (c) change dramatically.