Sensitivity analysis of an epidemic model with a mass vaccination program of a homogeneous population

TL;DR

This study analyzes how uncertainties in disease transmission, latency, infectious period, mortality, and vaccination parameters affect cumulative infections $W$ and deaths $D$ in a mass-vaccination SEIR framework. It applies Latin Hypercube Sampling and Partial Rank Correlation Coefficient to quantify sensitivities to $β$, $1/κ$, $1/γ$, $α$, $r$, and $δ$ across a 140-day horizon. Key findings show $D$ is highly sensitive to $α$, with sensitivity to the rollout rate $δ$ increasing over time, while $W$ is initially sensitive to $κ$ and becomes more sensitive to $δ$ in the long run; $W$ is less influenced by $β$ and $γ$. The results underscore the practical importance of rapid vaccine rollout over vaccine efficacy in curbing disease spread and highlight the potential value of reducing mortality through healthcare improvements.

Abstract

The COVID-19 pandemic forced the rapid development of vaccines and the implementation of mass vaccination programs around the world. However, many hesitated to take the vaccine due to concerns about its effectiveness. By looking at an ordinary differential equation (ODE) model of disease spread that incorporates a mass vaccination program, this study aims to determine the sensitivity of the cumulative count of infected individuals ($W$) and the cumulative death count ($D$) to the following model parameters: disease transmission rate ($β$), reciprocal of the disease latency period ($κ$), reciprocal of the infectious period ($γ$), death ratio ($α$), vaccine efficacy rate ($r$), and vaccine rollout rate ($δ$). This was implemented using Latin hypercube sampling and partial rank correlation coefficient. Results show that $D$ is highly sensitive to $α$ and shows increasing sensitivity to $δ$ in the long run. On the other hand, $W$ is highly sensitive to $κ$ at the beginning of the simulation, but this weakens over time. In contrast, $W$ is not very sensitive to $δ$ initially but becomes very significant in the long run. This supports the importance of the vaccine rollout rate over the vaccine efficacy rate in curbing the spread of the disease in the population. It is also worthwhile to reduce the death ratio by developing a cure for the disease or improving the healthcare system as a whole.

Figures (15)

• Figure 1: Compartmental diagram of the SEIR model incorporating a mass vaccination program.
• Figure 2: Evolution of the cumulative infected count $W$ (in blue) and the cumulative death count $D$ (in red) for the following parameters: $\beta = 0.37$, $\kappa = 0.18$, $\gamma = 0.15$, $\alpha = 0.09$, $r=0.75$, and $\delta = 27887.0$.
• Figure 3: Evolution of the PRCC of the output parameters $D$ (Figure \ref{['subfig:Dbeta']}) and $W$ (Figure \ref{['subfig:Wbeta']}) with respect to $\beta$. The region between the two red lines indicate PRCC values that are not significantly different from 0 (where $p$-values are greater than 0.05), which is not the case for $\beta$.
• Figure 4: Scatter plots of the residuals of the rankings for $D$ (Figure \ref{['subfig:Dbeta7']} and \ref{['subfig:Dbeta140']}) and $W$ (Figure \ref{['subfig:Wbeta7']} and \ref{['subfig:Wbeta140']}) with respect to the residuals of the $\beta$ ranking.
• Figure 5: Evolution of the PRCC of the output parameters $D$ (Figure \ref{['subfig:Dkappa']}) and $W$ (Figure \ref{['subfig:Wkappa']}) with respect to $\kappa$. The region between the two red lines indicate PRCC values that are not significantly different from 0 (where $p$-values are greater than 0.05), which is not the case for $\kappa$.